Transcript for:
Electric Charges and Fields Overview

Greetings to everyone. Welcome to all of you Ashu Ghai 11th 12th pe and Physics one shot pe. So today we are going to complete it with Competency Based Questions Electric Charges and Field Co. So on this channel I completed my 12th with Physics and Chemistry. I have promised to teach. And yes, Chemistry one-shots start uploading Have gone. Chapter One, the Forest of Solutions Shot has taught with all my heart and mind. First I am teaching chemistry on YouTube. I have been teaching chemistry for 15-16 years. Are. But I had to make time for YouTube. because I last year or so Physics is a lot of study for two years continuously. So what about teaching physics this time? I am telling you there is a change. please this one Don't skip the part or else it will be one shot. Will not come. But yes, chemistry Every concept has been taught properly. every Questions on one concept are asked and then I will also ask extra questions. So the forest shot if not yet done with the solution chapter If you have seen it then go and see it. First thing. Second The thing is, how can this one shot be different? Going to do? If you have electric charges and You have seen my one shot of the field before. what you need to do and if you don't Have you seen this and this is your first time on this channel? Or you can watch my 12th one shot for the first time So what do you have to do, I'll tell you Let me explain. Look, now there's a person near me. There is a limited bandwidth. I am ninth I am teaching only this. I am teaching only 10th Am. I am teaching only 11th. 12th only I am teaching. There are also paid batches. then mine Science and Fun Experiment Wala also and There are offline classes as well. So a human being There is limited time available. So this year Because if you notice the chemistry Yes, I taught you honestly. But how are we teaching physics? every Doing two parts of a one shot. every one Divide each one-shot into two parts. Have been. Listen carefully to see how. so one All the concepts will be in one shot. Will come. concepts as well as all Derivations will come. All definitions will come. what you call a proper one shot in which we All the concepts are derived by everyone. I told you in my one shots The special thing was that I was in every one shot I will get the derivation done. So I each Got the derivation done by hand and that one shot I told you if you had my electric Have you seen the one shot of Charges and Fields? Or if you have seen any one shot then I will tell you all I get it done in derivation class. Meaning forest I get it done in the shot. So in one shot I Concepts and derivations were done. But I did not attempt the questions last year. We had the questions asked separately. But you all know that this year Physics What happened with the paper? I don't know then Let me tell you. This year Physics Paper One of the One of the difficult papers came. So this year How do we focus on question answers? do? We focus on question answers I will do more because I have worked hard. First in recording one shots. Sir We don't know where your one shot is. So What I'm doing in this video is 1 minute. Like introduce me to this, yes 2 minutes 3 minutes. So one r 58 to 59 minutes approximately 2 hours you You can say here I am posting my previous one shot. I'm combining what I recorded earlier I have done it and have also put Science and Fun So if you have seen that one shot on education If yes, you can skip the first 2 hours. But not after that because after that it The 2 hour one shot that I am giving you here. After that I have written to you here The best questions have to be asked once You should see the level of the questions. this question Very few teachers in CBSE level I will get it done for you. The questions I have here I will make you do two, four, five, six. If I today If I ask you 30 questions, then accept it. There will be six to seven such questions which Bhai Saheb Will leave you shaken. And each one of us Such questions will have to be asked in the session. to Will have to do it. That's why we are passing 12th this year. Will be prepared for the Physics paper. Otherwise, what happened to the children in NEET or The situation should not be like what happened in the board. Good. So What did I say? I said the first 2 I'll give you one shot here. If If you have seen my one shot then skip Do it. Then we will do it in the next half. There are questions. In the next half, we I am going to ask questions in which I I have brought all kinds of questions. MCQs I have brought it too. I have also brought the action region. Complete I will write it down. It will seem wrong. Assertion Region I have brought it too. and at the same time I have also brought subjective questions. All questions are subjective and objective Buddy. There is no need to worry. And Excellent Compatibility Based SFP QQ You take it. We call this the people Competency focused practice questions that That is also the USP of our Winner Series. Times. Many of these questions are from the Winner Series. are also going to happen. So I am saying again If you've seen this one-shot of mine, Skip the first 2 hours. But last We are asking questions about this. this opinion Skip it or there will be a problem. Let us go Ok. So here I am cutting the video. Am. To me you have my old face Will be visible. I used to be a little thinner and fuller One Shot you have to watch with your heart and mind. I have seen it, I have seen it recently Skip it. If you haven't seen it, watch the full Please come again after 2 hours for questions. I will also give you the time stamps below. Give. I will also pin it in the first comment. Let's meet. Love you. Now, because this is the first There is a chapter. So here we first have some We have to talk about the basics. Then we should move forward Needed Our 12th class part one Is. I am not talking about part two. Now! Part one, which you can read broadly There are many subdivisions but Broadley has two You can divide it into parts. Isn't it? Understanding Electric Charges and Fields First you have to understand that you are reading this chapter. Broadley can be divided into two parts. The first is Electrostatics. If we divide the charge You are studying at rest. That is, if a charge Particle is stopped at rest studying If you are talking about it then it is called electrostatics. It is said. And you can say that The first chapter and the second chapter, that is Our Chapter One and Chapter Two. This is both of the two The chapters are from our Electrostatics. In both of these, our charged particle He will remain at rest. Meaning no flow Will do. Transfer may happen. Move Dekho Move And there is a difference in flow. like inside a pipe Water is what it is, it flows. but if I picked up water in a bucket and went from here. If I take it there, we will not call it flow. We will call that move or transfer. or one Let me put the bucket into another bucket. Flow means what is flowing through the pipe. Thus, if a charged particle is in a wire What we call current is flowing, which We call it current. In all of your homes right now, you Where you are sitting, there is no light, fan, If AC or cooler is running then the wires of all those A charged particle is running in it. Such We call this study electrodynamics. Are. where a charged particle moves Is. And after the third second, which is our third It's done, it's fourth. All these chapters Let us turn to electrodynamics where the charged particle comes into motion Is. All two interstitial magnetism and so on which will be discussed directly and is indirectly dependent On top of electrodynamics itself. So short I say if a charged particle is stopped Let's call his studies Electrostatics. But if a charge The particle is running, if it is running then its We call this study electrodynamics. Are. So our first two chapters are on electrostatics. Now these Both definitions contain the same thing and That's coming electric charge. Electric Charges: So if someone asks you what the charges are Is? So there would be many definitions of charge. Are. The first definition is a charge of a property Due to which the electric field around Is born. or another definition of charge which I like better and you Maybe that will look good too. So Electric What then is a definition of charge? no such Any property that creates what surrounds it Do? Produce an electric field. That We call this property electric charge. Are. But another electric charge There is also a definition. What you hear and see You must know that whatever charge is It is of two types. Isn't it? positive And negative. Now positive charge chemistry According to this, when does it appear on any body? When it has more protons Let's go as compared to electrons. We Everyone knows that every atom in the world has Sorry inside. We all know that this is Equal number inside every atom in the world of electrons and protons. Due to which there is no overall charge on atoms. It doesn't happen. Atoms are neutral. Ye J J. Thomson himself has told this. but if I should tell you, for whatever reason, protons Whether there are more or fewer electrons give away electrons or take away protons Go. Chemistry wise, taking protons is very It is difficult. So electron obvious It is true that he must have given it. So the electron After giving, the protons are more goes. Less electrons. So in such a case What does the charge go to? Positive. Such as As an example, you all know. Sodium donates one electron According to Valency. then charge for that Plus comes. give calcium gives electrons. Aluminum is what it is It donates three electrons. So all this donates electrons, resulting in protons They become too much. So positive on these The charge comes. Exactly such a negative When will the charge come? When you have electrons There will be more. Now more electrons What are two ways to do it? That Take electrons or give protons. It is difficult to give up protons. of the nucleus He is sitting inside. Everyone knows. So Mainly The only way left is to gain electrons. Let it be done. Now who gains electrons? Is? Generally, non-metals such as Cl If electron gains then minus charge Comes. Sulfur gains two electrons Is. Oxygen also gains two electrons Is. So why am I talking about chemistry here? Have you started teaching? So this definition of charge also It is that such property which any body develops due to unequal amounts of electrons and protons. That means that It is true that if on any body If there is a charge then it is only one and only The reason would be that there are electrons and protons that have either electrons There are too many protons or there are too many protons Are. Did you understand what I said? well I give you Before moving forward, let me tell you in this one shot We also do all the derivations properly. Are going to do it. So this one shot will suit you. Not that this is a one shot. Complete proper chapter It will take only that. Yes, again. So How do I define electric charges? Can I? See A Property of Substance Which either results in loss or gain of Electrons. Why are we electrons? Are you saying? You know that protons It is very difficult to come and go. For him The composition of the nucleus has to be changed. Which is not that easy. Alldo it is possible. I will read it further. But if in simple language home I'm talking, I'm talking rub Are. talking to induction which is now We will do it. Well, charge by induction. There is no transfer. But if I say That I am rubbing and by rubbing I get charged Is being born. So that charge is obvious. It is all about the arrival or departure of electrons. It happens. So in this we can say that What is the charge? in which electrons and The amount of protons does not remain the same. Or There is also another definition, so I need another one of it. The definition should also be written. and what is that Is it brother? Who knows what might come in the exam. Property Which Produces Electric Field Around It. Isn't it? That means your Create an electric field around it. Such Property is also called a charge. Alldo Ye Not that fun a definition. Ok? Now The SI unit of charge is coulomb. This is us People probably know from 10th class to 9th class. I am coming. and the charge on an electron -1.6 * to the power of 10 You probably don't know this You can see it. It remains -19 coulomb. and this is If I talk about charged proton then it is the same remains 1.6 * to the power of 10 -19 just this The charge becomes plus. Charge on both It remains equal. So you have to understand this Will happen. So what is the charge? We understood this. Now There are two types of charge. positive There is a charge, a negative charge. Even a nursery class child knows that the Like charges are positive Positive: They repel each other. Negatives repel negatives. But unlike charges such as positive and Negative What do they do to each other? Attract. Aldo, no one knows the reason for this till date. I have been able to know. That is why it is called the fundamental law of It is called electrostatics. nobody I have understood why this happens. There are many exact reason theories. End That is why this is known as fundamental law. of electrostatics. that like charges repel each other and dislike Charges attract each other. How will the positive charge come? when the electron will decrease, protons will increase and negative When will the charge come? when the protons are reduced And more electrons. It is obvious. Conductor, look, this is a very LKG girl. I have to study. What is a conductor? who has They are free charges and they come from within themselves. Allows electricity to flow. Isn't it? You also know the insulator which has free Does not get charged through which electricity flows Can't happen. So this part I will tell you a little bit I will teach you quickly because all this is very basic. So our main studies start from here. goes and she is Electrostatic induction. Now Electrost and an experiment on it Will also see. Let's talk first What is electrostatic induction? See What we talked about here as well, what Do like charges repel each other? Yes. Do unlike charges attract? Yes. That is, two charges attract each other. Or you can repel. True False True. Now please look at me in the time stamp Make this one shot fun. You all know If you are studying in 11th class, 10th class then We're making these One Shots' comments section look like this Let's make it so that if the child comes, he should come somewhere, friend. Studies are also being done in the comments. So look The time stamp is 9 minutes and 10 minutes. nearby. Hit its time stamp and answer Me. The question is whether a charged body attracts or an uncharged body Can it repel? We know this, that A charged body is charged It can attract or repel. But what A charged body and an uncharged body On which there is no charge. does he Can it attract or repel? quickly Answer in the comment section. Just the video You can pause it and give it to me. Ok? So I hope You must have written that yes brother, attract Can not repel. yes an uncharged body Can be attracted by a charged body Not repelled. And we call that process are electrostatic induction. I hope You all must have done dirty things in your childhood. No, I am not talking about that. Whose am I Am I talking? What would you have done? What about some of the school children in their childhood? Must be doing it too. Cut pieces of paper like this Will be. They must have been broken like this, torn by hand and then the scales are rubbed into the hair And he must have attracted such paper and said I must be the magician. Isn't it brother? And We impressed people, especially him. will be. But son, you should know everything. He should be studying of electrostatic induction. How? Value Let's take a charged one here. There is a body. Ok? Let's assume you have There is a charged body here. Let Us Suppose There is a positive charge. How could it have come? This Must have given electrons to someone. right now he It is not a topic. And here we have a There is an uncharged body. Meaning of uncharged body There is no total charge on this. But this is Obviously there is plus or minus on this. plus minus plus minus means to say This means that the overall charge it has That is zero, right? But something on top of that The charge will remain. Hmm? Yes. Yes, yes, yes, yes, yes, yes, yes. Ok No? So, it has equal number of means electrons and protons, which is why This became an uncharged body. So, this charged The body is done, the uncharged body is done. as soon as I will bring this to him, what will happen? Look, as soon as I bring this to him, This uncharged body, this uncharged body, it absorbs its opposite charges into its It will pull you to the side. Or let's say on one hand that This will repel similar charges. Now What happened? Consider this piece of paper There was no charge for this, but This part of it has a negative charge. went and positive charge came on this part Went. So does positive attract negative? Will he? So here in between there's one Attraction will come. Isn't it? So what here A charged body reacts with an uncharged body Attracted to? Yes I did. But this Can never repel. Take care. The process in which redistribution of Charge takes place within a body when an electrically charged body brought to him Go. We call it people Electrostatic induction. take care electrostatic induction attraction Can cause. This attraction is caused by Can. Isn't it? But these repulsion causes can't. That is, a charged body is It can be attracted to an uncharged body But these two never repel each other. You will find if there is a pay charge and a pay charge Not there. Now take a quick look at the video here Let's watch this video first and then Let's talk further later or actually this I will also explain to you in the video that What is going on in this video? an audio Watch it or if there is a recording of the class then you You will understand, just watch this experiment. quickly. Made of aluminum. Aluminum is very light. what should I do now Have I been? Now I will rub it with my feelings I have been. So will there be any charge on this? Must have been? What charge would be generated? What difference does it make? Say. I its A video clip was made and brought. said there Someone is blowing from it. Last time I Had made it. The children are saying that sir is blowing It is from there, isn't it? Usha Sir, sit and blow He has been there, right? I heard. you We look so good as if we are blowing. But if I take it to him So look what is getting attracted From this. This can is coming here. Yes sir. We Fan-Vankha so that AC fan Don't be influenced. like this one over here What is happening? Attract. What happened here? When this cushion rubbed against my hair. These Suppose it comes positive. Now here's this can Was lying there. What comes here from induction? Must have gone? So what could be happening with this? Attract. Ok? Understand? So how does one An uncharged body is attracted by a charged body Might be possible. But don't repeal the process It is called electrostatic induction. Now This is a proof of electrostatic induction. It is device based, which we call Gold Leaf Electroscope. Now if I Let me ask you a question, let us suppose you There is a charged body nearby. Okay, right? Value Look, there is a charge on this body. So how do you know I will wonder if there is a charge on this or not? So There is a device for that called Gold Leaf. Electroscope. Its name Why Gold Leaf? because we will see now It has gold leaves attached to it. And Why was it called an electroscope? Scope means to see in a way. So Electroscope means charge To see. The charge is not visible. elder Seeing the charge means feeling our helps. And how does it work? These works Only on electrostatic induction. Let's understand How? So brother, one more thing, now we are going to Gold Leaf. We will also look at the electroscope. But the difference is There will be no more gold leaf electroscopes Will happen. There will be an aluminum leaf electroscope. Son, we are poor, aren't we? We never had so much I have never seen money in my life that we are gold That I should put a leaf here. Ok? So this Everything we have is made of metal. It is made of metal. Ok? It is made of metal. and around here Consider a glass container. Okay, right? glass plastic bus transparent It should be so that we can see through it. So this is insulating. Okay, right? It is insulating. Ok? Ok. Ok? What will happen now? If you accept me here I feel like I have no charge on this body. Is. This is something to understand. Diagram Vgram It will not come in your exam. Obviously C The thing is to make it. But suppose you think Do you have any charges on this? Correct Is? Someone is sitting on the charge. Correct. Correct Is. Correct. Correct. Correct. Now that you have this You will bring the thing to it. Isn't it? Value Let's say oh sorry, you accept this whole thing. If you bring the thing near it, then near it What will happen if I bring it? here Electrostatic induction will occur. Here We have put two gold leaves on it. Are there. Why choose gold now? all of you You know because gold is the most malleable and If you make thin sheets, they will be very light sheets. Now I like to take this positive to it Is it correct to say that here will bring negative charge through induction and all Positive: This will push it to the opposite side. You can say this in a way. And both of these Both will be repelled from each other and They will come here after being repelled. As soon as this There will be repulsion, we will understand what will happen on this Was it brother? There was a charge. So what happened? Anything It did not happen. Look, now when we I experimented with the can of Woh Woh. In that too, it was the same that brother, he was coming. If it is there then it means there is a charge on that pillow. But This is also a method. So it's all made of metal. It has happened. Keep in mind this is all made of metal. Is. And these are the gold leaves we have. We don't have to do so much labelling and webling. Probably to make diagrams in 12th class He will not even come. Never in 15 years Came. But gold if electroscope is such device that helps you tell Whether there is charge on your body or not. How brother? Induction took place. Negative Charge I came here. This is how it came about through positive induction. Like the same thing happened here too. When positive When I brought it near, the negative came here. positive I came here. Same thing happened here also. like now The charge will be same on both the leaves. What will I do to the other person? Will repel you. Now What if the charge on it was negative? It also repels. Yes. Negative on this If it had happened, it would have come positive here. here It would have come negative. They still love each other If they had repelled each other, anything would have happened. Will repel if there is any charge on this and this will make us understand that Brother, there was some charge on our body. So it has a limitation. This to you, this to you It tells you that there is a charge but it tells you that Does not tell whether the charge is positive or negative It is negative. Ok? quickly one Aluminum leaf electroscope. Not gold leaf, but aluminum leaf Look at the electroscope. then further Will grow rapidly. Now here I have my You can see a pillow at home in a bottle. You can tell I've put aluminum foil on it. Is. You ignore Usha Sir behind. But I put magnesium ribbon in a bottle. Helpfully hang aluminum foil below. I'll also zoom in. But if you carefully Look, as soon as I take the pillow near it I am going. I am not touching it. pass leke I am going. So how does this aluminum foil become a Moving away from each other. Isn't it? If I Let me charge a little more for this. So As I bring it closer. See This is how aluminum foil works if you carefully If you look, she is going away. Perfect Gold Leaf Like. So because of the gold leaf we I have taken aluminum foil. But if you get closer Look how it is going away. Touch We are not doing it here because touch If you do it, it will become conduction. here We're also looking to show induction. So How is it going away? So this is Goldf Electroscope or aluminum. Ok? So You saw the cheaper version of this, how it It works. Let's talk further. Now It comes to us that some three of the charge There are basic properties, of which The last property gives you a half in the exam. There are also high chances of MCQs coming. Who What is the charge? We understood. Charge two It is of type. How is his presence Let's detect it. Etsetra Etsetra. Now Charge follows three basic properties. The first property we have is Additivity. Now what does additivity mean? It happens that if we have charge then we Magnitude of direct charge and its sign You can add it with . in easy words The charge is added directly. meant to say What is? Let us suppose I have a There is a system, there is a container and in it I have There's a -3 coulomb charge sitting here. There is a 2 koolam charge sitting here. Here Pe is 10 coulombs. Let's assume -5 here. Coulomb. Now if I want to calculate the total charge So what do I do to find out the total charge? Will I do it? I will add q1, q2, q3 and q4. You will say this is a basic thing. So that's it Actually comparing that to Force This does not happen with me. because forces Vectors follow. go ahead The same will not happen with the electric field. Or with a lot of things. But the charge With we follow the additivity property Can. You can add them directly Irrespective of where those charges sit What direction do I have to take if I have to go through this whole process? Well, there is no system direction. If I want to charge this entire system. So I don't have to do anything. as much as I There are charges, just add them all. If we talk to Lets in this case then I have the first charge done, let's say -3. The second charge is done, let's say I have 10, The third charge is done, suppose I have two more I have the fourth one, let's say -5, so the sign Just keep this thing in mind that you have to add it with whether they have a negative sign or a positive sign So here five and two come to seven here If I get 12, I lose seven of my 12. It comes to five, right brother, so 5 coulomb plus The answer will come, you have to apply Charge Pay Plus. Just to clarify a little bit that you charge is fine but the point is that Here we will get the charge charge. Five five will come, right? Yes, it came in 12 and 12. to eight sorry 5 6 7 eight oh 12 out of eight gone I'll just say something seems a bit strange I am getting 4 coolam sorry charges here. If you understand then this type is nothing. Look, it's a basic thing, I think exam. Should any question arise in this, additivity The property charge shows the next Property is above conservation easement Questions may arise: what is conservation of name? It is clear from this that we neither charge You can neither create nor destroy Can. You can just transfer. charge cannot be created. to charge Cannot be made. We charge Can't even destroy it. But yes We transfer charge from one body to another. You can definitely transfer. This thing to you You will have to be careful. So the total charge of n Isolated means from which nothing can be taken. I am not giving it. Its total charge is That will remain constant. You can say it like this also. But the definition below is evergreen, son. There is a definition. Neither electric charges What can we do? You can create And what can we do? Destroy Can do. You can just transfer. This is a very basic question. ok sir. Its After all, the most important property which gives the most You must have got more questions in the exam That is the quantization of a couple of numbers. Charge. Now you all are 12th class students. so Isn't that the word quantization for you? There is a new word. the word quantization so you You already know it. When something is not continuous It is discreet, small It is in the form of packets, we call it Let us tell you that it is quantized. If I Let me ask you a question, whether you are What is the minimum charge on any body? Can you bring it? So the answer is an electron. Charge of. If electron is given then plus 1.6 into 10 to the power of -19 And if the electron is taken then the value of minus Will go. But this is the minimum charge which any We can create on the body. less that Cannot create charge. Well, if two Electrons will come and go into two Will be done. Do you understand? If three come then into I will become three. 10 will come into It will become 10. But the charge is always will be a multiple of the electron. Any Random values ​​cannot achieve that. If Should I say on any body, 2 * 10 Can Power-19 Coolam Charge come? So The answer cannot come. Because an electron So 1.6 to the power of 10 is -19. If two come 3.2 * to the power of 10 will give -19. Because That will always be a multiple of 1.6. So in 2 * 10 to the power of -19 coulomb charge not possible Is. This means charge any random Continuous cannot take a value. He always will be a multiple of the electron. If I If I enter a charged body, I get a electron, two electrons, three electrons, 10 electrons, 20 electrons, 50 electrons such number of You will get electrons. Do you believe it? Now if I have such a number of electrons there. Will meet. So that means the charge sitting in the form of small packets Is. in the form of electron-like packets He is sitting. That's why we call it charge. That it is quantized. Now if one If an electron comes then this much, if two come then it is 100% If two and three came into it, then three into it. So if May I ask you how much the total charge will be? Let's change the color so you can see a little bit more. Let me tell you separately that if I ask you any What will be the total charge on the body? So what? N * That charge became an electron. Understanding Went? n * charge on electron a The charge on the electron is into What does n mean? how many electrons does it The pass is more or less. Then the total charge If I represent it by q, then our Here you will get a formula q = ne. Here n is + - 1 + -2 + -3 like this Will remain. Because electrons can also be taken They are and can be given. If you have If you have taken electrons then the value of n will give you Have to take it in minus. If you find the value of e Plus, in simple words, electron If you have taken it then the overall charge will be in minus. If you have given it then it will be in plus. But these n There will always be a number like 2 3 4 5 6. What Do you call them that? It is called a natural number. Hole number. can also be a hole number if n If it becomes zero. But the total charge is will always be a multiple of e. Not so that is 1.5 * a will come in or any Random value. So whenever something belongs to someone If it is multiple then we say that it What is it brother? It is quantized. It is quantized. Like I studied in 11th class that the electromagnetic wave The energy they have is small It is available in the form of packets. It is quantized. it was said Planck's Quantum Theory. So here if You will read it is written it means that Electric Charge Can Not Vary Continuously. It is not continuously I can vary and any random value that Can't achieve it. Yes, that Discontinuously changes its value Which is multiple of 1.6. The Experimental The Fact That Electric Charge Acar Discretely we call this quantization of charge. They say. Quantization of Electric Charge means the total charge of the body. will always be an integral multiple. a basic Quantum of charge and basic quantum of What is the charge? is electron. Basic Quantum of charge is what electron is. So I spent a lot of time here because Son, because this is a question for you from here. Available in MCQ form in the exam There are full chances. Understand? So I think I've already done 10 slides. Are. My request would be that you do this much Read it one by one. Then read it. Make notes. Then we will proceed further in this chapter. Coolums is moving on to the most important thing Laws of electrostatics. ok let's go Brother. I hope you have read this much. Now this Towards the most important topic of the chapter Let's go. Coulomb's Law of Electrostatics. Coulomb's Law of While studying electrostatics, you will not find anywhere Somewhere remember the Universal Law of Gravitation Will come. What is this law actually? before that We have two charges let's say q1 and q2. and between the centers of these two charges What is the distance between me and the letters? r is. Okay, right? Both charges are very small. And the charges are lying at a distance r. Correct Is? Now Coulomb's Law of Electrostatics What do you say? that which is electrostatic There is force, Electro static Force between two charges. two charges The electrostatic force between That is the first thing, directly It is proportional to the product of charges. Here you will remember in a way our The law of gravitation, which states that Gravitational force is that directly Proportional is the product of masses Of. This is directly proportional Product of charges. Second thing He said that the force The electrostatic force is that of r² is inversely proportional. And maybe all of this Even with common sense you can understand that if If two charges are added, the force will increase and their If the distance between them increases, the force will decrease. But according to the law, square times less Will happen. Meaning if I double the distance then The force will be reduced four times. Distance Three If I multiply it, the force will be nine times less. Will go. Because square times inversely It is proportional. Now if we combine these two If you give it, the force will come to us. If I Let me first write this step that proportional to Q1 Q2 / R² so this gives us the force Will go. Did you understand? We have this force Will go. Now you all understand that proportional If you want to put equal sign then here We will add a constant. So brother f = k q1 q2 / r² You could say that This is the most important aspect of electrostatics. The formula you are studying today is f = k q1 q2 / r² which is matching From the gravitational force gm1 m2 / r². Now Here q1 and q2, you understand, are charges. r is the distance between them. But this k What is? So here you can say that k Obviously it is constant. But You can electrocute it You call it static force constant. This What do you say brother? electrostatic force Constant. And this is medium dependent. Is. This medium is dependent on what it means that is, if there is air between the two charges So its value is different. If there is water then its The value is different. If there is any metal then its The value is different. If there is a vacuum then it is different. The point is that its value depends on the medium. She does. Alldo if you remember that f = g The g that comes in the formula m1m2 / r² We had this, a universal constant Was. Universal constant means the whole Its value remained the same in the universe. But this is not the case with k here. K who Yes, it is not a universal constant. Its value changes with the change in medium. Now what is its value? you say so Can that for free space for free Space. Free space means right now you Consider it a vacuum. There is a slight difference but Ok. Now there is free space in 12th class and Consider vacuum to mean one thing. So for We have free space which is k. The value is 9 * 10 to the power of 9. It is a very big value. for free space its The value is 9 * 10 to the power of 9. Now What will be its unit? Look at the force What is a unit? Newton. What is it about? Meter Square. And what about this? Coolum* Coolum means Coolum Square. So what has come? Newton. meter square coulomb to power-2 newton meter square coulomb to the power -2 What becomes its full value? For Free space 9 * 10 to the power of 9 Newtons Meter Square Coulomb -2 for free space. That means this value that we have taken is It is for vacuum or free space. Yes, keep in mind we are physics experts. Vacuum while doing numericals, free Space and air are also considered the same. Aldo There is a difference between these three. in vacuum and air So you understand the difference in free space as well. It happens. But it's okay to vacuum, free up space and air. And spoke in some numerical There are two charges that can be placed in air. Has happened. Even then you can calculate the value of K in 9 * 10 You will keep the power of 9 only. Now one more thing to note Keep. As you can see here, We have a constant called K which That is absolutely correct. But the truth is that when Newton and Coulomb derived this formula. If it is done then K is not constant here Had come. I actually came here 1/ 4π is another constant that we call eps 0 Are. He considered him as K. Easy language I leave everything. Which is K, this is actually 1 / 4π It is 0. This 0 here, we call it Let's say Permittivity and NOT here mean we People talk about free space, i.e. vacuum. Have been. If I am in some other medium So instead of apps 0, I will put apps. But Now if I'm talking about free space So k is actually another one in itself is a constant and that is 1 / Equal to 40. That is, when the formula derives Suppose Coulomb did it, then f = 1 / 4π0 q1 q2 / r² would have come. Then he said Gotta do that. This is called a new constant. Let's accept it. So that must be considered as k. So According to me, it might have actually happened like this. Rest is fine. K is what we have a is a constant that we can further expand. And that happens to be 1/ 4π0 If so, then what we have electrostatic force, which is still kq1 q2 / r² will become 1 / 40 q1 q2 / r² So here we have it fully loaded The formula of the force will come. Understood? like now that we had a value of K in 9 * 10 to the power of 9 free space. Obviously It is true that if the value of K we had So I put in the value of K for 4π and then I can also find the value of 0. his We have value What is 10 to the power of -12 in 8.85 into? Is? 8.85 * to the power of 10 -12 and obviously C The thing is that its unit would be much larger than this. It must have become opposite. That is, Newton's Power-1 meter to power-2 coulomb square. Why? Because k is the same as 0 Look, these are reciprocal to each other. That means if this is above then this is below. So whatever the The unit of will be its opposite unit I did it, which is obvious. It came to us. So for free space The value of k was 9 * 10 to the power of 9 and Here its value is 8.85 * 10 Power-12. You remember these two values. Have to keep it. Numerical will come, you will have to solve it And apps 0 means permittivity then you will get even more It will be useful in many places. Now this is common sense The thing is that if k is depending on the medium If so, Apps 0 will also depend on the medium. That is, we have just now determined its value. The permittivity of free space is written. But if If this was for some other medium, we would have I will write the apps. And this is for us too It will be medium dependent. This is common sense It was about. Even if you don't write, you will understand. Should have gone. Because if K medium pe If it is depending then somewhere apps 0 Or the apps will also do it. Understand? Done Is. Now let's not talk here for long. And let's talk a little bit. then further Let's go and what is that? take a note point Let's take it. As you may know, we Find the relative density. Relative We have derived our refractive index. In previous classes. That's how we have It happens Relative Relative Permittivity: This is useful somewhere in this chapter. Will not come. Well, a lot of work in the next chapter. Will come. Relative permittivity Permittivity is also known as the Dyck constant. They say. We call the relative permittivity Also called dielectric constant. Name Relative permittivity can be found from Which we will show with Kapa. You can use a capital K. You can do it from also. What will this be? What is it will be? What does relative mean? When We divide someone into a vacuum Relative density in relation to What was it? We have density of substance Extracted with respect to the density of water. What was the Refactory Index? We Refactory Index Removed With Respect To air or vacuum. That's how we have What will be the relative permittivity? So obviously It is a matter of permittivity Medium with Respect to Permittivity of what? Yes brother, you are thinking correctly Yes, there is free space, right brother, this means Kappa, i.e., dialectic constant, i.e. Relative permittivity has become 0/10 because What is Apps 0 for What is Apps 0 for Apps 0 is free space for more apps For any medium, this is like this It won't be of much use anywhere in the chapter It will not be useful in NCERT but Yes, this is very much in the second chapter. It has become an important topic and will come before you. Going to do. Did you understand? So this is what we have Dialectic constant. So, but we Now a question may arise in your mind. We have to remember this formula of force Yes or this is the answer, both have to be done. Isn't it? There is nothing that will come to the same place And numerical can come over anyone. It's done. It's done. It's done. Done Went. Let us now discuss this chapter. about another topic which is Electric field. Then both of them together Will read. So far we have been talking about electrostatic I was talking about the force. Now we will talk of the electric field. See if I If I ask mathematically, it is a different matter. But Theoretically, let me ask whether the electric field What is? So electric field means a The area around the charge to which it reaches other can exert influence on the charges, We can apply force to it, we can call it electric. Field speaks. So if we talk theoretically So its definition becomes different. Mathematically different, theoretically you can say that You can say that the region or Space Around A Charge region around a charge up to V it can Apply electro static it can apply electrostatic force on other charges but this mathematical There is no definition. Got it, right? mathematical What will be the definition? Which gives me the formula May you also get it. So we can call the electric field How can you define it? Listen. accept it I have this charge, this is a charge I have. This is the charge for which I have to pay the electric The field has to be removed. So let's charge this q Is. I need an electric field for this Have to take it out. Now if I have to do this for If you want to remove the electric field then this is common sense. It gets to me that I'm around it Secondly, I need to look at the other charges around it. Will have to keep it. Otherwise I will buy it electric I will not be able to calculate the field. My point Do you understand? Like for an example, my There is a charge nearby. Here it is. Now I have to do this Deriving the electric field around the charge Is. So you have to keep another charge around it. Will have to. That's why it attracts or repels him Will do. So I've put a charge here. Which I am calling q not. These q not to We call it a test charge. We test this Why is it called charge? Because this charge Test its electric field here. He has come to do it. That's why it's called test. Charge. So we're calling this Source. Charge. And we're calling it test. Charge. Understood? Now if these charges are added together It's at a certain distance from the letters or whatever Right now distance does not matter, so this charge This produces an electric field around the It must have been because of which this force is on this Will apply. So it is very important to have it. And Accordingly, we have electric field The definition of also comes. What? Electro static Unit Tests on Force unit test charge on charge i.e. our Another definition of electric field for Let us ask what is electric field? Unit test on how much force is being applied Charge. That is, the electric field which we People are going to represent with E. Its There is a formula based on how much force is being applied. Unit test charges that I have brought. We call it electric. Field. So the electric field Theoretically, we have to understand the charge around The area where it had its influence Used to be. Mathematically speaking, how much Force is imposing this charge? another charge Pay per unit test charge which charge We are applying force to this also, electric Let's call it field. Now its unit and Before talking about direction, I would like to tell you all I would like to ask you a question, the answer to which you can give. Everyone has to give time to the comment section. Look at the stamp. What is the question? The question is According to you, this test charge is The charge can be any amount. 1 Coolam Do coulomb, 50 coulomb, 1 micro coulomb, 1 lakh Coolum how much so. But this test charge Should this test charge be small or Should it be bigger? You can comment me the answer to this Tell me in the section right now. these tests Should the charge be small or large? Needed? I'll write here until then. That Properties of Taste Charge. Tell me quickly, this charge is going to be huge. Should it be or should this charge be smaller? Yes Yes. Should this charge be large or small? Needed? So I hope you have written the answer till now. Have given it. So this charge is very small. Should be. Must be very small. Very How small is small? So the answer is infinite Tastefully small. It is also called vanishingly small. It is said that almost zero. That is, the test which The charge should be its magnitude tends Two zero. That means it should be almost zero. Because if its magnitude is high If it happens then he influences it from his field. Will do. We want to remove its force. We want to find out its field and not that one. So if it becomes strong then it will spread around itself. Will create a very strong field. And the influence that will occur will be due to this or What will happen to it? We won't be able to judge. that is Why is this charge so small? Needed And by conventional by conventional You can say bye Conventions, this test charge, we have Considered positive. It can also be negative But your and my directions match, a sign The match should be for the final result, hence our Physics calls it a negative instead of a negative Accepted it as positive. I am now speaking again Yes, this could have been negative also. But It is universally considered positive. So that our answers match each other. So test The value of charge tends to 0 and this What lasts forever? Remains positive. Did you understand this much? Now let's talk about its SI About the unit. And this is a scalar Is it a quantity or a vector? and if the vector is So what will be the direction? So the force The unit became Newton. and it's charged Coolum. So its unit came to be Newton per Coulomb. Very simple. Now what quantity is this one? Brother? is a vector quantity. This is a vector There is quantity. And its direction would have been It is positive charge to negative Charge. That means again this is a conventional In the direction, we assumed that The electric field travels from Positive charge to negative charge. i.e It starts with a positive charge and It ends on negative charge. Now If you all have maths then you have one thing What is that thing that might be bothering you? What is that? I Let me tell you. The formula we came up with for this What has he got? He has come to the force Unit test charge and here sir you say You are wondering what the value of the test charge is. Tends to should be 0. Now if its The value tends to zero and I am here If I put it then what will be the answer? Will you go? Not defined according to maths. But Don't worry about that because now we are together. Electric field for a point charge Going to take it out. And you will understand that electric field for a point charge The formula depends on the test charge. He doesn't do it at all. It's a 2 minute job. Come Just do it. You can say this chapter The first derivation is coming. Ok? So this We have a charge q which is The source is charged. is the source charge and we have What is to be calculated at its distance r? The electric field has to be removed. so me What do I need to keep here? what to say had been? What do I have to keep? absolutely right had been. I'll have to put one here. Test charge. Isn't it brother? a test charge I have to keep it here. Now I We have to find out how much this one point charge is Must be generating an electric field. First So let's take out the force. of the force The formula is k q1 q2 / r², very simple How much q1 do we have from the C derivation? q Is. q2 How much do we have? q is not. The distance between them in the up is called r² or First accept it. Also also what about the electric field Formula Force Upon has a test charge. Yes sir. Now how much force did we get? k q Not / r² / q not means test charge. what q not From q not cancelled? So congratulations brother yes. I was telling you that the Electric field, its formula has come kq / r². Now if you look at this formula You will get test charges anywhere. No. That was in the definition. But the point You can find formulas for charging anywhere. I will not get any test charge. A little more If we expand it, the electric field will come Will go to the forest. What can I write in place of K? Am? 1/40 If I stand in free space So q1 q2 / r² is what I have, say q1 q2 I have been. kq / r² came to me instead of 1 / 40 q / r² so for a point charge I have an electric field. The electric field has arrived and obviously The point is the direction of the electric field Plus if this is a positive charge then this It will always come from the positive. So somewhere on this side There will be an electric field. This is us right now We will create electric fields like this in future Will take it out like this. That is a matter for later. But This is because it is plus charge so electric The field moves from plus to minus. Is. So here's the plus. There is no minus anywhere. So it will go till infinity. Ok? So this We have an electric field for Point charge. The first derivation of this chapter Also there. So look at it honestly. Very It is a small derivation. Then we move forward Because now going forward, big derivations You are going to see it. Let's move on to a new topic Let's go on our way, children. and the name of the topic What do we have? is an electric dipole. Now if you remember this electric dipole So you have also studied chemistry. What happens? Electric dipole. So system of Two Equal and Opposite Charges Opposite Charges Separated Buy a small Distance. Understand what? or not necessary Small distance. I think it's small Do not get confused by the word because it is important It is not that it is small. But we who In this chapter we are going to study Most are going to do it for small. Separated by a distance. So, that is, if We have a charge sitting right here. +q and a charge is sitting here -q so Are these two charges equal and opposite? Yes. and the distance from the center of these Ours is 2a. Here we will define the distance as 2a. Why are you going to take it? That's it, you will understand Sir, distance is either a or l or r or d then we get 2a or 2l or You will understand now why you are going to take 2R. To simplify the calculations, but their Let's say the distance between the two points is x. Will it become an electric dipole? Answer: Yes, because it has two equal charges. There are opposite charges. Meaning their The magnitude is the same. If it is 10 coulombs If it happens then it will also be of 10 kulam. just one One will be plus and one will be minus. And There is a certain distance between them, so We call it electric dipole. Now comes after the electric dipole Electric dipole movement. you take care These electric dipole movements give you a boost in seconds It is also going to be very helpful in the chapter. It is going to help a lot. So a little Look carefully at what is electric. Dupole Movement. You learned this in chemistry I have read it. Just a small change will happen. tells am I? What is an electric dipole moment? It happens? So Product of Ether Charge product of either charge with Distance Between the charges. Understand what? That means that Take one of the two charges because Both charges are equal and opposite and The distance between them in the Multiply it. So we call its product People call it electric dipole moment. Let's talk about this with We call electric dipole moment as P. They are going to represent. If I talk I want this to give me an electric dipole moment If you want to find out, what is the formula? here charge means any one charge because both The charge is the same. into both of them What do I need to withdraw between charges? Distance. Now here charge any one charge If we talk about it, it is an obvious thing that will take charge q. and the distance between them We have taken 2A. So from here our Formula for Pass Electric Dipole Movement Will come. The distance between them in q* that we're going to take 2a throughout this chapter Are. So q* will come in 2a. So from here If I talk about its SI unit and If I talk from here, which one is this? Is there quantity also? Vector quantity and Its direction is negative. She remains positive. I hope you know There are two types of vectors in the world Are. One we assumed was Vector It happens. Meaning that we gave them something or the other. Directions are given. Like the force that is He is a born vector. she has The direction remains. Then you study it You can do it. Otherwise you will not study it. Can do it. There is such weight but such Displacement also occurs. but nowhere If you know anywhere, then electric dipole We have given the direction of the moment. Electric Direction of field source electric field From positive charge to negative charge we gave Is. So this is a vector whose We have assumed the direction. And that is From negative to positive. Ok? so one is a vector quantity. Now its SI unit Let's talk about it. Then the SI of the charge The unit is coulomb and distance is meter. Now what happens here is that Often the coolant meter, first of all, this is obvious It is clear that the Coulomb's cylinder R is smaller than the meter M. But still sometimes children do this in a hurry. Let's make it. So somewhere he Don't consider this as a centimeter. So I always I recommend it and what is in the books too It happens? A small difference between coulomb and meter Put a dash. This will justify it That basically what have you written here Is? Coulomb meter. So write the coulomb meter like this So it is good. Now the child says Why don't I write the meter first and then the coolum I will write it later. No, no, son, this is Something wrong will happen. No, no, like that one Friend, that kind of thing won't be wrong. How is this wrong Will it happen? This will become milli coulomb and Milli-coulomb means 10 to the power of 3 coulomb Will be done. Then this will be even more wrong. So That's why you can enjoy the dipole moment anywhere. You will use units when doing numericals. coulomb slash small slash speak dash Whatever you say, write it like this: coulomb meter Two is better. aldō in writing like this There is nothing wrong. But okay, confusion It should not happen to anyone. Ok? It's done. Now What is an electric dipole? Electric Dipole What is a moment? If we have understood this So we can move ahead. And now we have to look at the details of Dapol. For this, electric field has to be removed. he too At two different points. One is that we Its electric field at the axial point Have to take it out. The derivation is proper and a Its electric The field has to be calculated. I will explain What are you saying? Axial point and What is the equitorial point? in case I don't know. So here we have a plus charge and take it down a little bit Let's take it. Are we okay? So here we have a plus charge and this is what we have minus There is charge. Okay, right? Now between these two The distance in is 2a. You here It will also be understood that taking distance 2a There was a reason why we were here. now here what does that axial point mean first The matter is somewhere in this line. They speak of axial points. So what did I Did? At this point itself, there is an axial P Point taken. Now what is this axial point? Yes, because the axis is on the line of this dipole. Pay Axis Pay Point is called Axial point. Now what do I have at this point? Do you want to take it out? Electric field. first thing So the length of our dipole moment Yes, that is two and this point P It is at a distance R from the center of our dipole. Is No? We will write down the considerations etc. and the derivation before let us take a dipole like this By doing. Isn't it? So this is the P point which It is axial and is at a distance R from our center. Is. If you understand this much, then understand this also. You will know that this charge is from P. How far will it be? Look, this is the whole 2a, so this The one became a and this one also became a. Now If this part is a and this is r then r If I subtract a from r then this is r - a aa Will go. Just like this, this distance a and this one is a complete r so from here to here Till it will come to me r + a so understand Came? r + a Now listen. Now listen very carefully From. Why did we take 2A here? I hope You must have understood. I understood it So write yes in the comment section with a time stamp. With that yes we understood sir. did not understand Look, suppose we take its distance as a. I will remove it right now. But consider that Distance we take a. Then this one If the distance was a / 2 then it would be r - a / 2 and this is r a + r + a / 2 and from this we have Calculations will be very difficult going forward. Caste. It would have become difficult. That's why this mess We did not do this without falling into it. Our NCERT did this. our entire Physics has done this so that we have 2a here so that half of it becomes a and a. So that our calculation becomes easier. Now What do we have to do? What do we have at this point? Do you want to take it out? Electric field. So first What should I do? electric field removal I will take it for the one with +q. The formula is How far is the kq / +q one? So the answer is r + a distance away. So r + a² will come out. It is obvious. Now we are looking at the magnitude Wise is talking here. Okay, right? Now if I talk like this, electric For the field having -q then its charge is minus If it is of then -kq and r -a² will come. Now if I had total electric If the field is to be derived at the axial point then I need add for +q ones and add for -q ones Have to do it. It is very simple. Come add him We give. So kq / r + a² + kq / r - a² But remember there is a minus here. Now Here if you apply basic maths If you solve for the axial point kq will become common. what's left here Will you go? 1 / r + a² - 1 / r - a² Now here's the basics again What will we do by doing maths, brother? r + We will put the identity a² r - a². So a² , b² will come. Now up here will come r - a² - r + a² will open it. Let me tell you. Let's come to r - a² - r +a² Now listen, you will open r from r² from here, right? So r² to r² cancels a² to a² cancels. Here -2 will come and -2R will come here also It will be added. So overall here We had KQ outside at the Axial Point Here I solved -2R and here Even at -2R, it will become -4ar and below it will remain will go r² -a² Whole Square. Now listen carefully, Dapol The moment will come. I'm going to take the minus out of here. I am taking two out. Why? Look, K has just arrived. Q has arrived. If I two If it was taken out then what is left here? 2a survived. Isn't it? 2a survived. what are you now 2R sorry do you recognize 2a in q* yes? Do you recognize 2a in q*? Yes Brother we recognize 2a in q*. q* What is 2a in Dipole moment for us Is. What is there for us? It's a dipole moment. So here I am kpr / r² -a² gives the square root of Am. So I have this weird formula. The electric field will come at axial Point. Basic C is a derivation. Nothing Did. But in the exam, even more than this If this happens then derivation will definitely happen. But they will tell you that electric Field Axial Point Pe Nikalo for short Dpol. That is, if the dipole is small then the first The thing is if it is a small dipole then for short Dipole. First of all, in short dipole What does short mean here, that this Both are charges, they are very close to each other. They are close and this is the distance It will be relatively far away. That means this If there is a plus charge, then this is a minus charge. And The axial point at which you observe the electric field This is what you are taking out. So what about this case? In my case, our 2a is very small. Will go. And if 2a becomes smaller then common It makes sense that a is also very small. Will go. And if A is too much for us It will be smaller than R so I will ignore A I will find it anywhere, plus or minus happening so for short dapol a which is It will become much smaller than r, so wherever a is going to be plus or minus so here it is a² That will become even smaller, so I will divide a² I can ignore it. So if I divide a² by If I ignore it, I will get the formula. will go -2kpr/in down to a² zero. Then square to the power squared means r Power 4 will come. one r to one r cancels out Will go. Congratulations children. We have Electric field has arrived at the axial point Is. whose formula is -2kp / r This is a very important derivation. exam It is asked in. It's done. It's done. Now, in the same way, we Electric field at the equitorial point will have to be calculated. Now Equitorial What is a point? So here we have plus There is charge. This is the minus charge we have. The distance between these two again That's 2a distance. It's done. Now our On which point do you want to work brother? At the equitorial point. So this one which This point is the equitorial point It is called. Here's one of Pay Let's The point is P. Now this P point is behind the center. Like the bar, R is at a distance. ok sir. Correct Yes sir. Absolutely fine. Now from here its The distance that will be achieved if this is r and this is complete If it is 2a then this part will become a. So This part will be r² + a² from Pythagoras. similarly this one It will also happen. Ok? Now the previous ones The ease of the question was that whatever our p The point was that it was on the same line. So the force She had come, she had come to the field, she was attracted there only or There will be repulsion. But at the equitorial point which is our charge which is our point and Our charges are not in the same line. Is. So here we have a little vector Will have to apply it. Let's understand how? These are our What charge do you have brother? We have this +q charge and here we have -q charge. Now If I were to give the electric field at this point p So I have a Must have kept the test charge? Must have kept it. And what will that test charge be like? positive will be. Isn't it brother? So is this positive? Is it going to attract positive or Who is going to repel? So the answer is Repel Is going to do. Absolutely. And just like this Negative attracts positive Is it or is it going to repel? So the answer is It is attractive. positive negative Attracts the . So in this way, which The electric field is of +q type and it is here Will go. and electric field with -q It will be here for you. And both are very different in direction which has brought me here now Using the study of pay vectors will be. So here a little focus on the yellow color Will give. Ok? Let us see this angle. What it is is theta. So it is obvious that This angle will also be theta because The obtuse sides have obtuse angles. But We have learnt in 11th class that every one We can split the vector into two parts. So One piece of the one with +q became this and one This will be the piece. Isn't it brother? solid talk. If this angle is theta, then is this Will the angle also become theta? because this Suppose the line is transverse and this is parallel to this so this angle is also theta Will be done. Now what happens to theta? Is? cos . So this electric field cos theta of +q will become and this electric be the sin theta component of the field +q Will go. Who did I just break? +q of electric field only The component of the electric field. Similarly, if I change the component with -q If I break it, one will come here and the other will come here. Will go. Now again maths says that if this If the angle is theta then this angle is also theta Will go. Why brother? What do you call them? These are called alternate interior angles. So The one with theta is cos so here -q cos theta will come and this one of -q The component is sin theta Will go. Now what is the sin theta component? Came in opposite directions to each other? Absolutely came. Son, pay attention to this diagram. Something is so important without a diagram You will understand. What sin theta and sin here Theta components are opposite to each other. I have arrived. If yes then it will be cancelled. that you Write it in English in consideration. But are the components of cos theta the same? Is it in direction? Yes. So is that an ad? Will you go? Yes. Now you are not plus or minus. You will see. Because we include the direction Have already done. So now if I have total electric The field has to be drawn at the equitorial point. Now let's talk about magnitude cos theta of the electric field +q I will take the component. And here the electric I'll take the cos theta component of the field -q. But what about both of them? The electric field is the same. Why? What is the formula for electric field? It happens? kq / r² Do both have the same q? Now there will be no plus or minus. take direction I have done it. Yes. Do both have the same r? Yes. So what is the electric field of both? Will it happen? It will be beans. So here I am This is called the electric field in 2* with +q Let's take from cos theta. It's over Work. Come on, come on. Now, the electric field The formula for distance is kq / Square. Is their distance equal to r²? be the whole square of the under root of a² Will you go? Yes. running along our cos theta Is. Correct? Electric field will come 2 kq / will be saved here in r² + a². Now the matter Let's do cos of theta. according to Trigo What is cos? Base / Hypotenuse. Now If this angle is theta, then this will be Base i.e. a and hypotenuse we have It is r² + a², well maths says that Bhaiya, first of all what should I do here? If you take it inside then it will come here in q * 2a You know, you know what this is Do you know or not, do you know or not, this is the dipole moment Here r² + a² is 1 to the power of a. Here r² + a² to the power of 1/2. So this will become r² + a² to the power 3/2 is 1 and here pe one and Here it is half, so I added it and got 3/2 now. Congratulations, we have the formula. Electric field at equitorial point But have we just done this for normal dipole? Did it or did it for short Dpol? The answer is, we have just given this for normal dipole. Have done. Now the same thing happens if I do a short dipole I do it for which you will get help in the exam. You have to do it whenever you get this derivation quote. will go then same again for short dipole The thing will be that the a is much more than the r It will become smaller. How do I deal with this situation Can I imagine a short dapper? These I have plus charge. This minus charge I have it. Actually, even more than that This is close and this is somewhere else and this is far away There is a point. So r is much greater than a has become big. Because of which I call a I can ignore below. what had come formula we have electric Did this shake the field? I have some of this Did you shake it here? Isn't it? yes yes yes Yes, sorry, sorry, sorry. Let us go. so we have Here the electric field is equatorial What was the point pay formula? here comes. Well, I obviously think 2a in q* What can I write? I can write p. p I can write p and here it comes to r² + a² to the power 3/2. Now can I get the denominator? Can I ignore a? If the dipole If it is short then. Yes. So the formula will be kp / had r². I removed it from here. I have done it. So the power left is 3/2. Now here Pay to See to was cancelled. So take it brother Thankfully, we have an electric field. The formula also applies to the equitorial point. gone kp / r Now look carefully, we have electric How much did the minus come on the field axial If you ignore it because that direction 2kp/r came here 2kp / r 2kp / r But the formula that came here was kp /r So you could also say that In the electric field axial upon Electric Field Equatorial for short Dipol for short came brother Did you come for short, what is their ratio That 2:1 has come, it has definitely come. If the magnitude ratio becomes 2:1 then this Can help you in MCQs, done So there we have it for the electric dipole. Useful on axial and equitorial points goes. Now here we are going to discuss a section of this chapter. And we're going to make a very important derivation. Are. Very important derivation which Is torque on a dipole. Now Torque on a Dipole If I understand the first thing I would like to You can do this well by pausing the video. Take note from it. Don't be hasty. The first chapter is if it remains weak There will be a problem. ok sir? Now you first Let us understand what he is demanding. Let us tell you that I have an electric scooter here. The field is going. Ok? Let Us Say Mere A uniform is passing by Electric field. It is obvious. If If the electric field is going somewhere here It will be a plus charge somewhere here. somewhere here But there will be minus charge. So here I have The electric field is going. Correct? Correct Is. Correct. Ok? Now somewhere inside The dapper is lying there. In which here in Dapol We have plus Charge and here we have minus charge. Ok? And this line to Dapol is Is adding. That means this 2a distance should be ours. goes. Okay, right? This distance is ours goes 2A Now first of all you have to remember this What would that torque be? So 11th We have read in class that whenever we forces applied to objects that The line of action should be different and opposite. So she would rotate that object. in that It used to create a turning effect and we Torque said. turning effect of force We said torque. So, to produce torque The necessary condition is that two There must be opposing forces and their line The action should be different. if he Both forces are equal and opposite. and the line of action is different only Torque seemed to be 11th class. but if The forces are odd, one is more, one is less Is. But he is opposite and his line of The action is different, so torque was also applied and that translational motion, i.e. forward or backward Used to go. Now here we have to prove it. First of all, it will only be torque-driven. And then derive the formula for torque. Come First let us understand whether torque will be applied or not. It will take. Is this a plus charge and what? plus charge electric field direction I want to go. It is obvious that Why? There will be a plus somewhere here. Outside There will be a plus and there will be a minus only then The electric field is going here. This which The yellow electric field is the dipole. It is not. It is connected to some external electric There is a field. So what is this plus charge? Is this plus charge, this plus charge? in the direction of the electric field There will be a force above. Isn't it? So this plus Charge would like to go here. A Certain Force It will be applied on this. Let's say that force is ours Pass f a plus ones pe. then f + q Will this force be applied like this on the minus one? It will look exactly like this. This on the minus ones The force will be applied like this. And this force will be f -q. Now is this what we see? Clearly, these two forces are opposites. She is looking into direction. Think of this one It is a dipole. It seems like there is force on it. This It looks like this on me. So is there a torque on this? Will he be born? Because this will be a turn. This turn If it happens then what will be produced on it? a torque Will be born. Because you can use this force You can see the line of action here and this The line of action of the Wally Force is here. So His line of action is different. Is. So brother, it is certain that torque is produced. will be. But will only torque be produced? Will it rotate in one place or back and forth? Will also go. If these two forces are equal and If the opposite comes, it will prove it. That torque is being applied but it is moving back and forth will not go. So first of all, let's figure out that What will be the force on the charge with +q? Have we read in this chapter that Force Upon Electric Field Formula There is a charge in it which we keep. So What should be the formula for force here also? Will you go? If I have to take out the force electric field into charge Will go. So the electric field we have here I have taken the uniform. E is equal everywhere. So We will have an electric field of E and We have charge Q. Then the force will come We have QE. The Force will come to us. QE. Understand what? Yes. Now this same force, if I On whom should I take it out brother? On the one with -q. So The formula will be QE only. just what the difference Is? What is that charge? Of the minus. So the force You see what has come equal to this? Force above it is qe and the force on it is -qe. So what These two forces are equal and opposite. Are? I have definitely come. Both forces Equal and opposite. If these forces are equal And she has come opposite. So what is their net force? Whatever is the net force on these, if I If I add the ones with +q and the ones with -q What will be the net profit? It will come to zero. Now if the net force becomes zero then this So it is certain that this is not going to go ahead. behind because forces are equal and Are opposite. But their line of action It is different. So, write a line here. You as forces are equal and opposite but Having different lines of action. So these The forces will apply torque on the dipole. Now we have to extract that torque. So We learned the formula of torque in 11th class. I have read it. Ether Force Into Ether Force The perpendicular distance between them. We Studied in 11th class in Eider Force Into The perpendicular distance between them. torque Which we have been representing with Tau. Now Either force means any one force. from lats Their perpendicular distance in QE into. Come, let us now look carefully. Do these two This is a front line of action between the forces. Is. This is a F's line of action. So, Is the perpendicular distance between them It's done, do we have that distance? Is the green distance over? Yes. Now if this The distance is 2a, and our dipole moment and If the angle between the electric fields If it is theta, then the opposite of theta becomes sin theta. So what is this distance? the one in front is 2a sin theta, which is the middle Perpendicular distance will also be achieved. So Here we will have qe into What will come with the distance? is 2a sin theta 2a sin theta now over here What I'm doing is adding 2a to q*. I am writing this, you can understand why I am doing this. I am going to do it, did you understand, because in q* 2a will become we have dipole movement and Happy children, very much used There's going to be a board above it. This formula is sure to come numerically We have derived the Dupole and Pe Torque ka jo hai q sorry pe sin theta ware p is dipole moment e is electric field in which is placed and sin theta in theta is the angle between the dipole moment and Electric field now is torque a vector There is quantity, is there any quantity at all? and e are both vectors. Now let's give the vector. with vector if we have sin theta Yes, we had read in 11th class that this We can say cross product. product so am I another one of torque The formula can also be written in vector form. Am. Yes. So we have a formula for torque What came near? PE sin theta magnitude In. And if we talk in vector form then p vector cross e vector we have torque Will come. Now there are three of us at Tork's place. Let us read the special cases. Come. the first when Theta will be 0°. If theta is 0° Will the torque also become zero? Yes. of θ0 Meaning, this doll is lying like this. Now If this dipole is lying like this then this one The charge will be drawn here. This charge will be drawn here. No torque applied Will not done. We also understand it with common sense. You will understand the formula. accept accept accept Look, we have an electric field here. Now We have Dupole right here. this plus charge Is. This is a minus. So the plus one here Will be drawn. The one with minus has both of them here What will be the line of action? Beans. This It will be drawn here. No one here has this There will be no force and no torque. And The formula also says that if we have If theta becomes zero then the value of sin theta What happens? Zero on zero. So that means What torque do we have? Will you go? Zero will come. torque is what it is What will come to us? Zero. Similarly, if theta we have becomes 90° so you know that sin 90 has one value, so what We have torque that is equal to pe will go which is maximum this maximum You will get torque from this, right brother? You cannot apply too much torque, that is If the electric field is going this way and that If the dipole is positioned like this then the maximum torque will apply maximum torque and Again if theta becomes 180°, that is Our Dupola is lying like this. That means go here What is happening? Electric field. But The dipole has a negative charge on it. Went. Here comes the plus. It is obvious that Torque will still not be applied. First this It was being pulled here. pull it here Had been. What has happened now? Now like this It is being pulled here. pull it here Used to be. So we still have the net torque. It will be zero only. Because the line of action is still It is beans. So what will be the difference? what is the difference will be? Let me tell you. But even in this case We will have zero torque. because sin 180 is also zero. But here The most frequently asked question is It is asked that the one who is a dipole Is it in equilibrium or not? And What type of equilibrium is it? Is it a stable equilibrium or an unstable one? Is it Equilibrium? This question is asked a lot Is. Come listen now. Listen very carefully. If the torque we have is zero and the force we I have already proved the zero behind. So we all I have read in 11th class that if the force is also zero and if the torque is also zero then the What is an object called? is said to be in equilibrium. What is the object called? In Equilibrium. So it is certain that This is what it is, it is in equilibrium. Isn't it Brother? This is equilibrium and this which is the no equilibrium region because here The torque is not zero and this too in Is? is in equilibrium. But the question is It arises that equilibrium is of two types There is stable equilibrium and Unstable. There is also another neutral butt. What we're talking about right now There are two types of equilibrium. Stable and unstable. If I Displaced from its place I do it and he comes back to where he came from I had displaced him. so such We call equilibrium stable. Equilibrium. But if I tell someone I disturb him and he goes back to his place. could not be formed by equilibrium from where He had started. calls him Unstable. Understand that in this case, The Dappol is lying there. Right now I'll give you a I will also show the experiment. But if this One is lying in this case, Dappol and If I display it like this, It is pulled back by the electric field Will take. She will pull this also and it will come back like this Will go. Then I disturb then like this Come, it will come like this after shaking a little. Then I will disturb you and then you will come like this. So this Which equilibrium occurred? It became stable. Because I am disturbing it So what is it making back in its same place? Is? Equilibrium. But if I make this Should I just force it like this? So This one in the electric field puts it there This time he is trying to pull it and this one Here means at 180. So if I give it a little If I display too many like this then this The guy will pull it here and do it like this. So It is in equilibrium now, but very Is in a sensitive position. a little too much If I give you an angle, it will happen like this instantly. So What kind of equilibrium is this? Unstable. Because if you disturb it, it will come there Equilibrium will not be able to form a double where But he had made it earlier. Now in this video Let us understand this with the help of eggs. Stable Equilibrium Unstable What is Equilibrium? Egg two positions It will happen in. A normal one must have been kept. One we Must have been kept on salt. Keeping it normal If I disturb you, he will come there. Salt back Equilibrium will be achieved if kept on. But if disturbed, it goes back there. Equilibrium will have to be created. So come to him Understand stable and unstable equilibrium Are. Then here we have an obvious thing. What equilibrium do we have here? Is? Stable. We have already understood this. Because if disturbed, come back here Will go. And the equilibrium that will be created here He is unstable. There are a lot of MCQs On top of this. But this one once before Take a quick look at the experiment. This is an egg Is. If I place the egg like this and If I let it go, it will fall. This egg Let's take this cute one. a little here Should I put a stall? Place the egg on top of it If I do, is this equilibrium? Or But this equilibrium and this one What is the difference between equilibrium? you a little Understood. If I were to pick it up and leave it Am. I am picking it up and leaving it. pick up and leave I have been. So this is back to the same equilibrium. It is building where it built before. But what if I did this? Disturb Did it return to equilibrium there? Will you be able to? If I disturb it Look, it created a new equilibrium, but Not where but if I go to this one I keep the egg like this and disturb it. If yes, it will create the same equilibrium again. Where it was made earlier. Did it Created a new equilibrium? Yes. But there Did not make it. Where it was built earlier. There are two types of equilibrium. One There is unstable equilibrium. What It happens? Unstable equilibrium. I I am using eggs for that at night. Sorry. Sir, I am doing it for science. Yes. So I hope you understood through this video. that stable equilibrium and unstable What is equilibrium? one above it MCQs will definitely come. Let's talk About whom? electric field lines About this. electric field so we Understand. Now let's talk about electric field What are lines? what electric Do we see the field? The answer is electric We cannot see the field, but it is there. So it is. So we have some imaginary lines. are built around a charge that allows us to Representing that electric What does the field look like? Aldo, don't you see that? But we will read some of its properties. There are some properties that are assumed And there are some properties that we Written after observation. Okay, right? Let us go Come. So what are electric field lines? First of all, these electric field lines There are electric lines that you define Can you do that if I charge a little If I leave it, then that charge is positive. So he can move freely along that entire line. Pay. An electric field line is a There is an imaginary line in which if a small If I leave the positive charge then the same Will go in direction. Another definition of this Also there. An electric field line is a There is an imaginary line on which if you Direction of electric field at a point If you want, you can make a tangent. You You can make a tangent. You can make a tangent yes. Like we discussed magnetic field in 10th. I read the line. Such electric field lines also comes to us. So Electric You can give different definitions of field line. yes. What is the first definition? one such Imaginary line on which a positive charge is placed If you leave it, in the same direction, in the same line I will run. Or you can also say that such a imaginary line whose point is anywhere If you want an electric field Draw a tangent to the direction of electric current. Get the field. We will call that line electric. It is called a field line. Now the electric field Lines have certain properties. First this are always continuous smooth curves. Among these There are no breaks or sudden turns anywhere. Now How will the sudden turn happen brother? If there is a sudden turn then two tangents will be formed at this point Will go. Isn't it? Sudden turn means where A tangent there, a tangent here Here. Now the electric field at a single point There cannot be two directions. so There will be no sudden break or turn. these seconds Wally assumed that the electric field The lines will always originate from positive charges and It will end up going negative. positive will come out on charged and on negative charge They will go and end. which is why ever Cannot form a closed loop. How? These It starts from positive and goes to negative. of ends. So this is a closed loop. Will not make it. If you studied in 10th class You may recall that magnetic field lines They form a close loop because they are outside Runs from North to South and Inside South North Ake Close Loop. But it's not like that here It happens. Start with the positive and end with the negative They end. We studied the third property. It is said that if you make a tangent, you will get direction. Will go. Fourth is two electric fields Lines cannot intersect. Again 10th This is the concept of class. if you did it Two tangents will be formed at this point and one Two different vectors at the same point There may not be directions. Electric Field lines are always directed towards charged particles. Perpendicular means they will come out normal. If We have a charge here, so with this Electric field is always perpendicular It will come out. Don't come out at a certain angle like this Can. How will she always come out brother? It will turn out to be perpendicular. keep this in mind Is. After this, the electric field The closer the lines are to each other The stronger you get, the further you go. It will be week. As you have seen, we A uniform electric field is created here. So I tried to maintain distance everywhere. Be equal. But if there is electric somewhere Field lines look like electric fields somewhere Suppose the field line is going like this. go like this Has been. Obviously it does not intersect Must be. So here you can say that Electric field week because here is far away and the electric field here It is strong because there is electric power here. The field lines are nearby. Ok? and Seventh And a very important point says that Electric field lines are always a sorry Electric field lines are never parallel to a conductor. No travel inside the hollow conductor Can do it. Isn't it? We will make this a special They also give a name and that is Electrostatic Shielding. One of its There is also a special name and what is that name brother? Electrostatic Shielding. Electrostatic shielding means that electric field lines are never Hollow cannot go inside the conductor. If If this is a holoconductor, then the electric field If the line is coming from here then its surface It will pass through. Like you did at Seventh I have read it. If you remember that if you were a You are in an empty car, in an empty car means You are in the car. And if you get struck by lightning If you are there then stay inside the car. Because for you the car is a hollow conductor. So if lightning strikes, it will be from here. Will go back to earth. ionization and so on There are a lot of problems. But now the basic thing is this that electric field lines are never hollow Cannot travel inside the conductor Are. Electric field lines are always hollow. What is inside the conductor cannot go Are. You will always have to keep this in mind. What is it also called? also called electrostatic shielding Is. Now if I take this from a very small to a very Let me explain from the basics to the concepts. i you Come on, let's do this. looking straight Let's watch this video. then further Will increase. Let's watch this video See. Now look at one thing here. what did I Did? One, I hung up on Reema Ma'am. It has happened. Now you can see the signals here. You can see the signals coming in. What is the range of Wi-Fi or anything else right now? are in. There is one stick less here. If I I have also put aluminum on the bottom. Foil is kept. Isn't it? If you are here See how many poles are coming in right now. Of? Three. And the Wi-Fi signal is almost Are complete. Okay, right? Now if I were here what do I do with it Yes, I would have placed a pot on top for a second. Am. So now it has become a holo conductor. And I also put metal underneath. so one Type of complete hollow conductor The phone went inside. Now you know all this That the phone is electromagnetic travels on waves in which the electric field It also happens. So if I just take this from here If I remove it, the phone signals inside it If yes, they might have reduced. I am here I could have shown you the phone, but I will have to bring a third phone. Now! I am currently unavailable at the moment near me. So that's why I'm here to tell you I am showing you the signals it will have. If I open it up and show it to you, Look at how the signals will be represented. If I show you here, look, a The signal is still there, isn't it? Look, these lids have become two as soon as you remove them. As soon as I removed it, it became three, so now here for the time being Signal three is back but if I lid I you may have seen I There is no cut on camera either. The video is playing continuously, I I won't even edit, I'll just post it straight away so that If you can understand then after putting the lid on it Inside, actually, electrostatic Shielding all two phone signals Builds up quite well There must be a lot of signals going through here? Address. Come on brother, let's move ahead. Now the matter What are you talking about brother? That Electric field lines are different What shape are conductors made of? Regarding the properties we just studied We are looking at the electric field lines. We will draw whatever shape it is. First of all Positive charge is coming towards us. Ok Yes? If we talk about positive charge then If we have a positive charge, then Obviously, positive charge Electric field line perpendicular She will go out and look for the negative. Now since there is no negative here, Obviously, this is an electric field How far will the lines go? to infinity Will go. Isn't it? If I talk like this of a negative charge then the negative charge Where do electric field lines come from? Brother? It comes from the positive. And where did you come Do these end? Negative pay. Now here It is not positive. so that means Will come from Infinite. will come from somewhere and What will happen if it comes negative? Finish Will go. Isn't it brother? Very simple. right there If we talk about a dipole, that is, like Charges that are equal and opposite are Sitting across from each other. So if this plus charge We have it and this is a minus charge. So Considering the properties Electric field lines originate from the positive Is. It ends up going negative. and from the positive If you turn out to be perpendicular, then negative Only perpendicular ones will come. perpendicular Whatever comes out, it will come back perpendicular. are understanding yes? And what will not happen between you? These There will be no intersect either. And this one It will come out positive and it is obvious By roaming on the negative and walking a long distance, It will come. And here this one which is positive It will turn from infinity to negative. It will come back to me. So a bar in 10th class Like creating a magnetic field for magnets An electric field would be formed here. But if I talk here about one should I talk about it? About Like Charges In. So what are the like charges like? Do you produce an electric field, brother? So Like charges now this is positive and this It is positive. Now the thing to hear is that positive to and positive to electric Field lines emerge. Now from here if It will come out, if it comes out from here then this What will happen between you? Intersect then So going forward, this kind of turn Will go. Go ahead and see this as a kind of mood. Will go. Isn't it? But what are these between Won't it be? Cannot intersect. One In a way, you can say that this repel We were getting along with each other, so we came here and She moved away from the other. But this electric The field lines will look something like this. Fifth Let me talk about a sheet. So we'll also prove this derivation now. From. Electric field for a sheet The lines always come out uniform. As yet You can look at anyone's electric field. There is no uniform. If it is somewhere nearby It is somewhere far away. Somewhere it is near and somewhere else Pay is far away. So he is weak somewhere. He is powerful somewhere. But for one sheet Electric field lines mathematically also We will prove that there is a uniform. Now If there is a uniform, how will it come out? Strait The line will come out. How will the uniform be Will it come out? A straight line will emerge. Understand? Is it done? So in this way we apply the concept That brother is always perpendicular to the charge It starts with the positive, The negative ends. something like this We draw the electric field lines. Can do. Is it done? Now let's go here A small topic comes, which is area Vector. Now look at the problem, the problem I won't say it but what's the big deal? Till now we have in so many classes We learned that area is a scalar for us. It used to happen. Or have we ever done an area There was no talk of direction. But from now on For us, the area will be a vector. Correct Isn't it? From now on, area is a vector for us. It will happen because we have to study further. Gauss's theorem and the area in Gauss's theorem We have to consider only vectors. Otherwise studies are not possible. I Let me explain. See if the area after today If it is a vector for us, then one of its directions Will happen. Listen carefully. For Closed Bodies for Closed bodies Area Vector is always Perpendicularly outward, understand what's happening Is? If there is a closed body such as this It is a cube. You must have seen the cube. cube saw will be. Cube near cube a closed body Is. Now you know the area of ​​the cube. is cube Six heads are made up of six squares. It is made up of six surfaces. One by type So every square of every area The area vector will be perpendicularly out will be. That is, this square above For this the area vector is perpendicularly above will be. This one below is the area for this The vector will be perpendicularly down. This which The area vector for this is It will be perpendicularly here. In total, such There will be six area vectors here. Understanding had been? In total there are six areas here. will become vectors. But we understand this It comes because if I say here then I will get six area vectors Because there are six surfaces here. It is obvious that for the sake of God I Wherever I take the area vector, it will always be If it is perpendicularly above then there is only one. But at the same time, if I have a curved There is a body. Which of the following is a spherical body? Spherical body. So what did the area vector say? Went? Perpendicularly outward. So from here For a small area, let's say ds The area vector will be here. from here which The small area will be ds its area vector It will happen here. Little Joe ds from here Its area vector will be here. So How many area vectors do I get here? Will you go? The answer is infinite area vectors Will get it. Because here it is curved There is a body. Now if this is a curved body then I got a total of Infinite area vectors here Will meet. But here I have to understand the whole You will only get one. Because these flats and Perpendicularly outward in the same direction It is available. So the area vector is always Where does perpendicularly occur? would have been outward Is. But if there is no body closed. There is one sheet from the lettuce. Suppose a sheet Is. This is the sheet. Now there is no close in this sheet. So it is not there. So let me take the area vector here. Or should I take it here? So in that case, I'm concerned where do I need to put the area vector? Is? where it is with the electric field Making a smaller angle. If any body If it is closed then it is obvious that anything can happen. Whether there is an area electric field or not somewhere Also, the area vector is always perpendicular It will be outward. Now you and I will do something further Derivations are going to be done. We will understand them Too. But if I say like this, area Where is the vector for an open body? In this So nothing happens outward. In this the area The vector can be this or this. that case I will get electric field given to me. If If I have an electric field given then These electric fields There is a field. with the electric field The area vector that makes the smallest angle is Will go. Now like its area vector here also It could have happened and here too it is obvious That this area vector is small This one will create an angle. If I area If we took the vector here, it would create a bigger angle. So which angle should I take? Smaller Angle Have to take it. Have to take a smaller angle. So that case Then here we have the area vector Will go. So this is the area vector we have. Will go. So Aria, by the way, from childhood till now We didn't have Vector yet. But Why will that be a vector from now on? Because We need him. So I told you that there are some things that we Creates a vector by itself. Areas among them We have one. Ok? Come on. Now we Let's talk about electric flux. First So what does flux mean? These All we are doing is preparing for the Gauss theorem To read. What does flux mean? Is? Flux means to tear apart by type. So electric flux means What happened? that from a particular area How much do the electric field lines cut through it? threading it through It is happening. This is called Electric flux. From Let Us to Us This is an area. Okay, right? This is an area Is. The obvious thing is the area vector It will be here. If the electric field i I am making it. Okay, right? Now its area electric I have area vector here so taken because the electric field is also here Was going. This electric field was going E So what is electric flux? electric flux is Number of Electric Field Passing the Lines through an Area. Keep in mind perpendicularly. What if we don't go perpendicularly now? I am telling you I will do it, but for now this The electric field goes perpendicular to it Has been. Electric flux is known as phi. Shown below by e. We have the fifth In chapter A In the fifth chapter In the sixth chapter Magnetic flux will also come in EMI. So we will show it as b below the phi. So So you have to make it a habit from now on that you Put it in because there is electric power here. This is the flux. So from here we have what is the formula for electric flux will form? How many electric field lines does it have? crossing over Are you from a particular area? So Electric The formula for flux will come to us S in E *. Now this is the formula when electric field line area You are crossing perpendicularly. Now if he Not crossing perpendicularly. from lats electric field line area vector Not crossing perpendicularly. So Our area vector will be right here. Let's from s because it is perpendicularly outward It happens. And let the electric field be such that Is going. Now this time these two are together Not in the same direction. Meaning electric field line area It is not crossing perpendicularly. this case In which we will have electric flux What will be its formula? Listen. Our The definition says that the electric field There are lines and how they should be crossed. Perpendicularly. Now this electric field This is E, it will break into two pieces here. E That it will break into two pieces here. one this will become the component. This one The component will be done. So this one is for theta Which one is the companion? cos so be it will go to e cos theta and this component will become e sin theta. which one do we get Need components? This is an obvious thing We want the one with cos theta. So Electric Which component should I take instead of the field Will I take it? one with cos theta. Because I have that electric field lines are needed which Crossing the area perpendicularly. There is s along with it. Now if I do this To simplify a bit further, is this es cos theta will come up? Yes. Now listen carefully. Have I considered flux as a vector from today? Am? From today onwards I have considered area as a vector. Am. Electric field vector it occurs. I have already marked the area as a vector from today. I agree. and with two vectors when cos So I'll call it e vector. Vector. So I have the final formula. What will happen to the flux? e vector. Vector or e cos theta. If it is not perpendicular It is there. If it is perpendicular then it is straight. You can apply the formula for this in e * s. Now you all will have enough common sense to A little Joe Flux will be a little Joe Flux It will be an electric field. The dot is a small area, right? okay okay okay okay okay so this is our Now we have the SI unit of flux. Talk about very basic very basic SI Do we have units for the electric field? The unit is Newton per coulomb and area is in meter. square to newton meter square to coulomb We will have si unit electric This will be a scalar quantity of flux or Vector is the answer because this dot If it has come from the product then it is obvious This is a scalar quantity. any thing that What is the dot product that comes from? It is scalar. I have studied in 10th and 11th. So This means what quantity is this one Will you come to us? be a scalar quantity Will go. It's done. ok sir. ok sir. Correct Yes sir. Now you might be thinking that if I If you want to remove the flux, I have a method. that I can convert the electric field from area Let me multiply it. But actually, another one There is a method too. There is also an easier version called Flux. To derive which will come from Gauss's theorem. Now! What we feel is that the area into I will do electric field or e I will get flux which is correct The thing is. But to remove the flux There is also a simpler version called Gauss Theorem. As far as I know English Something probably ends with an S, so it has Apostrophe S doesn't come, right? Rest of the address No friend, maybe this is what happens to me. Little We are wrong. Isn't it? Let us go. But the point is that Gauss's theorem is a simple way to describe the flux To take out. What does Gauss's theorem say? If If you read Gauss's theorem just once, it saying that if there is a closed body and That closed body had something certain inside it. If the charge is stored then the flux It will be q / 0 i.e. how much charge it has Enclosed 1 / 0 times charge will become equal to. In simple words, If I had to give a total to any body If electric flux is to be removed, then one I already have this formula for e. If I do the integration, I get the flux But we also found another formula. and that is how much charge he has enclosed Already done. He enclosed his own with lettuce. Meaning it is kept within you. From the lates he q charge is held inside it. So total Using the flux formula we have q/0 Will go. It is obvious that we can prove it too. Are going to do it. But now you understand it right First, if I am in a closed body If we want to find out the electric flux for a formula so I have e vector vector is itself or small flux e vector dds. The total will be obtained by integration. but if I need an easier version. Me Just know that that body has within itself How much charge is enclosed? So The flux formula will also become q/0. Come Let us prove that this formula is Came from. So let us take we have a There is spherical charge. Well, I'm telling you one thing Am. I will explain any further derivations I have written it in advance so that our time Be safe because then this one shot will make you like this It will seem as if a detailed lecture has been made. So that's why I'm writing that derivation for you. I have brought it. So now more time for this chapter It is not going to happen. So here we have it There is a sphere whose radius is r. good a I will tell you something else because this is the first one of 12th. There's a shot. So my request would be that you Tell me one thing in the comment section. Derivations me yahan pe likhhi leke and explain it to him so that our One Shot will be a little shorter so you can quickly You will be able to revise it. Or do you want to No, one shot, no problem, let it become bigger. But you do all the derivations by hand. So Please give me some advice about this here to give. And don't write derivations by hand. do it. That would seem very conservative. If someone else reads it He will say, brother, what is the child saying? So Please write it in a way that you have done it, sir. asked, we are answering that derivation Do you want to bring it in writing or do some derivation? Do you understand, the comment section is a little better? It should be so. Come let's respect the teacher It increases. Yes. Now here from Let Us we have What have you done? a certain charge which is It is stored. Ok? A Certain The charge is stored. Let's say q Charge. Now I have to show that Joe Flux is that will equal q / 0. Let's do a show Are. Let us prove this. proof of this We do. Come on. Come on. the first of all If I want to find the total flux, What will be the total flux? electric flux e There will be integration of dot ds. Now because I'm a closed body integrationist. Am. So in the integration of the closed body A small ball comes. all the rules The regulations remain the same. Just change the symbol Is. because I'm going to take the ds here I'm going to take a little piece of it here. Pay. These ds I just told you this is a curved body So its infinite area will be vector. But let us suppose this is ds. Now all these I will integrate ds. If this is a sphere Will come for a closed body. Okay, right? Now tell me if I have enough flux The formula is E.DS. If I take this further If I solve it, I will get E ds cos Now let's take cos. Look what I have Area vector right here? Yes. And because this is a spherical charge, then for The electric field will also be here. and such Look anywhere. You can see it here. This is my will have the area vector. And right here in my There may also be an electric field coming out nearby. So if you look from anywhere, the area between the vector and the electric field The angle you will get is 0°. Now what would cos 0 be? Is it brother? cos 0 we get one. So this one survived. Now from here I have If the total electric flux is I go to a charging point to charge I want to take electric field. first thing is electric field will come out and that's it will go kq / r². We will prove this formula. Have already covered this in this chapter. of this chapter Perhaps it was the first derivation. These escape inside will go to me ds of closed surface. Now If I ds ds ds ds ds ds of this whole If I multiply it, will I integrate it? If I do it, do I have anything here? 4πr² will come. Why? Because this is a is a sphere and all the ds of the sphere are added I will do it. Total Curved Surface Area Mill Will go. which is 4πr² r² cancels out to r² Will go. You must have felt what was going to happen Going to do. And here we will have k if If I unfold it, it becomes 1/4π 0 was q was r² to r² cancel out was 4π I was saved, congratulations, 4π cancels out 4π. The formula for Gaya flux has come to us is q / 0 so from here we have Gauss He also proved the theorem that the flux q / 0 remains. It's done. Now because Gauss Theorem is only applicable for closed Surfaces. If in these cases we have any surface Does not come closed. If this were the case that we do not have any surface closed If it happens then in that case we have an imaginary You will have to take the surface to close it. See it as a reference. Suppose I have This is a wire. This is a wire. Now I don't The electric field at this particular point P Had to take it out. Suppose I am at this point P What was to be taken out? Electric field. So this The point was open. So I got around it Took the cylinder and closed it. Imaginary Took the cylinder and closed it. like this sheet Was. I am late to this point on this sheet The electric field had to be removed. So I Here also take a cylinder and close it. Gave. It was a sphere. This was close. But I need to know the electric field outside it. Had to take it out outside. So I there Took a sphere and closed it. So It happens. This is a hypothetical close surface which basically helps us So that we can apply the Gauss theorem there. Now this Obviously you will take a Guassian surface like this So that your calculations also do not increase. Yours The work will also become easier. That you slowly with You will understand the experience. Someone like this at one time Cannot learn. Now suppose I have There is a sheet and I am sitting around that sheet in a circle. What a foolish thing it would be if I took the sphere Will happen. How? The sheet is electric The field will be created like this. She will make it like this. This way Will make. She will make it like this. So every time its angle Look at what is there, it will become different. So how do I Will I solve it? I won't be able to do it. So So I need to get a surface that I can solve it also. Now comes Coolums Law from Gauss's Law. We have a small derivation is Coulomb's law from Gauss's law. After that we Three more derivations that I wrote down Yes, to save time. Chapter over. Let us go Come on. Coulomb's Law from Gauss's Law. How do? We have to prove Coulomb's law. Till now we were studying Coulomb's Law. But Now we want to prove it. So we What did you do? Here, let's take a sphere of radius r. On which there is some +q charge. Let's say these q There is charge. Now suppose I am at this point p Gauss theorem has to be applied. So here I am, a I'll take a Gaussian surface because it's outside. And if it is outside then it will not close. So I created an imaginary What have you taken? Gaussian Surface taken Is. whose radius I have taken capital r has been taken. Now I need to prove Coulomb's law. It has to be done by Gauss's law. How to do it? See According to Gauss's law. This time, Gauss's Law I can use it. Isn't it? So Gauss The law says that the total flux i.e. e dot ds is this is going to be equal to q / 0. Do you believe it? Well, I just proved it back then. That for a sphere, eds cos will be 0. Same reason cos will become zero here. Too. Because where the electric field will emerge Its area vector will also be the same everywhere. Now if I take the electric field from here If I bring it out, what will remain inside is ds ds ds ds this Whose ds is it? of the Gaussian surface. So this ds of a Gaussian surface if I integrate So this is a sphere and the sphere What does integration entail? 4π larger r Square of. Because always Joe ds Integration is that of a Gaussian surface It happens. Here the remainder will be q/0. Now because I'm telling Go Newton. Coulomb's Law Have to prove it. So I electric field what test Write the test charge in charge force upon Can I? What about the electric field What is the formula force/test charge? Today I just read it. 4πr² This will be multiplied by q / 0. This Take it to the Divide. Then the force will come We have 1/4π 0q q not / r² Now even a foolish child knows What is this? So brother, this is what we have. Force i.e. Coulomb's Law kq1 q2 / r² so I derived basically Coulomb's Law from Gauss Theorem Proved it. Now I would like to please Because we have a lot of derivations together. Have done. So before we move on quickly Pause the video. Please request Only then move forward otherwise it will not be beneficial. please pause Take it and go back once to whatever you have read. You can read it if you want. Ok? Is it done? Move ahead. I hope you have revised this then move ahead. You are here. Now let's have three people here. We are going to do the derivation for. one of our Will come near for a long wire. then a will come to us for the sheet and then one will come For the sphere we have. all three Derivation is very important. To all Let's talk about a long wire first. Which is going to be an infinite wire. I Why don't I take pink color here so that you Can you see it? So first of all, this is an infinite There is a wire on which we have charged plus I have taken it. Now that it's Infinite Wire So the charge on this will also be infinite. So So what did we do? We have here Lambda is the charge per unit length i.e. Linear charge density assumed. a wire Is. I have to focus on one particular point of it. Electric field has to be calculated at a distance. So first of all I said that point is not closed. Was. So what did I do to close it? Took it? Gaussian surface cylinder. Why did you take Cyldrical? You will understand now. and assuming lambda to be the linear charge Density i.e. q / l Now I will apply Gauss's theory Then the electric field e dotds q / 0 is Will go. Now this ds is the entire cylinder Is. So can I cut the cylinder into three pieces? Can I share? A circle, a circle and A curved surface area. Circle, circle and Curved surface area. So look what I Did? Divided it into three. ds1, ds2, ds3. s1 Who did I believe? Above To the circle containing. s2 assumes the lower ones Let s be the circle and s3 be the curved surface To the area. Now what about the circle above? And the electric field coming out from here The angle between them will be 90. Yes. So Here it is 90. Same as below The area vector for If the electric field is here then what is the angle Will be done? 90 means for both of us The angle that came closer became 90:90. cos 90 became zero zero. But the one who curved The surface area is like this and The electric field must also be coming out like this. So wherever the area of ​​the curved surface area The electric field will go there. So The angle formed here will become zero. Will go. Now next is Maths. These have gone away. cos0 became one. e came out. Now this which ds it's just curved because the cylinder The circle has reached zero. So just the curve And what happens to just the curve? 2πrh and the length of the cylinder we have taken What has she taken? I have taken it. So 2πrl is Will go. Remove the electric field from here. Will you take it? How will you take it out? can i replace q Should I write l in lambda*? Yes. instead of q Let me write l in lambda *. So from here Electric field oscillation lambda / 2π r 0 and what is lambda here? Linear Charge density. That is, how much is the charge? Unit length? How much charge is sitting on it Unit length? This is called linear Charge density. What should I say? Linear Charge density. Understand? Now what about this flower? From What if you notice? which is our The electric field is inversely Proportional to R is I. What is R? Distance from the Wire. as far as the wire The electric field will decrease because r with this inversely proportional and It should also happen. The further away you go from a wire Yes, the electric field should be that low. then the electric field is inversely proportional to r Went. So if I draw a graph here Here I will make How much distance am I going away from the wire? Am. And if I create an electric field here, Are electric field and r related to each other? Will inversely proportional come? So the answer Yes, absolutely. It's done. That's for sure. Now let us do the same thing with the sheet. For. For the sheet, you can understand if this sheet is again infinite sheet and I need this Working on point, I had to close. This time I took the cylinder again. We You could have taken cubes also but it is fine with cylinders. The work will also be done. Again because first wire If it was, I took unit length on charge. If there is a sheet this time, then there will be a charge on it. Unit area. Its symbol has been made Sigma. And we call this the surface charge density. Or it can also be called aerial charge density. Again Gauss's theorem says e ≡ q / 0 will be. And this time again I will cut it into three pieces. Give. There will be a circle, there will be a circle and One would be curved surface area. ok sir. But what's the difference? What sheet for Electric field here? and the cylinder The area vector for is here. So this time for the circle and for the cylinder circle The area for the circle will be in the same direction In. That means the angle will become zero. last time The angle of the cylinder with the circle was 90. This time the circles of the cylinder will be The angle will become zero. and because of the curved The electric field is going like this. And Area vector of the curve such such such such It will remain like this. So what will always happen to them? It will become perpendicular. What will happen? Perpendicular. So if I cut it into three pieces I do it again first, second, third then this turn which is our a circle and the circle Zero for that. But this time it's curved The angle will become 90. Now because this Both are circles. Both of these are beans. So I will write eds in 2 *. Because this and this The circle is the same. are at the same distance. So Everything will be the same for them. so into Keeping both equal, considered it as twice. Now Twice agreed. e came out. ds this time Last time ds was curved surface area because Curved was left. This time the ds is of the cylinder Circle. So what is the circumference of a cylinder? Just πr². The rest is maths. I charged The space σ * has πr² because area πr². πr² to πr² cancels out. electric field a σ/2 0. Now here's Sigma and Both epsilons are constants. So What will the electric field do? Constant. I told you we have proof too. and electric field at a distance Veriri is not doing it. anywhere you are You can see that the distance is not coming. i.e The distance you go for the sheet The electric field will remain constant. In practical life there is loss but Theoretically, whatever is there will remain constant. Understood? And the last derivation comes Electric Field for a Sphere. to be seen So, on the sphere, we do half the work using Coulomb's law. I had already done it at the time of proof. me three There is work to be done. Outside, on and inside. Understanding Went? Let's talk about the outside first. Pay. What will happen outside? first thing again to sigma, what is the charge on Unit area is that. Now here I am Can't break it into pieces. Because I guessed What surface have you taken? Cylinder. Oho Gaussian What surface have you taken? Sphere. what so far Was he taking it? Cylinder. So I'm cutting it into three pieces Was. But what am I taking now? Sphere. So This time it will not be broken into pieces. So what come Will you go? e.dsq/0. Same thing again. Its area vector is here and If the electric field is also there then what is the angle Will he come? 0° so eds cos 0 here Will go. I'll take e out. ds ds ds so The area of ​​a Gaussian surface which is 4π r² But the area in the charge will be q/a Whose will I take? The charge on which is 4π Small r² is Gaussian surface 4π large r² but The area on which the charge is made will be taken into account. How much is that here? 4π smaller r² than 4π It will be cancelled. come here to me will be the square root of σ/0 r/r, i.e. that will be inversely proportional to r. But if I talk about On the Sphere on The sphere means I have come to the sphere. So Is there a small r and a large r in On the Sphere? It will become equal. Yes. So r cancels out to r. Will go. σ/0 will approach. And if we talk Where? Inside. So you know everything inside. that the electric field is hollow Zero is for conductors. So this You know this sphere is hollow and electric field for hollow conductors The field is zero. Understand? So zero inside It will happen. Now if I make a graph of this I want to see which is a very important graph. I want to create distance here and here electric field so what unless I It does not come from the center to on, meaning until I don't come within its radius on the sphere Doesn't our electric vehicle arrive by then? The field will remain zero. Yes. i.e. from the center to r Its electric field will be zero. As The electric field will reach R immediately will increase to σ / 0. because on the How much is the sphere? σ / 0 and further is inversely related to R, so as If I increase, the electric field will decrease. i.e Zero on coming from center to on. after this As soon as it turns on, it suddenly increases to σ/0 and If I go out it will be less. So this one The part is representing the outside. where the electric field is inversely proportional to r Is. This point represents represent on and this part It is going inside. Very cute graph. This graph is asked many times in exams. Is. Now my request to you is that you All the derivations should be considered once, especially these three We have done it on board. Repeat these once Please do it. If you watch it, repeat it, it will be more You will understand better. So I hope you have one Have you completed the shot or you can click here I have skipped and come. Let's go to them now On question answers. again in this chapter The most common questions asked in the exam Those with torque and flux somewhere Are made from topics. You completed the chapter Must have taken it. You must remember every formula. Needed If you don't remember the formula yet, You should not answer these questions right now. First of all, memorize all the formulas and See which formula applies where. Is. After that, enjoy answering questions. More will come. Let's get started. So the most Let's start here with the first question. Come. oh what a question Brother? Ah Given a Uniform Electric Field. You have an electric field Given is in vector form which is 2 * 10's ^ 3 i cap is given. That means this The electric field is in the x direction is in. Ok? Find the flux of this Field through a square off side. One The square whose side you are given is 20 cm Because we need it in meters. will be. So it becomes 0.2 meters. Isn't it? Hus The plane is parallel to the yz plane. This to you now You have to look at the angle here. Now you all know So what do we have for the flux formula? Is? ES cos theta. So the electric field We have it. s means area we people We will take it out here. area because a If it is a square sheet then our area will be Square of the near side. So if I If I square it here, It comes to 0.04. which means 4 * in 10 Power -2 meters squared comes. So this So we got the area. what is left now Brother? Now how to find the remaining angle? Now everyone knows Let's say this is if we have the x axis. If we have this y axis and this is our If we have the z axis then our The electric field is going into the cap. Is. If the electric field i goes into the cap If she is there then she is going here. If this x Axis. This is the y axis and this is the z axis. With your respect, the electric field will go away. She has been here. And our square sheet Where is it lying? The square sheet is lying in the yz plane. That is, this square sheet of ours in the yz plane It is lying there. Now it lies in the yz plane So its area vector will be here. Its The area vector will be here. friend if this yz is a plane, then its area vector is here and The electric field is also here, so between the two Angle Area Vector and Electric in The angle between the fields is cos theta There is an angle of . So what is that angle? We have? Is 0°. That means that angle is our The pass is 0°. Now if we remove the flux, The formula will be ES cos Theta. How much electric field do we have? Is? 2 * to the power of 10 is 3. Our area Pass 4 * to the power of 10 -2. and cos Here it becomes zero. The value of cos 0 It becomes a forest. So just multiply Are. 4 * 2 becomes 8 and 10 to the power of 1 remains Went. So here it's 80 newton meters squared. Coolam - 1 answer comes. very basic very That's a good question. I am not difficult I will not ask this question. It is obvious that Not all questions will be difficult. Not so Isn't it difficult to complete the entire paper? Comes. We will get three from each chapter. Four to five questions will have to be difficult. Inside One Shot. And then when the extra If you are asking questions then every such You know if you were with me in 11th Used to study. We will discuss two or three chapters of each chapter. Question answers were also done after the chapter. Are. Then we will add more questions to it and This time during exam days when live I can guarantee that we will go like this will bring questions that if there is any in the paper Unseen questions also came which were not there last time. If it happens, you will be prepared for it. Let go Let's move on. very very cute This is a wonderful question. Very exam These types of questions come up. what to say is saying look plot a graph Showing the variation of magnitude of Coulombs Force versus 1/r². The first thing that Coulomb's force is inversely proportional to r² is but directly proportional to so 1 / r² isn't it? If these give us the graph If you had asked me to make it, what would be the confusion here? Here the graph is in the middle of 1/r² Is. If this graph were in the middle of r² then It becomes inversely proportional. But these 1/ r² is the graph in the middle. first of all You have to understand this. Okay, right? don't understand Let me tell you. Here we have The force will come. If this were the graph of r² The graph appears inversely proportional. But this r² does not. This is 1 / r². So 1/ with r² then the force is directly proportional Is. So obviously the graph is straight The line will go straight. But if you read further here I have told you about two different pairs It is in the middle. The first pair is 1 microcoulomb And two microcoulombs and the other is 1 microcoulomb Coolum and -3 now because there's a minus here Even then it won't make any difference because you Magnitude of force has been said. Alldo One Force comes in plus and one in minus Because both these charges are in plus, then K Q1 would have been in Q2 Plus. But here K Q1 Q2 would have been in the negative. But we need magnitude If you have said so, then we don't need to worry. Is. We have been told the magnitude. ok now It is certain that the graph will be straight. line but the slope of one graph is will be higher than the graph. Now whose Which one will have more slope, brother? Slope for the one with the greater force It will be more. Now because the force is q1 is also directly proportional to q2. Which one charges more? So the answer The charge is higher for those with 1 and -3. So this is the force that is Force for one micro Coolam and -3 micro For the Coolum people and this is the force. Force for which one and two microcoolers One Micro Coolam and 2 Micro Coolam for Good for if here too too micro If there was a coolant, then the graphs of both would overlap. would have overlapped or would we have had to calculate the magnitude If I had not said it, if I had just said force then a The graph of falls in negative f, that is, Would have come in our fourth quadrant. But What have we just been told here? Magnitude has been said. So, brother to us It has to be made with respect to magnitude. This is a very lovely question. very good The question is. It's done. That's for sure. Let's move forward Let's grow. Let's move ahead. on the next question Let's come. What is the question brother? saying to Charges of Magnitude. There is a charge We have +4q and one charge of just q Of. R located at point A0 and -3a0 Okay, let's go here to the Cartesian plane. Let's make it. One is sitting at A0 and one is sitting - At 3a0. Okay, right? See if this is our Pass is zero. This is what we have A. These are our Pass is 2a. This is what we have 3a. Isn't it? These We have -a. This is what we have -2a. These We have -3a. Let's accept it like this. Okay, right? Now where is one charge sitting? Pay? On A. This is a charge sitting. it remained. It is sitting q Coolum. or not, it is +4q coulomb. This is a charge of +4q coulombs One is sitting here. Very good. Where are you sitting? a 0 at. and one sitting is -3a0 at. Which one? The one with q. -3a0 Pay. He is sitting here. -3a0 per q. Ok? This one. Ok. Ok. Ok. He is sitting here. Correct Is? What is the electric flux due to? to the charges through a sphere of radius 2a? You have to tell how much flux will be in such a From the sphere whose radius is 2a we have And where is its centre? Origin Pay. intelligence Apply. If its center is at the origin and it If the radius is 2a then it will be something like this. Roughly Talking please. something like this will happen Because its radius is 2a. 2a is the radius. Now you tell me if it has a 2A radius. Firstly, the AC is running very fast. If its 2A If the radius is Brother, he keeps this Q inside him. Will not be able to enclose. To this Q person So he does not even enclose himself within himself. Will get it. Because this charge is sitting at -3a Pay. Its center is at the origin and its radius is 2A. So this charge has been enclosed. But this charge should not be enclosed. Found. Now if this is so then according to Gauss The total flux theorem we have That is charge enclosed by apps 0 OK Charge Enclosed by Apps 0 OK hi bhaiya ok bhaiya now how much is the charge Enclosed this answer is 4q this Enclosed by apps 0 this is with us Our lovely little answer would have come Is. Is it done? If this were the radius Suppose we have 4a of 4a if this radius let us from na let us from na here somewhere 4a would be if it were of radius 4a Both these charges get included in it. And 5Q would have come but right now it is not like that. If it is then it is a different matter. So cute but It's a lovely question. Isn't it brother? Let's move forward Let's grow. Coming to the next question. Oho This is a wonderful question. This is the question that I I am telling you that every In a set I have three to four Take five, sometimes more such questions I will bring you something that will make you think. do. This question is very cute. one this The question is very sweet. This is a very question It's cute. This question is very cute. There are many more such questions which are quite They are lovely. Ok? a few I will also give homework. Come let's discuss Are. a plane surface in the shape of a square of Side 1 cm. is placed in an Electric field. You get an electric field I have given it. How much is it? 100 coulombs per 100 newtons and this is in i cap Is going. Ok? True that his unit The vector normal to its surface is making A given by this angle. That means that whatever you The unit vector is what it forms. Direction to you 0.8 cap + 0.6k cap is given. what about I mean, I will tell you. Find the Electric Flux Through the Surface. Now Surface Square And I have also given you its side. Side How much have you given brother? Meaning of question I will explain if you don't understand. Side If there is one, then power of 10 -2 meters are given. Is. So how much area is there? to whom We represent by s. of the side It's square. Square mean of the side 10 to the power of -4 meters squared. Now I have also given you the area. To you Electric field is also provided. So save What? You have to remove the flux. of flux What is the formula, brother? of flux The formula is e s cos theta. of flux The formula is es cos theta. So you If you can get cos theta from here, it would be fun. Go. Now how do we find cos theta? These It is something to understand, brother. cos theta how Will you take it out? The vector that has been given to us is given to us 0.8 cap 0.6k cap. That means if we have If it is a vector then what is this 0? At Ho Went. Because i cap has 0.8 runs and k 0.6 has run in the cap. Ok? 0.6 is running. Irrespective of that. Now accept this X- axis and this is the Z axis. That's why K I took the cap, right? Ok? Now Imagine let's say we're saying that electric The field is going. electric field going There is a direction. electric field It is in i direction. But the unit vector coming out of the area 0.8 I cap and 0.6k in cap. So between them We have to find the angle. So basically We have to calculate this angle. Is. Calculate this angle. Is. Now what to do to calculate this angle i cos theta because i either first theta should I take it out? Look, I will tell you a long and detailed work. I have many children, what a long and wide task do. Here he first tries to find theta. What will you do for it? We'll find tan theta. tan What is theta? in perpendicular upon There is a base. and then from there theta and then cos theta. so long There is no need to do extensive work. We We will directly calculate cos theta from here. How Will you take it out? Look brother, what is cos theta? Is? cos theta is in base upon Hypotenuse. Now you will say sir, the base is there. What is the base? It is 8. But the hypotenuse How much is it? So is the hypotenuse. if these It is 8. This is six. So isn't this a forest? Went. How? Pythagorean number of eight and six A triplet is formed. that gives us what Is? Gives 10. Eight and six gives 10 So 8.61 friend, do the rest like this under route Square of perpendicular and base Square like we do normal so even so What answer will we get one day? Will go. Hey brother, tell me, will you do this much? You can do this much at least. You can do this much at least. Say Sure? How much did this bring to us? 0.8 ye How much did we get? 0.6 then 0.8 and 0.6 What will become the Pythagorean triplet of? Forest Will be done. Or should I do it? Will you make it sure? It came to 0.64 and it came to 0.36. So 0.64 How much is 0.36? It became a forest. and the forest Under Route One is done. So from here we have Hypotenuse one is reached. The forest has arrived. So take it brother Congratulations. The value of cos theta is 8. Is. This is brother conceptual Question. Have to understand. This is it brother Conceptual question. Do you understand? Understanding had been? Ok. Ok. Ok. Come. If Now that you understand, let's take out the flux. What is the formula for flux? Flux we have e s cos Theta. The formula for flux is e cos Theta. e How much do we have? It is 100. s How much did we get? 10 to the power of -4 Is. And cos theta gives us 0.8. Let's solve this. 8 * 10 out of this I will raise it to the power of -5. So 8 * 10 Power-3 will survive. Newton meter² Coulomb - 1 Take care of the calculations etc. a little of that I am weak but this is the answer we have. Will go. What a lovely question it looks like But this is a game changing question. This is a game-changing question. It's done sir. It is a sure thing, Mr. Move ahead. Let's go. Let's come to the next question. We next Coming to the question. NCERT if you made So there was a question in NCERT in which It was said that we have a cube or Actually there is one sheet. top of the center of the sheet A charge has been placed. So tell me from a sheet How much will it make? So we delayed that. Lay down that one cube. Remember? a cube Lie down. and then the flux for the cube came q / 0. So I came for a face q/0 of 16 is exactly like this question But this is a very next level question. NCERT is the exemplar and we have It has also been included in the Winner series, it is fine. What will be the total flux through the face of The cube as given in the figure which side of Length A if charge Q is placed we have charge Q is placed at different places. where and where It is kept, come and see. First we put him It's on the corner of the cube. First of all we It is placed at the corner of the cube. Now if If you want to apply Gauss's theorem, The charge on that particular area It should lie symmetrically. Now if I I am placing this Q charge on the corner. Pay. So this is not closed, right? If I If I keep it on the corner then it will close It did not happen. So if it is not closed then close it. can I imagine doing this I am that its There are seven more cubes lying around. How? These I placed a charge here. Now its I've got another charge around here, imagine it. How? Like this room. the room in which You are sitting in the corner, charged. Is. Charge is sitting in his corner. Now The charge sitting in that corner How many rooms will you be sharing? The answer is Total eight rooms. How? One sharing your room Must have been. a room next to yours Must be sharing it too. one with this room He might also be sharing the room. and one more The diagonal one must also be sharing. Now you You will say there are only four. But these four There are four rooms upstairs too, in whose base this share It is happening. The room you are sitting in If there is a charge in the corner of your room Even below your upper room, he You will find the charge sitting there, right? That is, a charge The one who is sitting in the corner, he How many more cubes are actually being shared? There are a total of eight cubes, that is, seven more If you are sharing a cube, your How much will come in the share, one eighth will come So if I take out the flux where it is is sitting on a which I am calling a So what would that be if it were q/0? The full charge would have sat in the middle but this If he is sitting in the corner then he will get seven more Will be sharing rooms. Total eight rooms Must be sharing. So the part you You will get q / 8, that is, a total of q / 0 You will get 1st. So q / 8 is 0. how small I have to explain this thing so much. Look, now let's come to point B. Look B Where is the point? B point is the mid point of An Edge of the Cube. That means sitting here B point has happened. Look, he is sitting Point. He is sitting. Now on the first corner was sitting. Now it sits at this B point It has happened. That is, if you assume this is a room then He is sitting on this side of the room. sitting here Is. Now four people are sharing this room. They must be. The corner room has a total of eight rooms. Were sharing. But the one sitting on the edge If there are four of them, they must be doing it. How? One So this room, the one next to it, one The one above it and the one diagonal to it. further The four of you wouldn't be sharing, would you? Brother. Because this is in the middle of the side. So this The atom has four rooms, one this, one this, one One below this and one below this. Four share a room Must be doing it. If four people are sharing a room If q/4 is 0 then q/4 will become 0. Very true. Very true. After this c means center of the Face. Okay, you can do it, listen to the wrong thing. Here The charge is sitting. He is sitting here. The charge is sitting here. Now if the charge He is sitting here. That means your room Sitting face-first against any wall Is. He is sitting on the wall. So that means Half of it went into this room and half into that. In the room. Imagine it on any one wall Take. Half will be in one room, half in another. It will be in the room. on any wall Just imagine it. Half will be in one room, Half will be in one room. So the total The flux generated will be the total flux C The total flux generated at the point will be q / Half of 0. Why brother, why half? Because Half the charge is for this room. half charge This room is done. What a lovely question. Done. Excellent. Let's move on. oh my God finally finally finally finally question of The Day If You Got It Done Brother, you have won half the battle because this year Which happened to be the 2025 paper which is the 2025 NEET paper Many such things will happen in 2024 as well. We received questions. So this question We call this actual conceptual based. Why do you say that? Because this question These are our 11th class, our 12th Multiple chapters in class 12th also Connecting each other. Multiple Concepts There are questions. They are very funny. Let's read Are. Read carefully. It could be the first Even if you don't understand it in turn, absolutely Look carefully. I just recently did this It was done in a paid batch. That's why I remember. Those children who are from paid batch will know. I asked this question recently. Two Charges -q each r placed fixed. That means two charges Is. Both are -q's. Take care, Dappol Not there. Both are -q's. R Fixed R Fixed separated by distance 2d their The distance between is 2d. a third charge of q Another charge +q and mass m was placed there. At the mid point. It was placed at the midpoint. And after placing it at the mid point slowly slowly slowly we made our way up Displaced. Ok? Now when you leave If we leave this out, will you understand? I come to know that when you take this charge up If you leave it, it will oscillate like this. If you don't understand then I will tell you. I will tell you, I will do it now, but this oscillation He will start doing it. As soon as it starts oscillating You will have to do this show. to show that This q charge will perform a Simple Harmonic Motion and that simple The time period of harmonic motion will be You have to show that he will come. That is, 8π 0md / q² to the power 1/2 looks a little strange It seems. But nothing to worry about Not there. Look, first of all we We have to prove this with the diagram. Correct Isn't it? Now we have this diagram which There is a diagram inside this, if I say a little Let me do the construction and then its derivation I will do it. see how? Here we have -q There is charge and this is the +q charge we have. So It is a matter of common sense that the force applied on this She must be looking here. Ok? This The force that must be applied on the It must be looking like this. Similarly, on this one also The force that must be applied on this one too Whatever force is being applied there is being applied here. Will happen. Okay, right? The force must be deployed here. Force here. Now its force is here. his The force is here. We will do it with force pieces. We will split the force into two pieces. Ok? How? This is a piece. One Its component has arrived. This is a component He has arrived. Cut it into two pieces like this Will give. This component has arrived. One of its This component has arrived. Now if this is theta So you know this one f sin theta is the component. and also F sin theta is the component. and the components below Which ones? f cos theta. Two such components will be f cos of theta. and both beans Will be in direction. And these ones The components will drag this here. When these are like If it comes, they will pull it here. So this is Bhaiya is about to oscillate. But at the same time Also, we have to understand that sin theta Components cancel each other out and add the component of cos theta Will be. Now we have to find the time period. So what is planning? First I will remove I'll keep the force and the force equal to kx. Because in SHM the force is kx. I'll take out k from there and then the time period I will put it in the formula of which would be is 2π m / k. This is my planning. Got the planning? I will take out the force first. I'm going to put that equal to kx. From there k I will extract and put the time period formula I will do it. This is my plan. Come on brother, this We proceed as per the plan. First of all Let us find out what will be the net force? To all First, take out the net Force. So the net force will be 2F cos Theta. The net force will be 2F cos theta. Force The formula is k q1 q2 which is q² will be upon in r². Now what is r? This is d And this is x. It is said in the question. If this is d. This is x so what happened? x² + d² becomes x² + d². Isn't it? If this d This is x, so the distance between them is that will be x² + d² and that will also be squared. moving along cos theta. First this Let's solve it a little bit. Come on. here I have arrived Square root of 2k in square up cancels x² + d² right? Now from here cos Let's put the value of theta. if these If angle is theta then what is cos theta? Base / Hypotenuse. If this is theta then Base is done for us x base is done for us for x and the hypotenuse is done for us x² + d² x² + d² becomes Ok? So far everything It's going fine. The formula for force has arrived. We have 2k q² x upon our have x² + d² raised to its power 1. Its power Is 1/2. So the power becomes 3/2. Now He shouted at us in the question It has happened. not just shouted Is. So it is said that the x is is much less than d. It is very small. So here than I will ignore x. Us It is said in the question that the x which is d is much smaller than. So from here if I change x If I ignore it, the net force will come. I will have 2k q² x coming up d² to the power of 3/2 now to two here as well It will be cancelled. So the net force will be 2k q² x / dq arrived. This net force comes to me Went. Now I told Net Force that I'm going to set the net force equal to kx. Am. Because brother, net force in SHM The net force in SHM is It is also equal to kx. This makes our Who will get what? Look at x canceling out x. Will go. k I will get 2k this k is different Yes brother. This K is different. let's do this Are. Let's do this. This K is not expanded We also do this so that you don't get confused. Go. Isn't it? Because this K is the force constant It happens. And this one which is K, We have the 1/40 one. So here it comes to And here comes q². I came here x /dq and here we had 1/ 40. Ok? Now you will not be confused. x will be cut off from x. So we have the value of k Will it come? If I cut it with this then it will come to Will go. So q² x to x has canceled out. q² has arrived at upon dq dq 2π 0 I don't know anything yet. I mean I So I have done it. But I have a plan for you told us what to do according to Is. We got the k out first. Now you remember What we have to do is to have a time period of The formula used to be 2π m / k 2π m/k if you remember. Ok? Now Here m is m. But instead of k I What did you put? Look at q² put. And this whole mess went up. Who is it Strong brother? dq 2pi0 isn't it it went up. now here See what will happen together? Now because 2π I have it inside so I'm sorry it's outside. If I take 2π in, then this much You all must know maths that I have mq² So it is there. But if I take 2π in If I go then he 4π² will be formed. And also I have inside first since itself is 2π and with 0 being d. Got it, the work is done? How Done? Look now, look now, see the miracle. How much is 4 * 2? It's 8 now. be π² * π Went. It became π. Also I have m. Also I have apps 0d. in upon I have q². Congratulations. This is the proof What was to be done? 8π 8π m m 0 dq dq / q² / q² under root under root Meaning, Power Half, congratulations brother, on this question A like is made for. For this question A like is created. No one asked this question If it comes in your paper then those who I saw the shot, that brother will say thank you While sitting in the paper. made for this question There is one like. Now let us see that it is not about the question but about the question. It is not a matter of if such a similar If the question came in our exam then we What needs to be done is not necessary, isn't it? Exactly this should come because as far as I am concerned Yes, this is an exemplar question. Now if If this is an exemplar question then it may be It may not come directly. He may come. But Someone change the value. What to know here plus Put a plus there and put a minus there. Distance Change it. Change something but similar A question may arise. So you have a thought I know the process. What to do now? Come on come Coming to the next question. That's a good question. What is the question saying brother? saying to Electric dipoles of dipole moment. Two electric dipole, the former of which It is called dipole moment i.e. P1. Give put 1.2 * to the power of 10 -30 coulomb meter. And P2 is what we've been given. How much? 2.4 * to the power of 10 -30 Again Coolam meter is given. Ok? Good are placed in two different Electric field. both separately is placed in an electric field. This How much is placed in the electric field? 5 * in 10 to the power of 4. 5 out of 10* Newton per coulomb placed in the power of 4 In. Ok? Ok. And it has been kept. Brother, at what price has this been kept? So the answer is 15 * 10 to the power of 4 newtons per coulomb Was kept in. Ok? So this electric There is a field and this is a dipole moment. What Want to remove it? Find the ratio of maximum Torque. First of all, the formula for torque Everyone remembers. The formula for torque is PE sin is theta. But you get maximum torque I have said it. So the maximum torque at sin theta It becomes a forest. And whose maximum torque Does it come out equal? becomes equal to PE. Correct? So the maximum torque first ka upon The ratio of maximum torque to second in Have to take it out. So P1E1 should be removed from above. P2E2 is correct. It's simple. Ok? Now how much is our P1 Near? So the answer is 1.2 * to the power of 10 -30 And how much E1 do we have? 5 out of 10* The power is 4. How much is P2 in Upon? 2.4 * 10 to the power of -30 and this we have 15 * 10 to the power of 4 is . This is cancelled by Went. This got cancelled by this. to this Kata three came. Cut it with this, come. So This brings us to 1:6. Please I I am a little weak in calculations. You Check the calculations, there might be some mistake. But Did you understand the format? Doing P1 E1 and P2 E2 Is. The rest of the calculations were probably done correctly. I have. okay brother? It's done. Got the game? Excellent. Come on, let's move ahead. Now watch this LKG The question is. But LKG questions also Come to the exam. Son, it's not like that Is. They are saying that the figure shows three points. charges +2q -q + ​​3q to charges +2q and -q R enclosed within the surfaces. But one charge is out. You need to know the flux Have to take it out. Will you remember which ones are in flux? charges which are enclosed inside There are. I have brought three-four such questions. everyone Let's do it together. Come on. Ok? But The total flux in this one will be The net charge enclosed by will be 0. Now the net Which are the charge enclosed? The answer is +2q is enclosed inside it and -q It is enclosed inside it. The one with 3q is outside Isn't it brother? The one with 3q is out. So from this If this is cancelled then what has happened? + 1q only Saved. What's left of Apnon?0 So here we have it. The charge arrived. It's simple, friend, there is something No. There is nothing there. Come like this and more Have brought questions. There are more questions on this. They do it. Come on. like a theoretical There was a question that didn't seem to be there. But It is just above this. Like this is also a question. Look, this is an exemplar of NCERT. The Electric Flux Through the Surface. To you I want to tell which of these surfaces is electric Will the flux be the same or different or what will be? Everyone's shape is different, but everyone Look at the charge, it is the same. This also has +q charge It is stored. This also has +q charge It is stored. This also has +q charge It is stored. This one also +q so what all But what happened to the flux became the same? Answer Yes yes. The flux formed on all will be the same. will form. So the answer is same for all the figures. I have asked for electric flux, it will be the same. On all the figures. Ok? Another question too It was probably above it. Yes, this is action There is a region. But besides that, a dipole I also brought a question, friend. Where did he go? Dapol One. Yes, here it is. Look how much this question is. Is good. is saying that there is an arbitrary surface And he enclosed a dipole within himself. Already done. Any such random surface and he has enclosed it within himself Is. Whom? To a dapol. Now any one If I create a surface with my mind here Actually, you can create any surface. Sir I remembered this amoeba here. Yes. So Here if I have a charge of +q and here Pay I have -q charge and we have a The dipole itself was enclosed inside it. So it is a matter of common sense that whenever a If the dipole is enclosed then the flux What will be the formula for a flux? Is? Net Charge Enclosed by Apps is 0 No. Now a dipole whenever you enclosed then one charge will be of +q and one charge will be of -q will be of. One charge will be +q. One The charge will be -q. Then our total will come Pass zero. Isn't it? hey hey what is happening Is it friend? Totally oh well, I have this pen Second. Whatever total charge comes, it will come. Zero. No matter what the surface is, if you If the dipole is enclosed then the flux Your zero flux will be created. Come on come Let's come back. Let's come back. coming back Are. Brother, come on, let's get to the question. Are. what question Is? The question is saying a conducting sphere of Radius is a sphere whose radius gives you 10 cm Which is 0.1 meter given. Okay, right? has an unknown charge if the Electric field 20 cm. from the Center i.e. capital R gives you 20 cm. Give It is kept. Its radius is 1 meter. But 2 What have you been given on the meter? Electric The field is given. Isn't it? Electric Field I have given it. How much is it? 1.5 * 10 key Coulomb is given to the power of 3 Newtons. Correct Is? Ok. Ok. Come on. End Points Radially inwards coming inwards. Inward It is coming, it means there is negative charge. If the electric field were going out This means it has a positive charge. Is. But if it is coming inward then it means Has a negative charge. You have to remove the charge On this. It is a very simple question. How to do it? What? The formula for the electric field is remains close to σ / 0 σ / r². saying the right thing Am. This is the formula we have for a Conductor Outside It. This is the formula. If You've seen the entire one-shot, then the derivation. You must have seen it. This is the last derivation one shot of. Don't lie. Ok? Let's go now The electric field we have is 1.5. Sir What will come of this? This will bring up Sigma. There is planning. Now Sigma has come once As soon as I got Sigma Sigma has arrived. formula charge of sigma Upon contains area. I work from there I will do it. Well, you can also do that Open it here. Ok? one for you And make the job easier. see how? This formula So you remember, right? Now if you open it You give it. Suppose you open it here. If so, then the formula for the electric field is That's it. Now what should I write in place of q? Am? What am I writing instead of sigma? Area in charge upon. What would the area be Is? What is 4pr² area? 4pr² and who do I have with me? r² / r² And It is 0 anyway. Now watch r² cancel out to r² Went. I replaced Sigma with Charge Upon. In the area. It's the same thing, isn't it, friend? Now 1 / 40 so we have k anyway. Look, the fool has returned home after wandering around. How? did I get it kq / r² what Is this happening to him, friend? Get only KQ / r² I am gone. The fool returned home. How? I wrote K 1/40 as k. Take Now place the electric field. how much here Is? 1.5 into the power of 10 is 3. K's The value 9 * to the power of 10 is 9. charge I have to take it out. Whoever comes last I will put a minus because it is said inward. And What is the distance mentioned? 0.2 of 0.2 Square. The square of 0.2 is 0.4. So I will get this much charge. in the last Write it down because the magn electric field If it is inward then it should come in minus. You will do the calculations, friend. So much calculation So it is yours. Come on, it's done. Moving forward Are. Look, I'm going to skip this question again. Was going to. I said friend, I won't do it, but I thought it was very basic. so such There should also be basic questions. Okay, right? Now There are a couple more basic questions. such two protons In a molecule. two in one molecule protons that are in between you Distance has been maintained. How much have you given brother? 3*Power of 10-10m Distance It is in between them. Ok? Find the electrostatic force exerted by one Proton on another. You have to take out the force. No fuss straight talk. Force formula k q1 q2 / r² or d² whatever it is. Good. Now K The value of 9 * 10 to the power of 9. Are both charges protons? Now let q1 be Whether q2 is both protons. Proton Pay The charge 1.6 * 10 to the power is -19. So here both q1 and q2 are same. So 1.6 * 10 to the power of -19 squared I can. Upon Me Distance Hai 3 * Whole square of 10 to the power of 10. Ok? So son, solve it here. again me I am telling you again, be a little sensible. Many children will think that sir, don't do the calculations. Yes friend, even if I do it, it will not be easy for you all. I know I will do it with a calculator so you can understand. Be a little smart, many children are thinking Sir must have put the last one shot, I I would like to tell this to him also, but only a little. Be smart, there is a person in 24 hours How much work can you do, tell me new Give me one shots, I will also give you new one shots. But then see how many durations will come I will be able to give two one shots in a month, that is, one one of physics, one of chemistry or the other Even less because there is so much work for one person. pass or I should tell you that son all I have already read the one shot, read it or I will I am helping you so much that I Getting one shots re-edited here Am. I have them crisped. You If you have noticed, there are cuts in between. Those edits have been crisp. somewhere if I have said something useless which I can study. There is no connection at that time. So all of that I have removed it from inside. then here I am asking you lovely questions on my life. Ok? Come on. It's done. Ahead Let's grow. Let's move ahead. We are the best One of the questions. Isn't this a lovely question? See. We have met today for these questions. We. This is a lovely question. For these questions meet. Try making it once. Effort Check whether you are able to make it or not. try it do it. Who knows, it might happen, friend. At least try it. Yes. Who knows what might happen. Come on. 64 Conducting drops. To make it accessible. Meaning I am moving forward. 64 conducting The drops all have a radius of 0.02 meters. i.e Give you the radius of the smaller drops has been kept 0.02 Meter and each carrying charge of each pay I have given you the charge, I have given it to you 5 Micro Means 10 to the Power -6 Coolum R Combined to form a bigger drop. Such 64 There are drops. We have created a bigger drop. You have to tell me what the ratio will be? Surface Charge density of larger drop to smaller Drop. Planning and planning We do. See if you have a Surface Charge Density Bigger Drop Upon Smaller Drop If I want to find out, what will be the formula? The formula will be charge upon area. Here also charge upon area. Ok? This is planning. Now it is important to remove the charge It's easy. How? Use your brain. This charge is smaller It is on drop. Smaller drop pay. So Big The charge on drop will be 64 times Smaller drop k. It's a matter of common sense. Because whatever charges are there on 64 are all for advertising. Done. So it is 64 times, right? So if I'm going to divide Q1 by Q2 so 64. It will come directly. Because charge 64 times Is. Be smart. The charge is 64 times. Ok? Ok? So what remains in σ2 / σ1 is What area do I have left? Now the area Let's take it out. We understood this. Now what It's fair to say there were 64 drops. So what The volume of the new drop will be the same as the old one. This will be 64 times the drop. Volume will be. Area No. Volume. Volume 64 It will be times. Now what is the formula for volume? It happens? The formula for volume is 4/ 3 pie r Okay, right? And what will happen here too? 4/3 π r just has to be this 64 times. So 4 / 3π to 4 / 3π cancels out. Here's the cube. Here Pay is cube. Everyone must know so much maths that If I were here Pay if I want to take r 2 here. I am doing cube root, right? cube root tax I have been there. So what will r2 bring to me? 4 times r1. Why? Because 4 of Square 16 64 6 4 Square 16 16 * I mean 4 64, that is, brother, this 64 Four comes in cube root. That means that The r is quadrupled. r who is It has quadrupled. Now what is area? The area is π r1² and this will be π r2² and The above is running 64 with me. Look at this brother How lovely Maths, how lovely Physics. Ok? Now here the pie is cancelled out. Went. The radius is four times that. four of Square is 16. So I came here I have the square of r1. arrived here How much does 16 r1² into come? 64. From here This also got cancelled. Cut it into four I have arrived. Congratulations. The answer came out to be 4:1. Answer 4:1 has arrived. How lovely maths wisdom is. I have worked with him. I have, right? Have to appreciate it. I have no charge Did not make a sound. I did not use it Did. No, I did not use it. Look here I used it. only need to do Not there. When asked to calculate the ratio I need it, I have to use it somewhere. Didn't do it. Because the ratio has to be calculated. Be smart, friend. Be wise. Ok. Correct Is. Ok. Ok. Let's move on. Coming to the next question. Yes. This question is very It is easy. It is very easy. Children don't know Why are you confused, come. straightforward Deal with it. Number one question comes up. These The bigger the question, the easier it appears. Is. Come here. They are saying there is a square. There is a square which has corners brother. A A is corner, B is corner, C is corner and D is corner Is. Ok? The charge is pending brother. Corner It is lying on one of the pei. forest what is it Brother? What is this? 1 ml micro. Brother Sir, this is the time, brother, come here son. There has been some mistake, if it is micro then this Is it sitting? Is there 1 microcooler? Yes Yes This is sitting -2 microcoulombs this is sitting It is 1 microcooler and it is sitting Again -2 microcoolers this problem has happened You also understand something, remove it here. Ok? Now I don't know you, before you If my one shots or question answer ones Have I ever seen a lecture somewhere by mistake? I have told you son, whenever you take out the force If the vector is to be extracted, any other It has a symmetric structure. telling you It is a square with a side of 30 cm Is. You have to force out a On the charge which is sitting at the centre. Four is sitting in the center. Hey brother Look, no matter how many people are sitting at the centre Be from Coolum. Is this one charging and this one Is the charge equal to? Yes, as powerfully as This charge will repel it with that much force This will also repel it. As powerful as this It will attract it with such force It will attract. So the net force is zero. It has to happen, right? And anyway, how many times have you taught whenever vectors are to be extracted and Have a symmetric structure. like here and here It is beans. There are beans here and here. So vectors They will cancel each other out, right? The forces will cancel each other out. No. And as a result, the net force is zero. Will go. There is no need to solve it. Correct Is? Number one will come. not more than this Will come. Ok? Come. This is a question of NCERT. I don't know, I did this during one shot. Has it happened or not? I don't remember. But I think it's a good question. So let's do it Are. what a question? It says check that This is the ratio. Who is this ratio? k e² / g mass of electron mass of proton It is dimensionless. You have to show that this It is dimensionless. This entire quantity I'll take the x value and it's dimensionless. Is. After that, leave everything else. look up a Table of Physical Constants. These are saying If you want the value of all constants So take it. We all know that we know is 9 * 10 to the power is 9. e of the electron There is charge. Who is capital g? Universal The gravitational constant is 6.67 to the power of 10. -1 is the mass of the electron, the mass of the proton Is. So we know the value of everyone. Well, we First of all, you have to show whether it is units or Is it dimensionless or not? So first we Let's take out its unit from here. See This is a very amazing thing. If any unit of If it does not come then it also has some dimensions Will not come. If no unit arrives If it is there then it will not have any dimensions. So we will remember the unit of k. Newton meter² Coulomb-2 is the unit of k. What will be the unit of charge of electron? Coolum is his square so Coolum Square. Will remember 11th class. has a capital g Newton meter² kg - 2 Newton meter² kg - 2 Here comes the mass of the electron mass of Proton. So both are mass, so kg It will become square. Now look at this It got cancelled. I cut it with a different color so that Looks like this cut it. This cut it off. This whole thing got cut off by this. What is this? Came unitless. Now if these units have come then Use your brain and guess what will be x. If it comes unitless If so, then what will x be? It will also be dimensionless. m0 l0 t0. Ok? After this you are saying that this Find the value of the ratio and tell whether it The value of the ratio will be very large or Very little? The answer is it will be very big. How? See how the big one will come? is this kee² which is the distance between two charges What is electrostatic force? And gme mp between two a electron and a proton K is the gravitational force. Divide by r² Divide / r² comes in both. has been removed Is. Now, we all know that electrostatic force gravitational force It is much stronger than. So this ratio It should be much bigger. Still, if Look, we are putting its rough values. Are. Rough rough k's value is 9 * 10 Power is 9. Square of rough rough e 10 to the power of -19 squared to the power of 10 How much did it cost? -38 has arrived. Mass of in Upon electron 10 to the power -31 mass of proton 10 to the power -27. Now you see all this The power of 10 in the values ​​will be very large. It should also come. Because electrostatic force Much stronger than the gravitational force Is. So their ratio is also a very large number. Will come. Whoever comes here, whatever the number You will get a very big number. Enough You will get a big number. This basic work is important Which I made you do. Come on. Ok. It's done. Let's ask this question I am giving you homework because There are lots of questions in NCERT. I hope You might have done this one too. This one too Must have done it. So I'm going to ask you this question I am giving homework. You can read the question yes. This is a cylinder. Everything else you There is a given in the question. I just gave you this Gave it. This is a gap of 0.1 meter. everything else There is a given in the question. Homework for you It happens. This question is a normal question. Let's come to some MCQs. come come come Come come come brother. Come see what they're saying is a point positive charge. This one There is a positive charge. q isn't it? It has a and brought the isolated conducting sphere Went. So which is the most correct diagram? If If you remember this is a plus charge. if these If there is a plus charge then when there is a plus charge around If I bring any other charge then It will take a negative charge on the nearby area. He will come and go to a distant area. It will bring positive charge. this process What do you say? This process is called Electrostatic induction. Now in this one If this is a positive charge, then from here Correct. Now, towards whom is the positive going? On the negative side. And from here the field leaves Has been. So I think this is great Is. How are you feeling? what-what Are there mistakes? See what's wrong with it? In this, if it is positive here then here It must have come positive. The field is coming here Is. So this went wrong. All angles in this is not 90°. So this also went wrong. this is Brother, something went terribly wrong. Everything is going wrong in this. not at 90° Is she coming or going? So this went wrong. This means that whatever our correct answer becomes Yes, she becomes figure one. Be figure one She goes. We have done this. We did this Have taken it. We have done this. ok come on this They also come here. Let's come to this also. come back Have been. But first come some MCQs We do. The one I saw in the back was aluminum I have left the question. quite good There is a question. But let's get to this first. Come. Which of the following graph shows the correct Variation in magnitude of torque on n Electric dipole rotated in uniform Electric field from stationary Equilibrium to Unstable Equilibrium What an arrow you have hit, brother, with just one arrow First of all, you have hit two or three targets simultaneously. Stable Equilibrium Stable When is equilibrium unstable from 0°? You are going to equilibrium, that is, at 180° Are you going to tell everyone the formula for torque? You know PE is sin theta. Now if you From stable equilibrium to unstable You are going to equilibrium, that is, you are going from 0° If you are going 180° then it simply means this If you are going from 0° to 180° then its This means that the value of sin is zero. Where will it go before? 90 means forest. I hope You know the value of sin is first 0 and then π/2 Then π i.e. 90 increases first to 180 It is there and then it decreases. So if the value of sin If it increases like this then the torque will also increase like this. It will first increase and then decrease. Isn't it brother? First It will increase and then decrease. So, the graph of sin is like The torque will be the same. Bus Magnitude It will be different. So the answer came a. If sin theta If the value of increases from 0 to 90, then the torque will also increase. will increase and then decrease from 90 to 180 so torque will also be less. It is the best sir. It is the best sir. Come Go and come. An object has charge of 1 Coulomb. An object is charged with 1 coulomb It was already there. It was already there. You gave him 5 * to the power of 10 gives 18 more electrons Given. Give electrons. what is the charge on that will be? Listen brother. Listen with great love. which that The charge already paid was 1 coulomb. Who The charge given to him later is how much What will happen? 5 * to the power of 10 is 18 The charge of the electron is given. So Charge on electron is 1.6 * to the power of 10 It is -19. But it is a minus. Correct Is? Now if I do 1.6 in 5 * then it will come to 8. at Will you come? 16 * is 580. So 1.6 * I became 5 8. And it became -8. It became -8. And how much power of 10 is left? -1 left. So We have given it a charge of -0.8 coulomb. So He already had a Coolum. You gave him a -8 Coolum and gave it away. So 2 Coolam 2 Coolam He has charge left. How much Nice and basic question. How cute and Basic question. Come on, let's move ahead. next Question. hey hey hey Hey, what is happening? Yes, it's okay now, right? It's okay now, right? Come see how much again Lovely question. three charges q q q Not and -q this is -q. This is q. this q not Is. R placed as shown in the figure. The Magnitude of the net force. Net F You have to take it out. Very nice question. See. This one is Charge Plus. This charge There is a plus. So this charge, this charge What will he do? Will repel. So he will come here. Let's make the pen a little thicker. We will repel. So the force came here. The force has arrived here. It's done. Good. Now this one The charge will attract this one charge. Will it repel? The answer is it will attract. So This force has come here. Ok? angle How much is it? 90. Both forces Magnitude wise they will be equal. So We have a force in kq q not upon What is the distance? a² and the other one too Is. So if both forces then this is it. f1 and f2 is both. Now the net force Formula when angle is 90. We all know is f² + f², right? Isn't it? Hey Perpendicular Is. So what have we got? 2f² means f 2 has arrived. Now the value of f What did we have? k q q0 / a² its 2 Times which option? lol how cute The question is. Children should not be scared after seeing the diagram Let's go. Look what should I do with this? Some? No to do. Don't do anything, friend. Its use also He did not do it as an option. so much Let me give you something. child looking at the diagram Gets scared. Gets nervous. Here you go, one more Good question. You've seen this question a lot. will be. I put it on a bearded head I have done a lot on Instagram too. And me Let me tell you, we spent an hour here. I think this is how much this question is This is the answer part, this too will take one hour. It will become too much while recording. You Imagine we are four in a paid batch. Each chapter takes more than five hours. Let's answer questions. Alldo Parts Sometimes it takes 1 hour, sometimes 2 hours, sometimes 3 hours. And they're doing it now in the papers and then During holidays and tests, during the assignment. So for each chapter There are multiple time questions. And me I believe in this a little less. I A little less for the kids to do from home I give you work because together we have more I will make you do it sitting here, brother. Do it now. I am talking about the paid batch. I have been. Even if in a 2 hour class you Make 50 questions, I will make 50 questions but It will be fun only if we make it together. So that's it. Okay, right? Okay, the rest is available on YouTube now. Tell me this one shot is like 3 hours 2 hours 3 The hour will become 3 sah hours. half the children They will be scared to see it but they don't know it. How much content is there inside it? ok no let's go In one experiment, there were some lattice spheres On whom there were some charges. 3 coulomb O 3 electron five electron - 3 Electron. Neither of them was added. Now The joint was separated. So find out more about them What charges may apply? what is the charge now It is possible? Look at these shorts when not paired If so, then these charges were on him. Now the pair that will So the charges will change, if it is more on someone Go, after coming in less contact with someone. But yes, the total charge will remain the same. No. What is the total charge? Three to Total The charge which is Q net is five of the electron. It is of five electrons. So the total charge of which of these is five of the electron. It may belong to anyone. this is There can be no answer anyway. Why? Because there cannot be 5.5 electrons. 3 5 There cannot be electrons. Now, besides that Who has five electrons on him? Is the charge coming? It is coming on this, no, it is coming remained. I am not coming. This is not there either. come to this Used to be. Six and six went seven out of 12. come to this Used to be. Coming to this. Coming to this Brother. Isn't it? Seven and these are eight out of 12. No So brother is also coming. B is coming. B come Used to be. Okay, right? Done. Its net charge is also What is coming is q net which is 5 The electron is coming plus. and come It is definitely needed. That's what we needed. Come on. Correct Is? What's the next question? The Total Electric Flux erasing erasing so difficult word meaning nikla raha ho from a close Surface enclosing an alpha particle. Take They are saying that there is a close surface inside it. It is an alpha particle. It's just an alpha particle. So how much flux will be produced? an alpha particle How much is the pay charge? an alpha The charge of two electrons on the particle It happens. Alpha particle has a charge of +2 It happens. Two electrons have a charge. So what is the flux of this q? 2q q its 2 and done together. So This gives us a net flux of 2e/0 2ee / 0 means 2e / 0, this is our answer. Is it done? Come on. Well, all these questions Should I give you some homework questions too, friend? Some questions I will also give you homework. So this question is very It is very easy. Look, this is homework. Ok? The issue is about the action region. This question also It is very easy. Looks tall and wide Is. There is homework. Isn't it? Look at some of these how easy. Let's do this. Easy Is. I am getting it done. Otherwise you will say everything Gave homework. They are saying there is a bubble. Ok? You put some charge on that bubble Sprayed it. Now either positive charge must have sprayed either negative charge Must have sprayed. You must have done something. If the charge spray is positive then The charges will repel each other. Repel If you do this, what will be the radius? Increase Will be done. What a lovely question. one behind The question regarding aluminium is left. No Stupid question. I just did the same question For the square. Ye for Square Rectangle to Triangle. Sorry. what to say Am I? This is for the triangle. Isn't it? Half the children must have guessed it. What is the answer to this, but read it comfortably. There is no hurry. Actions cause resentment. Come on. All these questions are homework. Ok? There is homework. Well, you can comment their answers. You can also write on the section. Agerson Reese I brought it, friend. Yes. Come let these Assertion Reese We do. Then the one with aluminum at the back I have left the question and will do it. are saying If a proton and an electron are Placed in the same uniform electric field, so their Acceleration will be different. Correct. The force on them will be the same. Because The force is qe. The charges for both are same. The electric fields of both are the same. Force It will be beans. But the acceleration will be different. Because acceleration is force. There is a month. and electrons and protons The month varies. So the assertion is correct. Acceleration of a charge is dependent of It's mass. This is also absolutely correct. And It is also giving correct explanation. So A is answered. Ok? See the next question. Saying there are four point charges q1, q2, q3, q4 are inside q1 and q2. q3 and q4 is out. Edge shown in the figure. The Flux over the shorn Gaussian surface depends only on Charge q3 and q4. It is wrong. on q3 and q4 It will not depend. will pay q1 and q2. Yes, electric field at all the points on The Guassian surface will depend only on on q1 and q2. It is absolutely correct because Hollow does not penetrate the conductor. So The action was incorrect. But the region which Yes, it comes to us correct. It's done. Okay, now this question, then that aluminum Let's move on to that one. a negative charge in n electric field moves along the Direction of the electric field. wrong thing Is. in the direction of the electric field The positive charge goes away. negative then his Goes opposite. on negative charge a force Acts in opposite direction. negative Force on a charge is opposite to the electric field It seems so. Correct. The action is wrong. Reese Whatever it is, it is absolutely correct. Where Brother, is our aluminium question answered? Here's our aluminum question. From the mind to the heart because the last question is Son. Make it with all your heart and mind. Then we move ahead. And please comment section But please do tell me before leaving. please tell me that You want the next one shot from the second chapter Or you may want to know more questions and answers of this chapter. Needed I think I did pretty well You have got its questions answered. Some? Homework has also been given which you will repeat. But I think we'll have to in the next one. You should go to the second chapter. The rest is yours What is your advice? What do you want to say? Please tell us in the comment section. quickly Please give the answer to this. Yes sir. We are saying that there is a one paisa coin which It is made of aluminium. and its weight How much is that? It is 27 grams. Ok? It has a square shape, it is diagonal. Perhaps This will be of no use. that electrically It is neutral. Meaning, as much as inside it There are so many electrons inside it There are protons. So you have to tell me about that What is the negative charge and positive charge? Ok? See what is planning? Planning This is that first I take this out of my How many moles of aluminum does he have? In coins. I will extract the atom from the mole. From the atom I will get electrons and I will get charge from the electron. These There is planning. So first I remove am moles of electrons sorry moles of Aluminium. Formula of Moles Given Mass Molar mass in apon. So the given month is also 27. The molar mass is also 27. So we got 1 mole. Correct Is? Now I can take it out Atoms of aluminum. How to extract atoms Are? All the moles obtained are calculated by Agadro I will multiply it by the number. So, Agadro If multiplied by the number then it becomes 6.02 * 10 Power 23 atoms arrived. Atoms. Ok? Now I want to find the number of electrons. How many are there? Each aluminum has 13 ie There are 13 electrons. 13 There are electrons. its atomic number It is 13. So 6.02 * to the power of 10 is 23 and Each one has 13 electrons. So I got so many electrons. Now I Let me find out how much negative charge there is? Did you understand this planning? Negative Charge How much is it? How many electrons came? 6.02 * 10 I have 13 to the power of 23* The electrons have arrived. and each electron How much is the pay charge? would have been minus Is. 1.6 * to the power of 10 -19 Multiplied it. So much minus charge Went. Similarly, because it says If the positive and negative charges are equal then If this much minus has come then this much plus A charge of Rs. will also be applicable. If it is done then brother it is because of this Happy to be with us here, this is the best One shot where we initially started with concepts that you may have seen before Yes, and here we have these conceptual questions so that our one shot It is complete and at the same time I have Also gave homework for the questions. So this is what You will get this PPT containing questions. As soon as One Shot is uploaded on Telegram After two-three hours, you will get this PPT. If you get these questions on Telegram Please repeat this as many times as you can. Question homework has been given, please everyone Excellent questions, I have yet to repeat them. Share your opinion in the comment section and how One Shot felt a cute bit about it Leaving a comment and liking the session, see you Love you love you love in the next one shot