Transcript for:
Moving Charges and Magnetism Overview

Hello kids, hope you are doing well Will be. today we are full chapter one shot all in One shot all in one shot means all Derivation Moving Charges End of this Chapter Which is chapter number four of magnetism Yours for Class 12th Physics and more Numericals concepts, everything in it We are going to do it in super easy language. So if you watch this video from start to end then you don't need to read anything else Will need it. Concepts of the whole chapter are yours It will become clear in very simple language. So Don't miss the video and watch it from beginning to end Till then you will see where I am important I will tell you, please tick that also. so welcome To Arvind Academy. I am Arvind sir. Me More than 25 years of teaching experience and easy physics with arvind sir i I will tell you physics in simple language I teach. Let's get started. And yes do not subscribe to arvind academy channel Don't forget it. Easy Physics with Arvind Sir Let's start it. as you saw Chapter Number Four Moving Charges and Magnetism Full Chapter All in One Shot Sari Things are going to be covered here. several children Sir it is said that its PDF can be found If you go, you will get the PDF. just u Download the Arvind Academy app. Visit their store section and click here You will see class 12th free PDF and All the PDFs that are inside it are unlocked. Is. If you click it will be downloaded. So There is nothing to worry about. Big thumbnail I have also made it from the same thing as you Don't have any problem. So Arvind Academy App Download it. Go to the Store section. Take free PDF from there and start your studies You can use it for . this is for you Telegram channel is Arvind Academy telegram Channel. You can join here. Description You will find a link in which you can Productivity should improve. That means whatever you study do it in the right direction and its The results came. Isn't it? It should not happen that studies also Do it and the result may also be less and this will be your Drona course is very good for this 2.1 There are also live classes in this course Son, I will take it in the evening. Other than this Every question of NCERT exercise and I have solved every question of NCERT examples Recorded by myself and in easy language do you get. of the last 10 years PYQs are also recorded and given inside it Are. Apart from this there are MCQs, Assertion, Reasoning, case study, videos on all these, Assignments, hand written notes, everything to you It is found inside it. So you are here with me You can join Easy Physics with Arvind Sir With Drona in 2.1. many children It remains that if Sir joins now then you will be in four The chapters must have moved on. So from now on you If you want to join me then visit the place where I studied I am going to teach and in the first week of August I'm back to Chapter One from around I am going to start. So yours is absolutely You will get full opportunity to clear your doubts To clear it. Don't delay at all. You know how the paper is coming these days Are. Join me in Drona 2.1 Can be done. And those children who want to join Drona He wants to download Arvind Academy app Do it. The link will be found in the description. Go to its store section. There you will Dhrona will be visible. start studying with Do it. let's start the video Are. Because of which this video is being made of you one shot all in one shot full for help To cover the chapter. so the first thing comes This is the concept of magnetic field. So What is the concept of magnetic field? If I put this white magnet around a magnet, I took color and wrote and made a magnet like this. Let's say North and South. its around As far as we know about its magnetic effect We can feel the influence when we speak that the space that is around it is what we call It is said that there is a magnetic field. so where The influence of a magnet in space up to Can be felt. we call it that is that its magnetic field or magnetic There is a field. this is the magnetic field This is a vector quantity. Attention Keep it. as the electric field vector was Similarly, the magnetic field is a vector. And you use its symbol, capital B. and arrows are used to denote vector quantities For. And its unit is Tesla is the SI unit and the flux is weber As you already know. So Tesla is the Unit of magnetic field. Now interesting what happened to what was thought earlier that which is the magnetic field and the current Electricity is two different concepts Are. But in 1820 an assistant was appointed He was a scientist. He did such a Experiment with big simple or big simple A big impactful experiment together which is in the top 10 experiments that made me think about it or proved that magnetic field and current There are no different things. Two sides of the coin Are. How? let's watch. In 1820 Astard Experiment. what did they Did? took a circuit where he Made the current flow. When inside it He made the current flow and here If you keep a magnetic compass then you will When I kept it and as soon as I closed its key He saw this magnetic compass deflected from its place I did it and after that when I turned off this circuit When I gave it, the deflection ended and went back to where it was came and when the direction of current in it If placed opposite then its deflection will be on the other side The opposite side is done and then the circuit is turned off if you did it then go back, this proves it was held responsible for its deflection This is the current. because when it's on So deflection occurs. when it is closed it There is no deflection and when the opposite current in one direction current in the other direction If it is inserted then it goes in the other direction Deflection occurs. And this is because There is a magnetic compass. What is a magnetic needle? Take it. the ability to move it It happens only in magnetic field. like this It can't move. so if it's shaking So a magnetic field is being created around it Who is shaking it. what does this mean That a magnetic field is created because of this current that's shaking this compass Because this compass itself is a magnet It happens. So, this proves that the With this current you can generate a magnetic field Can make it. i.e. this is the current Electric and magnetic fields are different Things did not exist. The coin has two sides. This is a very solid experiment Was. well now that this has happened brother the current This creates a magnetic field. So the next The question arises that how much does a brother earn? You already know something in physics It won't work just by saying it happens. What is its impact? How much is it brother? So that we can make it better for humanity So that we can use it for. so now this is a formula comes or let's say magnet A basic formula of magnetism would be derived Which is called Biosavart Law. As You have studied Coulomb's law in electrostatics I had read that it was based on how much force was applied is, how much is the electric field charge Makes it. Similarly on magnetism There is a Biosavart law. So BioSavart Law This indicates that due to a current element How much magnetic field is generated and current What is called an element? this is also us now There are people to watch. So look at this one here A wire is taken in which current is flowing Is. A small elemental of this wire Fragment DL. which you use in calculus No, you call a very small part as DL. So The same elemental piece DL which you take. That is what you call current element. Complete If we talk, we call it IDL What? Current Element. Now in many books. They do not write it, they just write the DL. But This is what IDL means. Because Unless you allow current to flow then what is the use Magnetic field. so this is the DL or The IDL is what we call current Elementor. Isn't it? This is a very small element. Isn't it? Like there was talk of point charge same way. So because of this current element, this How much magnetic field is formed at point P? Is? This explains the Biosavart Law. So He said that brother from this DL this dl is the distance r from this point p is and this r is the theta angle from this dl If it is creating then what should be the magnetic field will go to db because current element from this idl A small db will be created from this. How much will that be? That would be μ0/4π idl sin theta / r² this is the function of BioSavart's law There is a formula. Now because this magnetic A field is a vector quantity And this is a scalar format. In this There is no direction anywhere. so better We will have to write its vector formula. This will be the advantage of writing vector formula that both the magnitude and direction We will get absorbed in it and we will discuss the whole thing clearly. Will be able to tell from. So this is the vector formula what I have written here vectorially goes Is. so this db vector because magnetic Field is a vector quantity. μ0 / 4π idl cross r what is this dl? This dl is it. And where is the direction of dl? That Direction refers to the direction of the current. Because if you are saying vector then where will you believe it Direction? then you will follow its direction which Current is flowing in that direction. This if it is going in this direction then go in this direction I got the direction of dl. so idl cross r and from here you are taking r so this is the value of r direction is done and below r okay so this formula is scalar only Magnitude tells and this formula tells everything This tells the whole story vectorly This is the formula and the μ note here is Son, there is a value, remember that too, 4π * Ampere and Meter at Power of 10 -7 Tesla And also remembering the μ note up 4 pi Keep it. It will be used in many places 10 Power of -7 with suitable units. So these 10 By remembering the power of -7 and the value of μ not Keep it. what is this μ knot Is? This is the permeability of the free Space. Like apps 0 used to be permittivity off The free space. Well, this would have been permeability It is in it. What is this permeability actually? Is? This is specifically in chapter number five. We will understand in Magnetism and Matter. So we leave it there because there But this is the topic. Good, you understood it. Now I mentioned direction IDL because IDL the current element is a vector Sourced because vector quantity Is. So this is the direction of IDL current It happens in direction. if we look here But I would like to take out the direction here. Where will the magnetic field be? This dl cross is r. i.e. the rule of vector cross product It will work. Right Hand Screw Rule. I remember No? Take out the right hand. Such right hand and Place your paw or palm in the direction of DL Give it. This is under the direction of DL and R. Bend the paw in that direction. So this is DL's placed the paw in the direction and pressed the R key Turned in direction. where is the thumb pointing Is? See, the thumb is coming inwards. This means that the magnetic field that will be created here It will be built inside. that is perpendicular Inward There is a magnetic field in the direction. These It is important to know because otherwise you will not be able to see the direction Can not catch it. So let’s hope this The thing must have reached you with great clarity. One I have also added a separate slide with directions off db to say what i understood there It is given basically. The same thing is written here. the vector one which is the right hand screw rule It is he who has to apply it. once again dl's The paw should be in right hand direction. Not the left, first thing. The vector cross product formula and This is the paw in the direction of dl and r Turn it in that direction. in which direction the thumb is the thumb is facing inwards so that is the direction because white color is visible It is not there. Direction is shown by cross Are. You will also know this, we will tell you further Are. When you make a cross like this it It means perpendicular inward Direction. And when you make a dot it's magnetic Use a vector to represent the field to show the quantity Perpendicular outward direction to show this perpendicular to whose plane you are in You are talking, you are writing on a copy Perpendicular to the plane of paper and me I am teaching here so perpendicular plane Understand this television or interactive board That perpendicular one is in the same plane as this one If he is perpendicular then you will be able to understand this and you will also know its direction You will definitely be able to get it out. exactly because this There are as many vector quantities as there are magnets No, it is very important for them to understand the direction Is. because if you don't follow the direction Then it will not take long for the meaning to be misinterpreted. Brother, your school is 2 km from your house. North Now I moved south for 2 km. So now Got very far away from school. that's the mess Your total will go away. catch the point anyway I must have come. We will also talk about some special cases Let us take this to help you understand. See if there is any wire, right? By the way current This is the biosavart law of the elements, this Applicable only to current element Is. Current of the applicable current element means the ideal small piece Just like we used to talk about point charge, For. Now if we talk about this wire So because if we understand this in detail If desired, this can be used in small current elements Can be broken. Isn't it? idl idl because It is in the same line. So in line with this wire Straight means scientifically theta = 0° or here If we talk about backwards then theta = 180° in The magnetic field at both points is yours comes to zero. because look at the formula idlb sin theta then sin 0 or sin 180° is It is not 1800. This is 180°. then sin 0 or At 180° your magnetic field will be zero. So keep in mind that if any straight wire How far is it in front or behind him Do you get a magnetic field? Zero. this here It was cleared by. Second, if at 90° to the wire maximum magnetic field when you go You will get it. because sin theta in sin 90 Whatever is maximum will come. So this thing Hold on because it's important Understand. I placed it before you. Now a question The one who has appeared in your board exam We do it too. So here it is written A wire Understand placed comfortably. Place a wire has been along The north south direction. right now it means Make a direction. Whenever the direction Let the conversation come to you. We do the same thing And we will recommend the same to you also. Immediately Make a direction. like no confusion yes. One second seems like two seconds. two three Seconds. So this is from North South East West Khat became. Now place a wire in this direction It has gone in the North South direction. Caries A Current of 8 amps. This wire has 8 amperes of current is flowing. his direction Have also been told. From South to North. These See from South to North. now take a photo of it If you take it, there will be more clarity. look at this, this South, look this was South and this son was North Was. So write South to North Current I. it The current is flowing from this side. Absolutely Whatever he said we clearly photographed it I have been represented. find the Magnetic field due to 1 cm. Grind. Now the 1 centimeter piece of this wire Have to catch it. Because of that 200 cm. away From this you will take in North East direction North East. This is at 45° to the North East Will go. These 45. At this point P, you will get The magnetic field has to be removed. Now here is a Keep in mind that the magnitude of R He is 200 cm. and because of which we need to remove current element idl or If I talk about dl, how much is that piece? 1 cm Isn't it? so here we are Biosavert law can be applied directly. Why? because this piece is Respect for this distance has become elemental because 1 centimetre is smaller than 200 centimetres It is very small. So we directly Will be able to apply Biosavert Law. BioSavart Law Applies to current element only Directly. Otherwise something else will be bigger So we have to integrate. I am understanding Is that what I am saying? so here directly Why are you able to apply the formula? Because Its size is very small. Same Should be. 200 while applying Biosuper Law In respect of centimeters. small when we In physics it is said that small is big Nothing happens in physics. Relative Small growns up. Isn't it? Sometimes even the earth The point object and the earth become smaller But we ourselves don't know where we are. will fly away in the air. Isn't it? so small we are There are people. Then you will think yourself to be great What will the earth understand? Then the ant is in front of you, The ant is bigger than the virus. Isn't it? Anyway, I got your point about the size So here the value of I was given as 8 ampere We have given a note in the question and have kept another dl 1 cm If you want you can use SI system If I am working then 1Power of 10-2 I wrote down the meter. The value of r is 200 cm. and theta 45°. now directly here Will be able to apply Biosavert Law. I told this I have tried to, I have tried to direct Why are you able to install bios about law? These It is important to know in Physics. Otherwise The teacher will do the rest and you will do well And later you won’t be able to do it. Because You missed that concept. Isn't it? so here But now we have calculated the value of μ0/4 Pi The value is 10^-7. And i means 8 amperes. see this 8 Ampere. and dl is mentioned here which is 110 power-2 absolutely easy There is no problem with this and sin will become 45° theta 45° I understood the point and the r's went down Square means 200 cm is 2 meters so the square of 2 meters means four Now solve this, here we have tried to solve sin 45 1 / 2 and the value of 1/2 is 0.707 Take advantage of alternating current You will get it in chapter number seven AC or We will now talk about alternating current So I don't know if you have read it, if you haven't read it then 1 / 2 It comes to many places so I got it repaired goes 0 707 Anyways write here 810^-91/2 I have written down 4 for calculation now Solve this and here comes your 2 / 2 This four will come with 2. This four will be subtracted from the other four. So this is two so 2 / 2 is 10 to the power - 9 and This will leave 2 2 with a value of 1.414. 1.410 to the power-9 Tesla this is right here Your value has come, keep this in mind that it is 2 The value is 1.414 and is used where Whatever the case may be, if it works till 1.4 then use it and Remember 1/ 2 is 0.707 These figures will be very useful for your calculations That is why I have written it. Isn't it? You So, he is intelligent. So you take note of this Take it. Here this numerical is useful for you Is. Let us take a step further and Let's understand things. so here it comes Magnetic field due to two state current Carrying conductor. Now this photo here Am I making it up or will I tell you this It is not directly in your course. But There is nothing much in knowing this. just one There are slides as you can understand them better. so you Through that you will be able to understand the whole thing easily. These What is? This is a finite wire. Finite What is a wire? of finite wire length you know its next one You know both the ends. we took the Took 2 meters long by 1 meter long. this one It is finite wire. whose length is finite. I know it. there is a second wire Which is called infinite wire. He is our Now we are completely in the course Will talk. but in this finite wire We know both its ends End A Value Two If it is not written then write A Give it a call B. This is finite wire. From this finite wire to point P if If we want to find out the magnetic field then P How will the point be made unique? one from here Perpendicular drops from the front Mixing this. and from this perpendicular this the angle that is being formed from this end if we are saying 1 and if this angle is 2 or are you calling it θ1 θ2 then That formula becomes the magnetic field Look at this: for finite length b = μ0 / 4π i / r sin 1 + sin 2 is correct if this angle is being mentioned then this How much magnetic field do you have here? There will be a magnetic field, you can remove it Are. Excellent. And if you need θ1 θ2 If it is needed then use cos instead of sin in it. Take it. So this becomes b = μ0 / 4π i / r cos θ1 + cos θ2 When is this for? Finite For the wire. then making it clear that Not directly in finite wire course Is. Many children write in the comments that Sir This is out of course. But by knowing this How long did it take 1 minute? By knowing this The clarity keeps increasing. So this Do not ignore it and nowadays the paper comes like this that many questions would have been of JE level Are. So don't make the mistake of leaving it out Do it, it may prove costly. the rest is you You are intelligent and you will do whatever you want. well now Look here, if this is of infinite length Let it be wired. That is, this wire is its I don't know the end. not both ends You will find out the address. Where does it begin and where does it end So what will happen? As you walk away, Look what is happening to this angle? These The angle is increasing. see it here now There was 1. When you reach here, you will be 1 big Went. So when this infinity goes away then this will be 1 What will happen? Trending to 90. What will happen to this 1? tending to 90 and this It will also be trending to 90. Now if we replace 1 with π/2 in this formula And if we put π / 2 in place of 2 then sin 90 + sin 90 sin is 901. If sin is 901 then 1 + 1 2 is here. If this two kills this two then 2πr will be left. This is what was printed. See how much It's a logical fit. b equ when our infinite If it is a long wire then it reaches around 90°. 2 also reached around 90°. Now, the value of b μ0i / 2πr is reached. because this is 1 + 1 equals 2 Had gone. If this two kills this four then two Saved. Work is done. So this is the formula This is your course of Finite Infinite Wire and its derivation is also from Ampere's law We'll do it again now. that derivation too It is in the course. so this is 100% in yours Course Directly. Understand? What is this? Magnetic created from infinite lens Field. Well, you must have understood the matter. Now When it comes to finding the direction of the current Straight is a current carrying wire. So from this How to get the direction? big Easy. Wire For one and from this, assume the current is It is in the direction. Take the right hand. Keep your thumb in this direction. That There is current in the direction and bend the claw This way. So the direction in which the claw is turning this is concentric circle type you Magnetic field will be found. ok like this It's not just a circle. it's done this way It is everywhere as it is made. So you put your thumb When you keep it and bend your paw, these rings become like this in the center But more rings will continue to form. one and the same The ring is not for everyone. same here too There will be rings. This is what I mean. Correct? So This is a method of extracting magnetic field. Right hand thumb to current carrying wire Place it and bend the claw. Well, this is one thing for you He also tells about the Jugaad. It's not a Jugaad but a Rule Is. That is called the slap rule. anytime If the magnetic field from a current element If you want to take it out then use the thumb of your right hand Give it to me and slap me. That You will be slapped in the direction, that direction It becomes a magnetic field. tell him There is the slap rule. like here the value Look, the current is flowing. Now someone asked you Brother tell me the magnetic field here P On point. So you will definitely get something out of this. And What's the second one? We have this here on the right hand side thumb of is placed and paw is placed in the direction of P Slapped in a tie. feels like a slap Fear. I became scared. It's going outside Is. So where is this magnetic field son? Went? on the outside. let's talk here These q points. So where is the magnetic field here? will be? So brother we call it ghostly claw It is not there. So, you will have to take it like this. and slap If it is going inside then there is magnetic The field will be on the inside. So it is quite easy It falls upon it. What is this? slap rule Slap rule. well what is written in the books We are already telling you that. This makes you Magnetic field current needs to be extracted anywhere Because of the element you can remove it from the body Are. Isn't it? Keep it up nicely. be easy It will go to you. ok great. Understand this. Now here's this graph, which is fine, It has a wire of infinite length The formula we read is B = μ0/ 2pi II / R In this, if the steady current of the rest of the thing is We also talk about steady current. Are. Steady current means the current which The flow is happening, it does not change with time It has been happening. If 5 amperes of current is flowing So it is only 5 amperes, neither is it decreasing nor increasing by 4.9 5.1 is good. So B is proportional to 1 / It will become R. It means rectangular Hyperbola. Shape of Rectangular Hyperbola This happens. I Rectangular Hyperbola Why am I using Word? So that If it is written somewhere in MCQ then you will understand How to get in shape doesn't matter. Isn't it? More I use technical words only when It may be a compulsion. Otherwise easy to explain Easy physics of words with Arvind Sir. They How it will happen? That is why it will happen. So here it Let's say the rectangular hyperbola B is Proportional to 1/R which is the straight current Carrying wire is made from The photo or graph of the magnetic field B is Where is B vs R from? this wire How far are you from? As the distance As you keep increasing your size, you will get this shape I will keep getting it. hope this thing You might have caught it too. Now a very Let me ask you a lovely question. come on board It is done and it is trending like this Which you call hot question. So attention learn this question from them because this is a Ability to ask 10 questions He keeps it with you. This will clear the concept. let's watch. so let's go here now Let's take blue colour. otherwise something about this If you write it white on white it will not be visible. The figure shows two current carrying wires at one end Two. Look this is one, this is one and this is number two. This is it. As if you could recognize it. Good talk. Find the Magnet Magnitudes and direction of the magnetic field at point PQR. This is point P. This is point Q. This point is R Is. The photo remains. also made in board Was. And it is being said that magnetic field on PQR magnitude of the field and its direction Tell. That means remove B completely. completely means vector quantity then Find both the magnitude and direction. Let's start the extraction process Are. So here we see the first p point Let's do the story. p in points The first wire will create a magnetic field. And This is because both are current carrying but Look at the direction of the current. one is here and are condensed into one. like you hold The feet are here. current in opposite direction Is. So here we have to see that What is the direction of the magnetic field Is. I wrote it here, but I Let me explain it to you first. See this first one The current was I1, if you want then call it I1 Son and I2 are much better because It is different. So this slap rule was applied in I1 Give it a try or put in a rotating ruler. this thumb went and outwards at point P There is a magnetic field. Can you see it? And If you put it inside then it will turn inwards Is. Looking at this, look here B1 The magnetic field due to this forest Perpendicular to the plane in outward Direction. This is the rule that has been applied. Look at the I1 thumb slap in direction here and this outside this so if you come into this then thumb down and this is on the inside right this two so this The direction of both the magnetic fields They are opposite to each other. That means its The values ​​will subtract from each other because vectors When they are opposite in quantity then Have to minus. now here is bp Let's take the value. Subtract b1 - b2 It will have to be Let's subtract B2 from B1. see What is the result? Now, the second one we have I applied that this wire, when the wire It is given to us and until it is said Until then we treat it as infinite wire Are. It looks like this in the photo It's just a piece. We will not accept this. what are we Will you agree? Infinite Wire. When he will say that This is finite. Normally he will not say this to you According to the syllabus. But if you tell us then we Then we will apply the finite formula. Otherwise it is infinite for us. so this Pasted the infinite formula. μ0 / The current formula for 2π / r1 is infinite I told you. Magnetic field for this one This R1 means this R1 means this distance R1 from here and this second μ2 of μ0 I2 / 2π R2 R2 means distance from here son because this will be R2 of this P point For. Good son. Now enter the value in the formula Put μ0 / 2π and it becomes common. Take i1 / R1 - i2 / R2 from here. Any There is no problem. The values ​​fit Inside this. This is the value of μ0 4π * The value of 10 to the power of -7 upon 2π I1 The current flowing through it became 20 amperes and Look at its R1, R1 was this much, which is it is 10 cm or 1 m minus I2 It is 30 amperes and what is R2 in it? from here to here so 10 10 30 So how simple is 0.3 meter and how to fly it Give me two from here so this will be saved two bhai sahab so 2 * Solve your problem by taking common solution from here So this will come to the power of 2 * 10 -5 If you remove this decimal, you will add a zero on top You can reduce it by taking 100 commons, reduce the rest If you remove it then you will get the value, then this After calculation 210 power-5 Tesla came in and came back positive. coming positive what does it mean? that B1 was greater than B2 only then Then our result will be positive. It means net The direction of the magnetic field is the same as that of B1 It will be in direction. Because B1 dominates is doing this because it has come positive then B1 It is heavier than B2. Then it came positive It is big. Otherwise, if the result is negative, B2 is bigger Would. So here this is the direction of B1 where was he? Perpendicular outward. So Perpendicular outward direction The direction is done and so is the magnitude Done. We figured out this whole thing for P Gave. Now we can quickly find out the values ​​for Q and R. We will take it because we have understood the whole system Are. We have to repeat that. watch now here at Q now at Q means here Look here, this is caught and hit inside. so this The magnetic field here is due to this Made. Look, let me make it. this B1 this It was made inside and because of this he did it like this Inside both are in the same direction. This means both of them will be united The magnetic field is in the same direction. Add it and now from here R1 R2 Both are equal to 10 10 cm. Then BQ = B1 + B2 and keep these four with the same value as Here we brought 4π * 10 -7 / 2π 20 amperes Current of 0.10 plus current of 30 amperes 0.10 Because the distance between the two here is 10:10 Cm. Is. Now if we solve this, then we get 10 ^ -4 Tesla and because the magnetic field If both of them were inside then both of them had a cross i.e. in the perpendicular inward direction The magnetic field arrived. quite clearly We could understand this thing. Now the third player is here. It comes. Now watch the conversation of this r magnetic field at r here now If you look at it, it is made from forest The magnetic field is inside. Cross look at this. And turn it upside down like this. he is out Is towards. So this cross then minus It will have to be do b1 - b2 or b2 - b1 and Check positive and negative, who is bigger Small So look here br we have b2 - b1 I did it. You can make someone bigger, someone else bigger We can subtract it from . the final result which will come plus minus it becomes clear that the We had reduced that first quantity Was it bigger or the other one was bigger? Then B2- So what we did with B1 is 4π * 10 to the power -7 and that's it. This comes to 30 /0.10 because it is written as B2 So this is the current of B2 and the distance from here is 10 Cm. Look at this. Then take the distance from I1 If you go here then it will be 30 cm. So this is -20/ 0.30. Now that you have solved this, You got the value positive. positive Meeting means here B2 is greater than B1 Was. Then it came positive. small from big Decreased. So the direction which will be finalized will be of B2 will be. Because B2 is larger. Now let's look at B2 View direction perpendicular outward It is in the direction. so this is perpendicular Came in the outward direction. these three are you Nice very nice question very important And JE level question came in the exam and Will keep coming. You should do it. I would move away Am. You can pause and take notes. Variant question. Come on I think you You must have understood this. carry it forward One step. Now magnetic field at the center of the circular current loop. Now this circular Is there a current loop or loop has current in it such that It is flowing. How much is at the center of this case Is there a magnetic field? then its value is B = μ0 I / 2R is the magnetic field and the magnetic I have already told you that if the field If we make a cross then the perpendicular inward direction is Time Interactive Panel Perpendicular to TV And if you are reading or writing then your It is called a plain of paper. and the second dot If applied then outward plane to the plane. talk You can understand it. just the other thing It is important that in this current carrying loop You can calculate the direction of the magnetic field center. How to get it out? It is written like this. We I will explain it to you very easily. to do What is? nothing to be done. Assume like this We made a loop. They make it so that It's small because brother, there might be a current from somewhere Will you put it? It doesn't happen like this. Where to insert it from? Let's break it from here. so that Meaning this photo will be made like this many times To you. Now assume the direction of current is like this Is. Current is flowing like this and we need it The magnetic field has to be removed at the centre. So What is the plan? You have to take the right hand and the direction in which the current is flowing, its The paw has to be bent in that direction. These We folded our claws. the direction in which the thumb I am going in, that is the direction of Magnetic field. Where are you going? the inside On the side. So brother, this is the magnetic field inside On the side. If the direction of current here is like this would have been Then where would the magnetic field be if you You should have taken the right hand. The thumb bends like this I would have come towards you. It's a simple thing. So Here the direction of the magnetic field is It would be in the perpendicular outward direction. It is written here that current carrying Your magnetic field in a circular loop How to take out the direction? Hold on to it. Direction is a very important aspect Magnetic for this chapter. Isn't it? And Let us take the formula B = μ0i / 2r and the There was an infinitely long wire in it here The pie arrives. Method of remembering μ0i / 2πr in that and in this you can see it. And Here, if there are n turns, then from n Please multiply it. do not delete it I have been. He is so intelligent. from here n It has been multiplied. That's all. If this same Suppose there are such entries in i then from n Multiply the magnetic field. This is the story. Now comes its derivation. These which we call the center of a current carrying circular loop But where did this formula come from? very simple This is a derivation. So this formed a loop. in the loop now because the Biosavart Law is the only law we Let's apply it. That is our fundamental type of law is for magnetism. jugaad from that Let's create it. then use integration because that is the current element For. So it is not direct for everybody It will take place. It will be applied for current element. from that You can integrate. let's watch. Here we have a small piece to tell you So now we take the current element Took it. dl current element actually vo idl Is. Current carrying must be done. then dl Is the current element. now this is from dl to r How is the direction brother? dl then tangentially It happens. the little piece is tangent and So what is the radius of this vector? How much are they both making between them? 90° then from this current element Yours What is the direction of the r vector? 90 so this You have applied Biosa Water Lore. dv = μ0/ 4π idl sin 90 because of this dl and r is 90 and if you take dl anywhere then this It will only be 90 because it moved tangentially your dl and r will always be 90 so this is going to be 90 for each element and r² means the square of the radius, that too fixed Is. So here you can write it as sin 91 by doing μ0/4π idl / r² is not a problem. But the point It must be kept in mind that db is a current The magnetic field obtained from the element. Now if we want the whole loop then this Integrate through the length. Isn't it? So This is through integrating this db b To get. So there is integration Given μ0 / 4π idl / r² you know that Things which are constants in integration They come out of the integration. So μ0 / 4π is a constant and will go away. The current in the wire is steady current and it went out will go. The radius constant is gone will go. Then nothing will be left inside. Then, μ0 / 4π / r² integration dl now integration dl means total length of this loop so total what is length perimeter or circumference whatever language you speak i.e. 2πr is then just μ0 / 4πi / r² and its The value becomes 2πr. Now, from this 2π, this is from r. If you finish the square and subtract it from 2π, this will be you can write two here then the value of b What happened? μ0 Where is i/2r written? Here it is written μ0i / 2r and If the number of turns in this is let us say n. As I said, this loop has n If there are bars then the formula will become μ0 ni / 2r See, it went away easily. this derivation It is very simple and important for you. Is No? So if this brother comes then he will give you some really good lines I want to write, write it with love and difficulty It won't take more than 1 minute or 2 minutes You should grab this as well, let's move on Now comes this very important step Derivation is heavy in this one so we are And the other one will be made of solid wire. This is very important and there are big derivatives It comes in. So a good way to do both of these Will have to do it from. so the magnetic field on the Axis of circular current carrying loop. Now What it is is that this is a current carrying loop. As that I placed a loop type ring here Was. It is not visible. I saw it. these values Here is a loop. Like this right now we have created a centre But the matter was taken up. Now we are saying that Brother we will take it out on its axis On point. Isn't it? The point is understood No? Earlier we were at its centre. What are we saying now? on its axis Will take it out. So this story is based on access Is. Now that you have understood this photo then what next We take the conversation forward. Now this in it You are watching current carrying from here. Where It is very important to see it from here. Otherwise There is a lot of confusion. makes eyes Are. Now this guy here is watching this. So this way the current is moving anticlockwise. now this is the center of the loop due to the current Is. This is the distance where the magnetic The field to be found is at a small r distance. The radius of this loop is r. So here the The magnetic field will be the same as the loop Apply the formula. like this it is on the outside Will go. if he is looking at this If anticlockwise then out and if clockwise If he goes then he will be inside here. you understand that Must have gone. How much value is generated? Then b = μ0IR² Remember this: 2r² + r² to the power 3/2. is mandatory. And like I said this Bhaiya is a vector quantity b then its It is necessary to write the formula with vector. So b = μ0² 2r² + r² to the power 3/2 i cap because This was considered the x axis and in this direction This is a magnetic field. then write i caps Gave. i cap is the unit vector in Positive x direction. You must know it. So this becomes a magnetic field. now over here Look, if we talk about the center, then this In the formula, you can put the value of small r as zero. Put it in. this is small r so pull it It will come here and as soon as you solve it The same as we have been deducing b = μ0 ni / 2r will come. And if this r is far away from this r It should become very big. Go very far away. So What would you do? replace this r² with this square You will make it zero. sorry make this r² zero Will you give? Don't make it zero. this its There is zero respect in comparison. And Then if you solve it, it will be μ0 ni r² 2r Will go. So this far away center And this is at the center. I hope this is Could you get the point? Now this clock face rule is this You will know that whenever in any loop There should be such current. The meaning of such a current Look anticlockwise, can you see the arrow? If it is made like this then it is North Face and when we talk about the South Face So this is how they produce current in a clockwise direction If the direction of the current is then it is North face they call it clock face rule so I will use it wherever I get the chance It lives in books so we asked you to explain Should not be retreated from. Now we will do it The derivation is the same as that of the current carrying loop Which we had to take out on axis. Isn't it? Come I do it with love. It will be great fun. will understand carefully. So here we have a Current carrying circular loop taken. look we Stay from here. Now when the photo is made, the eyes They make it go away. No problem. appear Can you see it hasn't gone out yet On the board. Should not be visible. Well try it anyway I have done it so that it becomes visible. that's why the bandage Let us know how much is coming It is in the camera. yes well. So, this is a current There is a carrying loop. And this is its center O. Where we want to extract the magnetic field, The point P on its axis is the point which that is at a distance X. from its center and its Radius is taken small r. There is clarity. What do we do now? a small current The elements are taken on this circular loop. Because the incident is according to the Biosafety Law It will happen. so here idl or just dl Write it down. The matter is the same. This is why it was given a forest that there are two magnetic fields here right now we I will show you so that you don't get confused One is written. All precautions have been taken. Now this The magnetic field here is dl Will make it. Removing it again. these db Will make it. One one. because these i cross these r Isn't it?. So when you do I cross SS then it will happen like this in the direction perpendicular to the line dv Makes it. Excellent. Now if this angle is phi This angle of yours will also be fine. Why Will be done? because from here to here See, if it is 90° then this is 90 - fi, this much And this is also 90, so 90 out of 90 - 5 If you subtract then phi will remain. So this is the phi angle. Took two components of this DB. take one If the angle taken was phi then db cos phi and one along the axis so this db sin fi so We understood the matter after paying attention You can listen to it again, it isn't fun now What happens is that the current carrying loop which Whatever happens is symmetrical. So this we will find another element opposite to Will go. Opposite this there is no current here If you take the element then its opposite is everywhere here I will get it. Same happens in a circular loop It happens. now this dl has the same file of this dl would be making an angle and its magnetic field is to written this to this db is Direction will be in which is perpendicular To this dotted line. Now if this is a phi angle So in the same way this will become a phi angle. So this DB cos phi down component and DB sin of DB Fi horizontal or along the axis. Now this The DB cos fi are opposite to each other I am in direction. so cancel this I will give. That is, we have only dB sin phi The magnetic field produced is the hand It will take place. This DB cos fi is of no use Because one is killing the other. So much We should understand this matter. Right now we are using db We will integrate sin phi. So We are integrating db sin phi because because db cos fi has no impact because both these components are one They are killing the other one. hopefully You might have understood the matter. Now this its I have written the parameters so that you can write It appears that there is a current carrying circular loop. The current is I. The radius is r. point p along the Axis x Distance from center. It is such as Let there be clarity on what we have put in the photo Things have been said. now db cos fi will cancel Out only db sin fi will be there. that we I have already explained it to you. Now if we have to use db Current Element Bioswirth Law has to be derived Will apply. So how much would the db be? μ0 / 4π idl / s² right? this idl this this which is here The value of db comes, it comes db to find out that idl / r² which is here comes r that sin theta etc sin theta here but it's going to be 90 as you can see Between this dl and this s, brother, this dl and s This is a 90° three dimensional figure in the middle of so this is sin 91 so this The value becomes db = μ0/4πl /s² This became the Biosavort Law. now over here The total magnetic field at point P is given by When we go to find the total magnetic field at P What would you do? this db sin fi this sin Fi this is the one. to this db sin fi we will integrate it so that you Magnetic field was found. Now one of these The thing is db which has been found above. sin Fi has not been received yet. so sin fi this We will take it out from the triangle. if you write sin then Perpendicular / Hypotenuse r / s aa Will go. Look at this, here sin = r / s You can see the triangle, right? Look at this triangle. So this sin fi r / s perpendicular / Hypotenuse. Now in this formula we have used db I kept the value of here. See μ0 / 4pil / s² and sin which is this, put this sin from here Gave. That is sin π r / s Now the value constants in this are will go out of integration. we know it is just that. and you see all the value is constant. μ0/4π is a constant. Current In the loop is constant. s is a constant. This is a constant isn't it? It will change It is not there. and after that this is r radius of the this radius of the lube that too is constant. So everybody jumped out. Only one dl left. now integrate this dl If you go through the loop you will get 2πr. These Look, 2πr has arrived. Now you can calculate this 2πr from here If you subtract 2π, this will remain 2. and be this gone μ0² /s 2 This was the only thing left. Now the s that comes here That s is there, so it is an oblique distance. It is difficult for us to see this sideways Measuring distance. So what should we do? These In a right angle triangle this s is divided by this x and r I will convert it into . because the radius of the loop so measure it once thing is over and x Very easy to measure. Brother, measure it directly how much Is? Place to measure skew. So this s we call We will replace this r and x with the help of Pythagoras From. So apply Pythagoras here. So s² or s = under r² + x² this is the hypotenuse While finding the under root of r² + x², that is, evened out. and here in place of the s If you cube its s, that is, its power, then it will be 3/2 Look, your formula is ready. this is a Scalar formula with magnitude. And If you want to give me directions, I will open my eyes Had made it. If you consider this as the x axis then Put the +i cap on the positive x axis. That is, if this is clockwise or anticlockwise If there is current then +i cap will turn clockwise then -i will come. There is just this much difference. These The formula was made. Look here we have n If there were circles in this then multiply by n Gave. Nothing is very easy. n to μ0 ni r² and this is the formula written. that is the proving of this good derivation that this current from the carrying circular loop on its axis How much magnetic field will be obtained? This you You can pause and take notes if you want or You can understand it well. Let's go one step further Let's move forward. now this be along the axis What roughly is the graph of an off loop? Is? So this was the formula that we had Remember this when you make a graph on the basis of Take some magnetic field at the center is maximum here when r is zero and when r is u If you increase it then its graph will look like this If possible, grab a little bit of it sometime It should be asked because the paper comes crooked these days. if it seems difficult in your eyes then If you don't read it, you won't be able to handle it The story is set there. Now it comes Magnetic field at the center due to Circular segment. Now what happens is that the Take the complete segment of the current carrying coil Not found. Found a piece of it. on this too I get questions. Brother this whole circle is like this It couldn't be done. I only got this piece here From P to q. then at its center How much magnetic field will there be? So sometimes you These give the length of the arc. Sometimes this theta I will give it to you. Well, we know its relation Is. θ = arc / radius. theta in radians will be. So θ = arc / radius. we are from one You can take out another one. Yet I gave two I have created formulas that can help you solve the problem. So if you are given the length i.e. give this PQ Its length is kept and the current in it is I. So How much magnetic field will be formed at O? μ0/4π What is I / A² * L A? Radius is written. Yes this radius. And if we talk about theta, If theta is not given then angle = arc up You can compare the calculations with the radius. Then B is not μ0/4π i theta / A where in the form of theta. Now Look at it this way if you are told to do so Suppose this is a semi circular loop. like this There is no stick below. I do not understand this either Is. I will just remove it or if it is Even if it remains, it won't make any difference. But Still, I want to remove it here. These Suppose it is drawn here. these cm It is a circle. so you can tell on the semi circle So what is theta? tell me exactly You can. How much is this theta now? π This is a semi circle. cm Circle. Now if you replace this theta with π then it will be a semi circle Will come out for. Look, π is placed here And subtracted pi from π. μ0 i / 4 4a value If it comes out and it is a complete circle, then you will put 2π So if you look at that formula, the whole circle So what is the 2π angle formed here? So b How much did this swelling amount to μ0 / 4π i / r or a * 2π so if you subtract this from 2π then it will give a If it goes then μ0i/2a look there, if it swells then this will happen is very good fulla and in difficult situation this will help you out so you can catch it Please stay. hope you got clarity It will be. It is important to tell this. Otherwise you can read it all They will take it but will not be able to take it out. we are such want to teach easy physics with Arvind Sir and you were able to bring out the questions as well. You may feel that you are benefiting from reading it. Confidence is increasing. questions are coming out Are. So this is real fun. Otherwise, everyone has read it have been. Isn't it? So anyway, now this is a board Let us take more questions which have already arrived. Big Famous The question is. This question comes up a lot. very simple There are a lot too. Come let us see. So Here I am going to go from white to white now. Let's see. We would have redone it right now Are. I will change it later. too very small Identical circular loops. this is a number loop Is. Look at this and this is the second number loop As you can see. Both Identical means identical loops. Caring Equal currents I current flows in both It has been happening. As shown in the direction. right now we Again probably made photos. Place each one vertically. what does vertically mean Is? I tell you, please read this completely today. Vid Respect to the plain of the paper. These Look, this is the story. If not then I don't understand you will find it. Don't think of this board as a plane of paper Is. You write it on your book. Copy I write on it. But now it is like this here Is. So this loop is like this. Its Perpend this perpendicular. If you touch it now, it will be written there. So But you are looking at this, it is so perpendicular. And how is this second one? This way It is perpendicular. This is how you can understand 3D and this It is like this. Isn't it? both brothers are like this It became perpendicular. also perpendicular to this Done. so with their geometrical axis Because they have said that its axis And both its axes are perpendicular. So this shape or a configuration or arrangement It is in front of you. that you enjoy without understanding He will not come. perpendicular to each other as seen In the figure we tried to give clarity has done. It is written find the magnitude and direction of the net magnetic field Produced at point A point O this point It is O. How much magnetic field do you feel here? Will it be made and what will be its direction? Both I just have to tell you. So let's change this color. It is necessary and this color should be slightly light green Are. We had explained this. Now look here from here you assume there are eyes Yours. You are looking at it like this. Isn't it? so this See how this looks to you? Clockwise Direction. You are talking here. So When you turn the paw clockwise like this Magnetic field: Where will the thumb fall? here will come. This loop is clockwise. turn it on like this Given. so look at this B1 this is one this is one So this is B1 along this direction Let us assume that the axis is and its distance from the center is are X . He has given XX. And Similarly its distance from here is also X. And When you look from here, this loop also looks like this Rotating anticlockwise when viewed from above Thumbs up like this. So this is B2. Meaning of B2 This is the magnetic field created by this two. Both these magnetic fields are connected to each other Are at 90°. You can see this at 90 is on its axis and this is on the x axis And the axis itself is at 90. then both are 90° But it is. And what is interesting is that The magnitude of B1 and B2 is also the same. Why? Because there is an identical loop, the current It is the same and the distance is also the same. Because which there is a formula see this along the The Axis one we just read that if this distance is given by x and This is for r so everything is in this formula same is for both i same r same x same. So here b1 = b2. Now when B1 and B2 come Immediately I remembered or thought that When two vectors Two vectors look like equal vectors At one point their resultant The angle bisector passes through the middle. Two Same, whether it is force or anything else. So Here B1 being equal to B2 means that Their net effect will go right through the middle of it. center means angle bisector is 90 so this 45 and these 45, we have already given the direction Understand. You also understood. Now we further understand that B1 is equal to B2 We have explained this to you. Why? And B1 is perpendicular to B2. then how much is B's net Will be done? two which are perpendicular vectors what are their results? p² + q² Under the root, the vectors are at 90° Are. So replace this b1² and this b2 with b1. Then what is b1² b1² i.e. b1 2 and b net Went? We put this over the value of b1 Gave. then μ0 / 2 2 which was irr² r² + x²^3/2. Now! Normally sometimes written as 4π. These That's absolutely correct. but in books it is It remains written. So we have 2π on the bottom and has been multiplied by 2π. like you are this Don't hesitate after looking at it. hey sir this We had read the formula in a book or I have it. Something else is written. you are nervous Let's go. So these are 2π and 2π up and down. It has been multiplied. this is the Magnitude of the magnetic field. And What is direction? From angle bisector Will go. Like I explained. So π / 4 from The axis of the coil One is the axis from the coil One axis of π/4 towards the coil The meaning of 'towards' should not be understood like this. This way Towards the Coil and this whole thing It became clear. This has already come in bold And it comes often. so this is very very Comes in the category of important. Absolutely Don't have any confusion in this. Once, Repeat this two or three times and see Which gets embedded in your mind. then take note You take this. You can pause and take notes. Excellent. Let's move ahead. Now it is ampere Circuital Law. Ampere's circuital law is very This is a wonderful law. It is just the same as it is Gauss law is an alternative form of Coulomb's law You had studied electrostatics, right? What does it mean to speak alternative form Is? The work that Coulombs Law did there. Same Gauss's law can do the job. in four lines If a symmetrical situation is found then this There is a story. that is the work here Biosavart law works that is your ampere The law can only work if it is symmetrical If I get the situation. Well this is it This is a conceptual matter. Now about your issue Let us talk about writing this Ampere Law also. It comes. What? This is actually a line integral of the magnetic field of a closed loop It seems to be for. The first thing seems to be Gauss's law It was for some close surface. So Empier The law will be valid only when a closed loop is open If there is a loop then it will not happen. then someone Line Integral of Magnetic in a Closed Loop Field B.DL this ring that is formed is close for the loop and the current through which the magnetic The relation between the field is being formed Establishes it. two things here There are some important things which I would like to tell. Maybe some other teacher will discuss this with us Don't know. otherwise you else its concept if If you missed it then go to chapter number eight There will be problem in displacement current. Sir because we teach completely, so our Connectivity remains. which thing of Where will she fall? where will this bomb fall Of? So we want to teach you first Are. Like when those bombs fall, you say Hey, we already knew it. so that It will become a normal thing. Well the first thing I I request you that for steady current this The law is applicable. of steady current It means that if this wire is in it If the current is 5 amperes then with time it will decrease by 5 The ampere is neither decreasing nor increasing. Correct? Second thing is that whatever loop you take, this loop The current that is there in it, like here you This is how you are entering the current and you are in this area If you are holding it then penetrate this area When the current penetrates it, only then we can see it It is called I Net. I net means 2 The ampere is going like this. 3 amperes as such If she is going then we will do 2-3 or two Will adjust the direction of the current. And the important thing is that the area I This area has been drawn, it is not necessary to buy a flat Is. You can take any kind of it. bag You can also take it. I mean it's like a loop Kept the mouth this big. Now instead of a bag Let us make a pot. pot pot There must be a place where you keep water for cooling Are. Suppose we made the pot like this. Correct? So this is his bottom and this is his mouth It is equal to this. Now if there is any current till here She went and returned like this, suppose you see this If it is not cut then it will not be taken in I. Both of these are the same case. A flat here There is an area and this is its area. this is its Meaning area. So keep this in mind here how is this area in ampere law There is a discount on taking it also. will tell you more details So we will discuss this for 15-20 minutes. It is not entering more than this. so much in You will score 100 runs in just one go. Did you get the point? After having steady current, the mouth of the The close loop is kept the same. but the area you Can change. I have made this pot. You You can make a crooked bag. Anything Tiffin box was made in NCERT. This way We did not make it very well. something like this created. by doing it like this So the bottom line is that he kept his face the same. But unless its area is cut Until then the current will not be counted here. Correct? I hope you would have understood this. So How do they write this? Ampere Circuit Law Gives a relation between the line integral of a. This is called the line integral of a. The total net current. If the net current means Somewhere 3 amperes are going up to 2 amperes Below, by doing 3 - 2 I net you write 1 ampere I will give. this net means which produces the field which in the field She is producing it. We also present its derivation People will do it now. So remember this often You get asked and it's super important. I added the points because it is the same thing Displacement Current in Chapter Number at inside electromagnetic waves It will be used in the topic. I will learn it now So you can do it in a jiffy. Real This is the concept. So it is necessary to learn Is. ok now proof of ampere law brother We prove Ampere's law, which lives in the books. ask in exam Yes, we will do it too. very small There is proof and to make it simple we Log for straight current carrying conductor Let us prove it. and do the same in the exam It happens to you. then consider it infinitely Long Current carrying conductor in which current I flows It is happening. We will make a photo of you now Front. They just make it. this current is the carrying conductor in which current I flows It has been happening. From BioSavart Law, The Magnitude of the magnetic field B Due To the current carrying conductor. The magnetic field which is generated by this current carrying conductor The field is at a distance r from it, here it becomes form is given by how much this is becoming From this current carrying conductor r will be Keep the distance in mind as per Gauss law Gaussian Surface Hypothetical or Imaginary in R it could have happened in the same way as per Ampere's Law Ampere Those imaginary things that we call circuit or ampere loop It is possible It is called the Empyrean Loop. That closed loop thing or what you're thinking about. Correct? So here we have b at this distance r There is a magnetic field. The value of an s How much is it? of infinitely long wire for μ0i / 2pi r And this is how we created an Empiric loop, which It is made by you here. What is this? This This is the Empyrean Loop. Empyrean Loop. This needs to be a closed loop. here at The direction of the magnetic field is It will happen tangentially. You know the current Turn the claw like this in the carrying wire. This way A magnetic field is created. So Magnetic The field is also here. and its current element The dl vector is also in the same direction. Then, What is the angle between dl and dl? 0°. We understood this as well. Excellent. Now take out BDL Are. Get your BDL from here. So BDL's That means BL BDL becomes cos 0° cos 0. 1 0 Where did you come from? This was explained. so this The value became BDL, so BDL became this value. Now integrate the line of B here Integral. So this line used to be Line integral of B.DL. now write it down We have BDL cos 0 and here cos 0 was 1 and b The magnetic field is the same here. Here It is also the same. Same thing here as well because everyone's r is The distance is being maintained. So b is a constant r At a distance. so b came out and Integration dl of closed loop is done. So This value is achieved when this closed loop You will do line integration of length Along then its value will come to 2πr. so this What is b * 2πr and b? b is written μ0i / 2πr then μ0i / 2πr and this 2πr here this 2πr and This 2πr is cut. What is the value now? These See, the value is μ0 * i and write it here. Given line integral of b.dl = μ0 and this was Ampere's law. So this ampere The law has been proven. So this is proving If you get into the exam then do it in this way Please prove it. hope you understand You must have found it. If you want you can pause and take down the note Can do it. Let's take one step further Are. Now there is application of Empire's law to a State conductor. Now that is a state current Carrying is the conductor. there is empire's law We will calculate it by applying it. Basically, from the infinitely long wire that is The magnetic field generated is known as Ampere Law I am going to apply it and take it out. so here it is is a current carrying conductor. From this here We had to find out the magnetic field B. So we took an empirical loop imaginary jo this one needs only number one I called him number one. Now look here what Is? Here the angle between B and DL is zero. Because whatever is the direction of B, that is the same Bend the paw in the direction of thumb I. So Direction of B and DL in the same direction So this value became zero. So here B.DL = μ0 I net This is the Amperian law. Ampere Law means this Ampere's Law Will use it here. now theta here Between B and DL is zero which I told you That the angle between B and DL is zero. So BDL cos 0 is written in this BDL cos 0 cos 0 will become 1. These μ are not * I out of this. How much is going? if this area is taken Then the penetrating current is I. and this value is Look, B is a constant. Why Constant Is? Wherever you take R, B is the same everywhere will get. I am talking about magnitude. This magnitude is written here. Then B is outside went on and the integration was done by dl = μ0 * I now this The integration dl means that the whole length If you integrate across, it becomes 2πr. So V * 2πr = μ0 * I then what is the value of B Went? μ0i / 2πr is the formula that If the infinitely long wire is How far is the distance perpendicularly The magnetic field will be μ0i / 2πr This story is over and the number of turns if this The story is about the number of turns in this It doesn't matter. So it is completed that What is its application? now the next question Or as proving it is there in NCERT It is very important. so this is means as important as it is because You will understand less. This is so important. I will write it twice at least. very very Importent And you can write this four to six times more. Take this. So let's move this forward Let us increase it. this is basically the question and this It comes as a derivation. its finals The result is also used. So It is written Figure 4.13 This figure is very good Not there. Now we will make a new figure, understood? Let me give you that 1.4 4.13 shows a long stat wire. This is a long There is wire. It is a thick wire. pipe is visible somewhere Used to be. We cannot see the pipe. oh please understand this is a wire yes Cylindrical circular cross section of it Consider a circular cross section as rough it is a wire what is its radius a this one Look, the radius of it is written a We will also make a photo of radius a, just make it first so that you can understand wait a bit it is like this Understand that this is a solid wire, cylindrical thick solid and its radius is a Carrying Steady Current I Because Attention Keep the ampere law for steady current only Seems like Does not apply to varying currents Is. So the current flowing in this That I is the steady current in the wire. The Current I is uniformly distributed. this which The current is full of it All the material is uniformly present in everything maintains the distribution. Across This Cross section calculate the magnetic field in the The region r is < a r is greater than A then see r is < A means R is greater than A means when it is out of the radius of the wire bigger and r is less than A means when became smaller than the radius i.e. inside the wire So the crime that they have committed here For the one who has taken r greater than A Empyrean loop two is made in the figure and which The loop for that is the inside Empyrean Loop It was made inside according to the dotted line Is. Well now I'm going to take the first case where But R is greater than A. I am white colour would like to have. That is, outside the wire Brother, the value of R is greater than A. So It's outside the wire. See this photo. This is a wire and its R which is bigger than A then Those R's have arrived. And this dotted line that I drew I have told you that this is an Empyrean loop. One An imaginary closed loop has been created. Its We will use magnetic field To remove. Correct? So it is written Taking Empyrean Loop Number Two. this joe two It was written for this, hence I wrote 'too'. to is A. Circle. The circle of this is Concentric with the cross section of the Wire. so the center of this and the center of this is cocentric. This is a very good thing. Now for This loop what will happen to this loop? Its length is 2πr because its radius is r so Its total length will be 2πr. and this this How much current is included in the loop which is different from I Has shown. Current Included By The Empyrean Loop. All the current is from inside it I am going into this case now. So that I write Gave. Look at the value of IE for this I Is equal. Did you understand it well? Now we Let's apply Ampere's law. so B dotdl which Dot = μ0i net This is Ampere's law. So Here B is constant. now here you know that is the magnetic field and that of dl direction is zero angle on both of them will form. Because here also you do the same thing Let's apply it. So this is the magnetic field direction tangentially and l are both same In the same direction. So that became zero. i.e. if θ 0 is parallel to each other then b here bl cos theta so cos theta cos 0 cos 0 becomes 1 and b remains constant everywhere because this is r this is r this is r that r But you will get the same thing everywhere, so b is outside come to the integration dl = μ0 * i net and If we integrate this, we will get 2πr The length of the whole circumference is then b * 2πr = μ0 * I I net means the amount of current involved. Excellent. Now I have written this here. B's How much is the value here? μ0 I / 2πr for R is greater than A i.e. outside the wire When we are referring to . μ0 2π constant only occurs. If study is current then I too It became constant. So B is proportional to R. When we are in current, we are outside the wire. Please take care. Another thing came to my mind. I want to tell you that this wire There is current flow in the wire. So when current flows inside the wire There is an electric field. In electrostatics, you read that In electrostatics this There is no electrostatic current flow It has been happening. So in electrostatics any The electric field inside a conductor is always It used to be zero. but because when here The charge is running so electric is here The field is inside the wire. Magnetic Field So there is an electric field as well. Little If you read it then you will understand my point clearly. You must be getting it. What does electrostatic mean? This happens where the charge doesn't work. So when charging When on rest, some conductor The electric field inside is zero. But when charges are moving conductors then the electric field inside is not zero It happens. then the electric field is There is something inside and there is a magnetic field as well. These Try to understand a little according to the paper these days You understood the concept. These are 1/r The situation looks like a rectangular hyperbola It has been happening. ok now let's talk about the case Number two when your r is A i.e. wire Now you jump inside, then when these wires of wire I made it big and this one is small Empyrean Loop This Empyrean Loop is made r is less than for a. Now see Now Current Inclosed. Now how much will be obtained from this Empyrean loop Is current flowing? Now this I flow It is not happening. I am all over the wire. These The more pink or red color you like, the more you like it It is visible. the current passing through it It is less. So in proportion to this its area That we will divide the current. so here But the value of IE is not I. is less than I. How much is that? since the current distribution There's uniform in this wire. So the current enclosed is proportional to the sectional Area. That is, this area is It will become proportional. So how much is the IEEE Will you go brother? How much current per unit area Is? I / πr² πa² I was the current going. I Should I write this here? Which colour is in my hand? If I write it, you can write that in πa² If the current is I then in a unit area i / πa² So how much current in πr²? I / πa² * πr² this is Current is closed in this circuit. These Unitary Principles which are in class six or He must have studied in class five. Correct? So this current is Went. There is nothing special about the proportion of the same area No. I explained it to you because sometimes you are at quarter to If you go here and there then don't go. So I The value of is IR² /πa² now this is pi pi Deal with it lovingly. So IR² / A² no problem. I came out. it was necessary Because we have Current Include by Imperian We need a loop. so now using amperes Law. This is Ampere's law. Integration B.DL = μ0 * I net. now here B because b is constant everywhere. We have understood. And is aligned to L. The angle is 0°. Then, Went out. The value of dl and μ0 I which We had calculated this IR² / A² put here I did it. There is no problem at all. just a little bit You have to pay attention. Now this integration dl so this is now this one The perimeter or circumference will come. whatever You read it by giving the name, the issue is the same. These It became 2πr. now look at this here you can see this A square of r will be eliminated. so this The value will become μ0i / 2πa² * r This is the magnetic field inside the wire and when r is less than a ie inside All these values ​​are we talking about If a is constant then b is proportional to r a So this becomes a linear relationship, right? If the line is straight then this graph is very important hey son, now you should also ask about this graph that has been made yes derivation is also very important For you. So see it here inside Whose story is this? r is less than A and When is this from? outside greater than a to Linear relationship inside this and there B is proportional to 1 / R and this is its Radius here the value of P. So you can also Practice well. couple of times Rewind and see. You have to pay any Must come to Surat. Let's take it one step further. Now the talk Now comes the solenoid. So the solenoid Sorry, let me drink some water. Isn't it? I speak because the whole video is in one go I will record it. Stop We Let's move ahead. So this is solenoid. This The magnetic field in the solenoid That is b = μ0 ni. Focus here Keep this n as the total number of There is turns upon length. which is called On Linear Turn Density or Number of Turns Unit length. how much per unit length What is the number of turns? So this is the total number of Turn This is the total length. and on its edges This magnetic field becomes half of it. Look at this. Find the magnetic field of this solenoid No longer in the course. three to four years ago Was in the course. Extracted from Imperial Law Were. Now if it is not in the course then there is no need to study Not required. hold on to this that its The magnetic field inside will remain this and end Half of this and the value of small n at the point We have already told you and I means current. so this If we draw a graph then the value of μb will be at b becomes like μ0 ni and at its end point Yours is done b/2, this is its graph. for the solenoid. now a question comes up Which is quite simple. do it with love I will take it. Let's take the red color first if If I have to write it on white. then a solenoid of Length 5 meters. The length of a solenoid is It is 5 meters. has a radius of 1 cm What is the radius? 1 cm and is made up of a 500 number of turns. There are 500 turns. It carries a current of 5 amperes. what is the magnitude of the magnetic Field inside the solenoid? Now this is very This is a very simple question brother. inside the This is the formula of solenoid. In this So radius has nothing to do with it. These r Some had given 1 cm. So you are confused Don't come brother, I have given that radius. You have to use it. Just more in this This small n is not given directly. So small n removal method n / l n given It was 500 tonnes. and what was the length given son?5 meter. Divide it by 5 meters. When If you cut it, this point will increase by one zero will go and this 1000 will come. 1000 Tonnes per meter this turn density or number of Unit length on turns your n has arrived. μ Note Keep the value of. i have already provided 5 ampere As far as 5 amperes are concerned, keep its value. The question is over. So this story is a length 5 meters etc. etc. you saw the formula For the magnetic field in the solenoid b = μ0 ni n is n / n that's for you to explain It is written that n has become 1000 as you saw Remember to apply formula μ0 Bhaiya that μ not is like 4π * 10 to the power of -7 If you can do it quickly then this is 4π * 10 to the power -7 * 1000 and current value five. calculate it Take it. So 6.28 * power of 10 -3 Tesla Your answer has arrived. with great love You can ask these questions. If you want you can pause it You can note this down. Let's take a step Let's move forward. Now new topic is interesting It comes. Force on a moving charge in a Magnetic field. When a magnetic field If any charge moves in the force Experience does. When a charge is moves in a magnetic field then it Force experience shows its value and Both directions will be discussed. So How much force is required for that? qvb sin theta. The value of this charge is this charge now If it is in scalar form then we can say speed Magnetic field and theta becomes v and b the angle between is because the force is That is a vector quantity so vectorily Writing out the formula will give more clarity. Now This velocity is written here. Then, f = q.v. Now in this formula when you enter the value of q If you keep it then keep it with sign. Positive Charge If there is a negative charge along with a plus then With a minus. And you know this force If we recall that the bit vector v is Crossb That means this force is dependent on both v and b It is perpendicular. mention this as well I have given it. f is perpendicular to both v and b That is, perpendicular to the velocity and Also perpendicular to the magnetic field. with in q with sign plus or minus It will be put in. these special cases MCQs etc are created. if the value Take a charge in a magnetic field is at rest, v is zero so there is no force It will take place. See this, as soon as V you hold zero If you give F it will become zero. so rest charge at Rest in the magnetic field will not Experience any force. Excellent. The second if theta is 0 or 180°. If theta is 0 or 180 then sin is 0 or 180 If you put it here the force will become zero. So That is, if the charge is of the magnetic field If the person is moving in the opposite direction then no force will be applied. If the charge is in the opposite direction of the magnetic field Even if I am moving, force will not be applied. So Even if the charge is stopped, there is no force. Charge moving in the direction of the magnetic field or even if it is moving in the opposite direction No force. Good charging if running at 90° The most important factor is the magnetic field The strongest force f will be felt maximum. Correct? Keep holding this here. Now it comes How to find the direction of this force Should I go? A simplified version was created for this This is Fleming's left hand rule. but this Only then it becomes applicable meaning applicable tax yet still take it When you remove the component, your magnetic An angle of 90° is formed between the field and v because it looks like this yes you make all three of them into pistols and remember What's the trick to keep Father Mother Child F For father this is a trick, father means force Mother means brother, thumb is the strongest It happens, you can say father, this mother has become mother Because M is for Mother M is for Magnetic field and sea for child or current to father Mother and child can be remembered like this. but when Both of them are perpendicular to each other are magnetic field and velocity so these He gives force easily. And if this If you want to apply it in any form then whenever Whatever angle the velocity is making, its two You take the components. A component you Are you able to fight with me? I this I am saying that suppose such magnetic There is a field. if you pay a little attention to reading If you can find it then see. Now what have we Did? Here we put a v which is the theta angle He is making it. so this is not perpendicular How do we apply it? because if we set these If you do b then this v will not be able to be set Used to be. So we take the two components of this v Can be done. Let's change the colour to blue. take this Take v cos theta and take v sin Theta. now because v cos theta is equal to b if there is some force in the direction Experience will not do because Mag is now There was a discussion that if the speed or velocity b If it is in the direction of then the game is over. So this v cos theta becomes perpendicular. now here This magnetic field and this lift up v. So whatever is applied on this, the thumb will be towards the inside. If it is positively charged, then it moves inwards The force will experience this. So this is this You can apply it with trikam even if V and A 90° angle is not formed between A and B. Well I recommend you cross The product one. Because he is yours Can't get rid of it. mean what i say have I been? Did you read this formula V cross B So what's in it? Vector cross in it A rule has to be imposed on the product. put that on Game over. So whenever you do v cross b You will get a story that means force Direction. so always use the same Do it. v Direction of force from cross B Take it out. And if you make this arrangement then you will get out will also come. But it seems to us that this You should learn because it is written everywhere It will be found. anyway you must have understood that I have tried to explain. several children When this point comes to the mind of the person then we said Finish it now. ok now let's talk further that in your course is that the motion of a Charged particle in a uniform magnetic field Field. Now see the marks of Kattam in it They are looking red. So the magnetic field is that perpendicular to the plain of paper In the inside direction. So, I have placed a cross. This cross was placed like this. These magnetic Direction of the field. The charge which you make in this Suppose you have made an entry, then a positive charge Have you got an entry made or should we consider it positive now If you see negative in the formula then No, you have entered the positive charge at 90° from magnetic field i.e. the magnetic The direction of V in the field is Is 90°. That is, this magnetic field is inside So V is entering like this. The magnetic field is If it is inwards then V is always 90° He is making it. from the magnetic field then this There is a story. So suppose a charge + q Projected Normally to the Magnetic Field. This is the direction of the magnetic field and this is the direction of v which is Perpendicular to the magnetic field. That time What will happen? Charge Will Experience a Perpendicular force to v and b. you know there will be a force inside it which is equal to v and b It will be perpendicular to both. so how much is that will be? f = qvb since qvb is sin theta but sin will become 90 because v and b of 90° between There is an angle. Now here this force f moves the particle In a circular path. This is the force which is v Both k and b are perpendicular to each other. This Because of this it will rotate on a circular path. So these charged particles are going round and round He will kill me. Now, I ask you a big question on this. that if it goes round and round then its radius Tell me. We will understand it now. now this magnitude lawrence force this magnetic Lawrence Force. This is the force that It is magnetic. This is called Magnetic Lawrence F says it. This will offer centripetal effect. This is the force to go round and round Offering you Centripetal F. so mv² /R which was centripetal flow. This Q.V. Meeting with Magnetic F. We have equated I did it. After equating, see this: One is cutting through a v. So take out r and This mv/qv became a formula. This If you want, you can memorize the formula. This But many questions are made of one mark each Or they also come in second number. But this story This will happen only when the charge is a perpendicular entry will do it because of the magnetic field. these meditations Keep this in mind, we have written it two more times further. Now Look, we have to find out the time period for this How much time does it take to complete the round Is? So the time period is circumference / Speed. So the circumference becomes 2πr speed It's done v. Brother, this total distance is 2πr. Speed It has v. So this is 2π / v. In place of this r This r means radius, this is the radius We have put the value. mv/qb. now here But this v and this v got cut. so what is the value Went? 2pm/qb. Now the interesting thing about this What has come in this time period? In this v Not there. That is, no matter how fast you Make an entry, no matter what the speed The time it will take to make the rotation Has nothing to do with speed. This talk Please take care. Increasing the speed increases the radius will go. But the time period will not change. These Now the time period will not change The frequency will not change. Because The value of frequency is 1/t corresponding to The opposite of the time period. So this is qv/ 2πm It happens. so this frequency is Independent From v. That is why its name The cyclotron frequency is inserted. One more topic would have been very important There was a cyclotron. Now that's in your course No, three-four years ago in the course Was. But its name is of this frequency falls at the cyclotron frequency. and this Velocity independent of speed it occurs. And keep this whole story in mind Ramayana is when the charge is projected is perpendicular to the magnetic field I have entered normally. If normal entry If he doesn't do it then we will talk about that too are going to. So when a normal entry is made then Will follow a circular path. Its radius is, Its time period and its frequency These. Good, I think you understood the point. Now let's do the next thing, suppose this Does not make perpendicular entries. He does it at an arbitrary angle. means instead of 90 Someone else catches the angle. So at any angle Let's see if it makes an entry on Theta. So this The trick I told you to solve the question You can divide this V into two components. I Use any color blue or dark blue here I would like to do it. I will take this. Look at this This is the direction of the magnetic field. These And this is V. We have completed two components of this V. One We took the component of the magnetic field In the direction which is written as V parallel. And Perpendicular to this magnetic field I have taken V perpendicular in direction. Now this V parallel magnetic field If the force is in the direction of then no force acts on it He won't do it. whichever force commits which crime Force Experience Will Charge V He will do it because it is perpendicular. So the one behind We did the scandal where we took V Replace V with perpendicular there. All work is finished. because that's the same role who is playing the role there, he is playing the role to the fullest Was. Well, we'll divert the question now. Which you can understand. The path here is Instead of being circular, you will get a helical path. What is a helical path? Spring type Path. Like I kept one here To show it, consider it like this Spring like path. Because this V It is perpendicular, it will rotate round and round and V Will take it forward in parallel. both cases together If it is there then it will move forward going round and round. So It will keep increasing like this. that is the language of physics I call it the helical path or Spring like path. don't write like spring Please give it to me. Please write helical. to your teacher You will like that only. This is the story. Let's see yes by deriving. so now we can be Resolved into a rectangular shape Components. V Parallel V Perpendicular like I taught you. So V is parallel along Magnetic field V cos theta. this brother this If it was theta, then this became V cos theta. and V Perpendicular to B then this V is perpendicular Vsin became theta. You could also understand this. V parallel unexpected by B I told you this Because it was under the direction of B. but due to V perpendicular charged particle Experience a Force. Because brother this V Force will be applied because of perpendicularity. They How much will it cost? magnet magnetic lorenz Force f = qv perpendicular * b then this Force makes the particle in circular motion. Now The value of r becomes mv perpendicular / qb which It was taken out backwards in place of the same v Perpendicular has come because that is the role now This is being fulfilled and here the value v Perpendicular's vsin theta so here The radius that comes out is mv sin theta / qb. These When is the story from? When the particle is B Any angle accept less than 90 if in this If you put 90 then sin will come to 91. so the same thing It will come. So you can make any arbitrary angle This story will continue when he is entering. Radius She has come. Time period 2π/v perpendicular. So this will come to 2π m / qb. There is no in this The change did not come. Correct? in the same way You will reverse the frequency of this. wrote If it is then it is good. helical path is what we understood have been done. The axis of the helical path will be She will be along. i.e. B is on its axis will remain. This is B so it doesn't rotate will find it. It will stay inside it. This too It is important. no helical path where are you You will not be able to understand. frequency corresponding to t reverse it to 1/t. now a term in this Here comes the pitch. What is that pitch? pitch It happens that in taking one round this the magnetic field is rotating in one revolution How linearly in the direction of the field where has this particle moved ahead direction is in the direction of B then one A dizziness such that even before completing If it is increasing then how much has it increased linearly This is what you call pitch, I have given this definition it is also written as so that in the exam I was even able to write it down, the formula is also in front of you that the linear distance travelled by the charge particle in the direction of magnetic Field During One Revolution In which direction is the magnetic field It is in direction and you will call it linear distance that is known as a pitch and pitch ka what happened to the formula v parallel brother this velocity into time period in one revolution one time at a time in taking one round It is taking time, multiply it by that So v parallel * t and v parallel was your v cos theta Look at this. so here is the time in period you convert v cos theta into 2π m The formula of this pitch was multiplied You can also remember to remove it quickly For. This became the story. Keep this in mind. These When is the story from? Any arbitrary angle When the charge entry is made. this clarity It is made from here. This is very important. You should come 100%. Let's move ahead. One The important question is here for you and This is also a question of the board. So big It is important. This must be done in a better way Let's do. It is written a A long state wire AB carries a current of 4 Ampere. This is a wire. It has 4 amperes The current is flowing. that is I Ok? A proton P proton positive It gets charged. Travels at 4 * 10 Keys Power 6 meters per second. at such a speed parallel to the wire There is a positive charge at a distance of 2 m which is It is made in the photo in the direction. such moves Doing parallel to the wire. in a direction opposite to the current as seen in the Figure. We saw it in this. Calculate the force which the magnetic field due to the Current carrying wire exits. This current There is a carrying wire, how much force is there on this charge Will you exert yourself? and on the proton also Specify is direction. so the direction is Let us end the game now. Any It is not a matter of problem. So for direction So look, this B here is this P point But where will it create the magnetic field? We have this Thumb in the direction of the magnetic field He placed it and folded his paw. then the magnetic field Where are you going? Inside. then the magnetic field The direction of the arrow became inwards. this is The direction of magnetic field. Excellent. Now where is the magnetic field and motion of charge Is? Here. So here is Fleming's left Use a hand rule. the magnetic field inside It is on the side. this and the charge positive going down Is. You can see it like this, right? Fleming's I have to take your left hand. I want to make a gun. all three thumbs and four fingers and which one Finger? Make your middle finger in a 90 degree position Is. What to do after that? Magnetic If the field is inside then the finger is inside and this was your This is the child or positive direction current Down here this force seems to be felt from a distance That is the direction of the force Away from the wire 90° to the wire Away from The Wire. So you can decide the direction of the force Got it done straight away. Now only one, now how much force This is left to be taken out. So magnets Magnetic field due to current carrying wire Because of this mag is current carrying wire The magnetic field that was being created here How much is being made, use that formula Give μ0i / 2πr Whenever you are told to wire, you don't need to go anywhere until You will hold the infinitely long wire only, right? So μ0i / 2πr is the magnetic field So you will calculate μ0 / 2π as 2 * 10 Power-7 has a value of 4π * 10 2π 2π kata 2 * 10 to power of -7 And what is the value of current? 4 amperes and How much was this r? It was r 2 meters. Now this Solve it. 4 * power of 10 -6 Tesla. This value is the magnetic field of. Now brother how much force does he have here Will you experience it? direction of B Perpendicular inside the plane. we gave you this I have already explained it. and required force How much will it be? QV sin theta and theta here 90 because the magnetic field is inside and If the velocity of the charge is here then this is the direction and the inside direction inside and this If it is perpendicular then this sin becomes 90 i.e. qvb is equal to q found in proton charge i.e. 1.6 * 10 to the power -19v So 4 * 10 to the power of 6 is this and this is v. I went and the magnetic field increased to four degrees The power of 4 * 10 is -6 sin 91 So we have one, now solve this 25.6 * Power of 10 - 19 Newton, this is what you got We have written the required force and direction hey di I already told you that force on proton will be away from the wire AB this wire AB It seems like an away force. So this is the whole question Your end is here. It is important. has come on the board. You can pause and note this You can take it down. Let's move on. Now is the force on a current carrying conductor in a Magnetic field. Now as you know that When current flows inside a wire then Brother when current flows then it means charge flow It is happening. So when the charge is in motion When force is applied then current flows off If there are charges then force is generated due to current flow It will take place. So I extended the story of that She goes. So let us see when a conductor In current we made this figure magnetic The field is shown in the z direction. i this Showed in direction y in direction And the force is shown in the x direction. The same formula seems to apply to direction The Left Hand of Magnetic Lawrence Fleming Ruley father mother child wala. Correct? If If you apply it, you will see this magnetic field Is. This is the direction of the current I and this is the force So, this seems like a force. the same formula looks The same direction will be taken. And What happened to the formula? f = iblb sin theta. And because force is a vector quantity. That's why this formula is the best For information. f=ILB. this is l's Where is the direction? the direction in which Current flows in it. so this is theta Between B and L and also the one belonging to L The direction will be in the direction of the current will be. So you understood this thing and if theta is 0° It is as you can see. So be the force It will go to zero. i.e. theta of the current is zero or 180 Either one. So if this current direction of current in the carrying wire in the direction of the magnetic field or If there is a force in the opposite direction, then Will not experience current carrying wire hold this if theta = 90° then The maximum force applied will be equal to ILB will be. This is the story. now direction of force How does it happen? Fleming's Left Hand Rule From. Now, we can use this formula which has come out People will do derivations. This derivation is also big It is important. And see how easily will conduct. There is a big key point in this This is where you can go wrong. that we too You will get very easy physics with Arvind sir I will explain it to you. let's watch. So look at this The current that was flowing was in this direction is in. So where are the electrons running? Will it be? in the opposite direction of the current. of current of conventional current in the opposite direction Let's take directions. this electron moves here have been. and how much time does the electron have to travel Is there speed? Drift Velocity. running from vd Are. So the magnetic force on each electron We just read how much force is there on one charge Seems like? QV sin theta and also write it in vector form I will give. So here the magnetic force is How much will the electron cost? That we have small f is written because the force on an electron Is. Here we write the charge qv cross b Were. Instead of q - e is written with with sign It is written. minus electron means minus and which is charged. and this drift velocity off electron vd cross b no problem Is. Now let us assume n to be the length of this conductor. Free electrons inside unit volume. Inside this conductor, small n free electrons present per unit volume Are. So brother how many electrons in it Are you present then in this conductor? So that's the total Number of electrons will become small n* Total Vol. because in one volume Small was n. How many are there in total volume? So what is the volume? Its cross section area a and its length l * l then this small n * al Now because an electron has so much force and there are this many electrons then we call this If we multiply this force then the total The force will come on the conductor so the total force on the conductor f = n * f sibling There was so much force on the electron and so many Everything is an electron so if you experience force All forces are multiplied by n Now here nl this when na this then scalar Quantity put out and this -v cross b I wrote it down. Now here's an interesting thing We are going to do what you will see now. So Here it is, look Ena This E here is also charged with E. Scalar Is. E pulled out L in focus here Please give it to me. l Please pay attention to this point. I should make this below E. like yours Looked there. This is below E so E and L We made the exchange. No problem now till. There is no problem. Now a little here We will struggle. I am writing that trick here Am. see if I write here ah one I write lv d and I write it here v d * l then there is no problem in this. a * b = b * a No problem yet. But if I start using it vectorially Should I apply the vector? Look here you Let me explain. Suppose here the vector i is v and here I am applying the vector on L Am. The magnitudes were equal. So in this VD The direction of the electron is here. And which direction is this L? Current The direction of which is here. So these two In direction a VD is here, L is here. So Here we have to replace a minus sign It will have to be done. Whether we put it here, whether we Put it here. The matter is the same. catch the point I am coming, what I am trying to tell you We are doing it. So these are in vd and l Due to the difference in direction, one Put a minus sign. and this is what Let me write Ramayana here. you don't write Write it down, I understood that I gave it like butter Is. Isn't it? If you want I can do it again Look, I will write it down. many children very They get confused. is there any confusion in this Not at all. And it cannot happen, and I will not I will not give it. See what I wrote? LVD And I have just written VD * L, now no one There is no problem. A * B = B * A great. Now Because the direction of VD and L is different. So if I put the vector over a VD. Let me plot the vector over L here. so this It is directionally opposite. so a sign here Put a minus or something here somewhere It will have to be done. We put it on. Now this equation Is equal. It is written here that IL Represents a Current Element Vector in the Direction of current. where is IL? in the current Direction of current. Then vector L and VD R in opposite direction. Brother this is L's Vector and VD vector in opposite direction Is. So -LVD = VD * L which I have written here Tried to explain. Now we will call this -LVD as VD * Will replace it with L. Focus here Please give it to me. Now here ENA VD this which this which The value was here we wrote it as VD * L Gave. VD so here without a vector There is quantity. There is no problem. Now this The value becomes ENA VD LB and we know i = What is ENA VD and ENA VD? This is i. Now i Comment here. Here, F = i and l crossb now you can find out this formula were trying to. this is your derivation Came out here. Take a note of this. It is an important derivation and like butter Got it removed. there can be no confusion If you are listening to me carefully. These I told you about the direction of force Fleming's Left Hand Ruley pictured It comes. So there is a positive charge There was direction. There was a power surge here. The same Father Keep using Mother Child. Fleming's Left Hand rule. Now comes the force between two Parallel current carrying conductors. This is also big It is an important topic. just like butter We will understand this also. So look here if there are two parallel wires are infinitely long and both have current If it is flowing in the same direction then There is attraction in this. Parallel Current Attracts same direction current. and anti Parallel Current Ripples. Here, if the current If the direction is opposite then there is repulsion It happens. We will now understand how it happens People. So this parallel attraction is the same Current in the same direction Current of attraction and opposite direction See, let me show repulsion. The value here It is determined that on one unit length of it because it is very long, infinitely long There is wire. How much force per unit length Seems like? So the total force that seems to be Let's assume we are talking about the one that is written f2 then f2 is the total force from its length Divide it. So this value is μ0 I1 I2 / 2πr and this force is equal to These forces F2 and F1 are equal. Creates action reaction pairs. As much F1 Force F1 Experience Will Be As Much As D2 F2 Only F2 will experience it. both same force I will experience it. bus direction opposite It will be done. then f1 = -f2 on both the wires There are equal opposite forces. its derivation is also important and question-wall also comes That's what you have to hold on to. remains very simple Is. Let us see its derivation. Now this Here we are taking the first case. Value take current in same direction Is. So because of this f1 here there is magnetic In which direction will the field be? So we do you know that the thumb which is like a straight wire The way to find the magnetic field for Keep the thumb in the direction of the current and the paw Turn it around. So this claw is going inwards See. So what happened? Magnetic Field Made the direction cross. now this cross This current is flowing in now. So the current Carrying conductor in magnetic field Went. So magnet Fleming's left hand Put a rule. This magnetic field was felt inside And the current is going up. The thumb is here. These See. You can see this thumb here, right? So This magnetic force was applied. and this is the scandal You can get it done here. look ahead, it was not made I have not made it, I will explain it to you. So Now look at this, this probably wasn't made Is. We will explain it now. then move on Are. Now suppose that because of I2 here The magnetic field has to be removed. so we are right Take the hand as if you are taking out the right hand. He grabbed his right hand and started slapping me. So How did the magnetic field form here? Such B2 Perpendicular because of In the outward direction. now the current on this Carrying conductor in magnetic field. So Apply Fleming's left hand rule. so this What happened? Magnetic field on your side, current On the top. So where is the thumb? this thumb on the inside. So this is the direction of the force Went. Hence attraction and this concept If you put it here you will get repulsion. Correct? So this magnetic field here Produced by I1 because of this here Magnetic field is created, its value How much is it? μ0 / 2π I1 / R Now the current carrying wire I2, this I2 wire if it is in this magnetic field then this will Experience a force so the value of F2 is will go to I2 LLB which is the formula ILB sin theta then I2 this current LB1 which is magnetic field is created and because this magnetic field And the angle in current is 90° so sin 90 Now this i2 will replace lb1 with the upper value Look, μ0 / 2π i1 / r and this is sin 90 It means forest. very comfortable no problem No. Now look what happened here? μ0 i1 i2 / 2πr this value is taken into L this L Take it under F2. this F2 / L and this value So what is μ0 i1 i2 / 2πr and what is F2 / L Is? force per unit length which is called small f2 have been. and similarly for the second one when you go for f1 If you figure out the formula for F1, you will get the same formula will come. See the same formula for both The beans are coming. This 2π is missing below In this. 2π this same formula is coming. So f1 = -f2 and this is your story. This is important. Remember this. these ripples Attraction and repulsion are also asked a lot Is. You can pause this and note it if you want. Take it. Let's do a numerical analysis of this We are busy now. so here for the numerical But let's hold on. This is the question. Two Long and parallel state wires A and B two The long ST & B are current carrying wires In which one has 8 ampere and one has 5 ampere The current is of. Let's make a photo. 8 in one ampere and one has 5 ampere beta current Is going. In the same direction. Now the beans If there is direction then tell me what will be the attraction Repulsion? Comment, pause the video and Comment. There is a current in the same direction. Repulsion of attraction 1 2 3 attraction same The direction of the current in which You get attraction. are separated by a Distance of 4 cm. The one between them The separation is 4 cm. Is. estimate the Force on a 10 cm. Section 10 cm. The section of wire A is 10 cm. on that The force has to be removed. then the force on unit length Will take it out. He gives it 10 units per unit length. Cm. Multiply it by. So 10 Cm. The force applied on it will come out. Now If you want to write on black here then take white Let's take it. Now look at this unit on force What will be the length of each wire? That formula is μ0 i1 i2 / 2πr so μ The value of the note was kept as 4π * 10 to the power -7 i1 i2 8 ampere 5 ampere so 8 * 5 and this 2π remains and r becomes 4 cm so 4 * 10 If you cut the power of -2 from this then this will happen and 42=8 then 54=20 so 2010 Power of -5 0 Kata Power of 10 -4 Very Very In simple terms, this becomes force per unit length. Now We don’t have this answer. We need 10 cm. I wanted a piece of it. so force on 10 Cm. How much will the section be? This f Multiply small f by l. So 2 * power of 10 -4 this is what came out and this Length 10 cm. change it to meter Take it. 1010 to power-2. Now this Calculate it. 2 * power of 10 -5 newton Your answer has arrived. Look, any problem Not there. You can take note of this, pause By doing. I hope you have understood this. And the force will be of attraction. this we give you I have already explained it. of the same direction There is current. Now you have this definition separately here There is a mention. Definition of 1 ampere. These it is important and this is there are definitions, one of them is this You are also asked to write about it Definition. So let us understand. this which I had read the formula, it is derived from this. See in this if the value of I1 I2 is 1 ampere do it And make the R between them 1 meter So this value of F will be μ0 / 2π whose The value is 210 to the power of 7 Newton on meter. What was the small F? On Newton meter. This is what is being said in the definition that two infinitely long wires are being taken Are. The same current is flowing in it. Those infinitely long wires are negligible Negligible cross section area. in Both wires are placed in vacuum 1 Meters away. now on this if at that time Unit 2 on Force * Power of 10 -7 Newton But the meter is installed, so there is flow in it The value of current will be called 1 ampere. This is what is written here. again you get this Let me explain it word by word. So 1 ampere Is that the value of steady current. Steady Meaning it will not change. 1 ampere vo value There is a steady current which keeps on flowing in each of the two wires parallel infinite Long Conductors of the Negligible Cross Sections that are long are infinitely long Conductors are of negligible cross section The current flowing through it is called 1 ampere. then I will say Placed in vacuum when placed in vacuum done at a distance of 1 meter when 1 They are kept at a distance of a meter from each other Products Between Force 2 2 * 10 Keys Power -7 Newton per meter. When these two are one 2 * 10 to the power of 7 Newton on the second When the meter starts applying force then the current flow she must be doing the same current in both of them we will do 1 I will say ampere. So you remember this Please take it. This is a theory to try to explain it. There will be no fun in repeating it again and again. So you understood this. now the current loop edge is a Let's talk about magnetic dipole. this which This is a current loop of a magnetic dipole He acts like that. Meaning of Magnetic Dipole As there was an electric dipole in which There used to be North and South. So even in this It is north and south and its magnetic There is also a dipole moment. So this Magnetic dipole moment is represented by small m Let us represent you. These vector quantities and its magnitude is ni n is the number of turns in the loop i is the current key The value a is the area vector The area is the area at this time and when the vector we will talk about vector and this is its How to find out the direction? That Current is flowing in that direction. Right Take the hand and move the paw in the same direction Turn it like this. then give the direction of the thumb Gives the direction of m. Look at this. then this is the direction of m and m = ni N cap. N cap means area direct area Normal to the same direction as the vector Follow the plane and right hand cross rule While doing it. i.e. the area vector is in direction then m = ni and complete If we look vectorially, then m = ni n cap then Current carrying loop as a magnetic dipole act If North and South do something then it becomes one How is North on one side and South on the other and North-South Let us find out, we have explained this also. North means the place where anticlockwise current and south means where clockwise Be current. This means South, so North South It will definitely be done. If you look from above, this is You have to go anticlockwise to North and down It became South. Correct? Now a very important thing that torque experienced by a current Loop in a Uniform Magnetic Field. These A North South Uniform Magnetic The field has been developed. The current here is a What will we do? Current Carrying Coil Will put. Right now we are putting in a rectangular coil Are. He experiences the force. They It turns when current is applied. So it is written torque Experienced by a current loop in a Magnetic Uniform Magnetic Field. Keep in mind that this formula is a Removing the for rectangular loop But in general all these are loops upon loops upon loops It works. whether it is circular or As it is, roughly. Isn't it these Generals? So The formula will be derived for the rectangular loop He will work for everyone. so how much is this Do you experience torque? niba sin Theta. This theta is the angle between what? These Angle between theta B and the area vector Is. and because we have told this to m that the value of m is nia then nia If you mix them then m will become cross b. So the torque It's m * b and m = nia m is magnetic Dapol Moment. Torque Maximum Several Times You are asked to take it out. then niab Because what will be the maximum? when sin theta sin becomes 90. So this torque is maximum The value will be . Let's take a look Its derivation and also how this torque is obtained Is. You should grab this as well. so it is written here has shone in the figure consider a rectangular Look at this coil pqrs, change the color a little will be. this is a p q q r s this rectangular There is a coil. Suspended in a Uniform Magnetic field B. This is from North to South The direction of the magnetic field is B which that it is not changing. Uniform Magnetic The field is there and that is all that is created. with it Axis perpendicular to the field. Its which This rectangular loop is the axis The axis is at 90° to this. Excellent. now theta What is? Angle between the direction of B And normal to the plane of the coil. These Call it area vector. this is normal Look at this area vector with direction and This is the angle theta between B. A And B R Sides. Here, A is this side of it is A and from here to here its length is breadth Whatever you want to say, this is B. and the current is How much is flowing inside? I Current Carrying If there is a loop then current must flow In this. Now according to Fleming left Hand rule the magnetic forces on Sides PS and QR this is PS this side and The forces applied on this side are equal The ends are opposite and are collinear Are. their collinear mean which There is only one line of force. So these Both of them have forces on each other I cancel it. i.e. the net force PS and will become zero at QR. because a force Suppose it looks like this and a force looks like this It seems. So what will you say about them that both Equal opposite is along the same line. If The force feels like this and like this then along the You don't say the same line. Meaning it is definitely parallel but at the same place But it is not along the same line. So this They do not get cancelled. if made in different place If you were there you would have done torque formation. So In these, which are equal and opposite on PS and QR are forces and are also collinear. so that will be cancelled out. Now let's talk On the other two sides i.e. the sides of PQ and SR But what is visible. now see forces on PQ and RS are equal and opposite but not Collinear. Brother the force being applied on this PQ yes it is on the top side. You are Fleming's If you apply the left hand rule then you will see Will go. This is the force. this magnetic field And this is the direction of the current. Thumb It's coming out on top. So this force It seems to be here. Look, the current has reversed. So The force was applied down. Look at this force and Look at this force. then both are collinear Not there. There are definitely equal opposites. But one he is not going along the line that a Cut out the other one. So this is torque for couple We will do the formation. will create torque. So These two do not cancel out. These Let's create torque. now this is its top There is a view. So keep your eyes here And watching from here. then this line to you It will look like this. These So here you see the meaning of M and B M This is M in the normal direction and this is B went and here this current down means this which There is current here, if you look from this side then it will go down If you look from here then you will see at this end Down at this end, up, this down and this up, you see It has been happening. Now the formula to find the torque what happened was that because both are equal Forcers appear to be in place. one of these forces Force into perpendicular distance. so here So we drew a triangle here. Dropped the extension line from here. These Made 90. Now we need this distance. So Look, this is a. This is theta so a sin theta. How will this be theta? If you want it to Increase it like this and calculate it Can be done. See. now this is theta so this The angle will become theta. now this angle this theta This is theta. So this is 90 - theta. this was 90 so this How can you do that if you want to find out theta? Correct? So if you look at this triangle, is complete arm A this theta so this is A sin theta So Force * Perpendicular Distance Force How much is it? ibb ibl happens, right? So what is your length? Is? b then i b * b and d becomes perpendicular A sin theta. now here ib and b * a ab What is sin theta ab? ab its area if it is length * breadth then you can write it here are iba sin theta nice. Now if if there are any two numbers in it then multiply it by n Give it. niba sinta and you write it as n ib can we write m ni m so this mb ssin theta or msv this formula is proof If you go then keep in mind that this torque We calculate this torque for any loop It will be valid for current carrying whether it Whether it is rectangular or circular, it is expected Let's understand this very well I might have come up with a question next time, look at this Let's take it. the maximum torque Acting on a coil of effective area 0.04 meter square is 410 to the power of -8 Newton meter. The value of torque is given here Is. Very easily. See the torque is given Is. And this area has also been given. These Maximum torque is given. Please take care. What is the value of maximum torque? n I A B n there is one if there is only one when that current in its its current i also give has been kept So find the magnetic induction It is kept as the meaning of magnetic induction magnetic field so here you can see tau max you know if we try to find out b so tau max /n so here is one so you i * a can you write the question is finished I Max The value of was given ah 4 * 10 ^ -8 4 * 10^-8 and what was the current inside it? Current Is 100 milli ampere. 100 * Power of 10 -6 And what was the area? 0.04 Now I have already solved this. Otherwise You will take it out in 2 minutes. Tau I have given it to you Max. b has to be taken out and here kept the value. Look, I showed you. This We will solve it. This is your Power of 10 -2 Tesla or Weber per meter square your The answer has come. This matter is over. Now its The next segment which becomes the question number five These are five mark questions and many of them Things get made. One is a galvanometer. Then there is the convert off galvanometer. all this There is a story. Anything can come from anywhere. A big question number five may also come. Come Let us quickly understand what a galvanometer is. Do you understand what happens first? so this The device is detection and measurement of the Small Currents. So, one finds out that The current flowing in a circuit is No detection. and along with that it It is a measurement that can measure small currents. If large current is applied to measure The one with ampere ampere will blow up. His For this, an ammeter has to be made which is a galvanometer We convert it into ammeter. So Normally this is almost impossible to measure current Comes. This comes under detection of current. Correct Is? Did you understand? The second is its principal It is very important that you ask in the exam are asked. So what is the principal? These Look, this coil is attached. So whenever the current Carrying Coil These uniform magnetic fields are maintained It experiences current dependent torque Is. The more the current, the greater the torque. Because of which this coil rotates and It deflects. With this coil we Pointer markers remain placed. So when this When the coil rotates the pointer will move and the reading will be We will get it. We will also go into detail about this I will understand. So you should remember this principle Please take it. Let me explain it once again. One This coil is the current carrying coil. This from above It is visible because you are looking at it. Isn't it? Otherwise, we will show you such rectangles right now. Rectangular. contains the frame and Tara you are wrapped in such a way Chakor-Chakor. then the current carrying coil placed In a magnetic field. This Current Carrying There is a coil and it is placed in a magnetic field Has been done Experience a Current Dependent torque. of Current Dependent Torque This means that the higher the current, the More torque. which tends to rotate the coil end produces the angular Deflection. It will apply torque to it and this It will rotate the coil like this. so when you rotate it The pointer that you have added is the marker, the arrow It will turn around. This is the principal. this is Variant for your exam. number five Let us ask this in the question. sure In this way you can understand. Now its us We will do the derivation now also. this is the alpha Angular deflection. this pointer is moving He has traveled so much, he is the alpha. so this The alpha is Angular deflection. Angular I am writing this deflection because both he looks like alpha type and this This is the sign of proportionality. Proportional As you can understand, one thing is not written Is. So this is angular deflection. this alpha Proportionality to current. So you will see here Al, we will prove it now. alpha = nba / k * i n is the number of turns in the Coil. these are the ones that are twisted and wrapped like this Insulated wire. B is the magnetic field which that once the heat is created then it will be fixed Has gone. The area is its cross section area Its area is of this coil and K is Spring Constant. On top of this, this That which is wrapped round and round is a spring. right now we I'll tell him who's going to bring the thorn back It works. Provides restoring torque. All this thing is fixed. once if You made the galvanometer and kept it in a box I did it. The company made the meaning and gave it to me. So there is no change in these. Brother in coils Can't change how many wire wraps you make. change magnet Can't. You will not change the area, you will change K No. Only I you will change to measure. So Alpha which is linear dependency I show He does. What is its benefit? That You get linear scaling. Linear What does scaling mean? Linear Scaling means that if a food is 5 is it showing ampere or is it showing 1 ampere If so, the next one is also 5 ampere show or should I say one food will do 1 ampere then every Eating one-A ampere is very easy for you to measure You can mark everything accordingly and it will be less Or there is no need to do much. So It is also easier to take these readings and It becomes easier to handle or make it Is. This is called linear scaling. These When does it become possible? When the alpha is angular Linearly from the deflection current Let's call it directly proportional. Directly proportional as much as I Alpha is directly proportional. So This is the story and K is Spring We call it constant or torsion constant This. Let's talk further. could understand You? Now let's talk about its construction I will take it son. So what about in construction? Let's take a frame. this which this It is visible in top view, this is a rectangle take a frame which is made of aluminum Is. Understand this way what happens to aluminium It is non magnetic metallic. These aluminum It is normally non-magnetic and metallic It happens. metallic because it has eddy current Made. If eddy current is not formed, then when it The needle will move, so when you take the reading If you go, it will shake like this. it is called Beating galvanometer. there was a parade If the army has beatings then You will have to wait. Assume the weight You are sitting to receive it. well this is the weight There is no use of taking it. and the thorn that that used to come of old That weighing scale is shaking like this. So you will have to wait, brother, you Wait so we can take the reading. But when eddy current is formed here then this The fork stops with a thud like this and Take the reading immediately. it's called Dead beat galvanometer. not getting beaten Is. It is not moving. So Dead Beat When will the galvanometer be made? When Eddie Currents are being generated. When are eddy currents formed? Is? When metallic frame is used. of metal Current starts flowing inside. and that Lens follows the law. That is, because of that She opposes the thing that she is becoming. So they oppose it. Understand this much, Eddie Current is not in your course. but here But you should memorize this much because the exam Let me ask. the second two ends which Are from Excels. This one and this one and that the one below because one above one below The one. There would have been a spring on it Is. Look at this, this is SP Spring Spring hair spring is phosphorus Of bronze material. Meaning of hair spring has a very thin spring one whose very It happens less. There is a thick spring. You must have seen it in the wheels of a train There is a very thick spring attached. yours which Shocker is your seat if you ride a bicycle So there is a spring in the seat below the bicycle too It is attached. now in today's mattresses If it didn't happen, I don't remember it. And the one who That fat thing got stuck in the shock of a motorcycle etc. There are springs. so it's very thin There is a spring. Its torsion constant It happens less. Meaning, if you twist it, it will twist. Will give very little restoring torque. so This is used. and do it quickly It does not break. don't do this many times It will break. second thing is to know both inner and this We would pivot up and down with a screw Are. So this is the spring Works to provide restoring torque. Now When it spins, it twists slowly the spring is slowly restoring it Stop it by applying torque, otherwise who will stop it? if these He is roaming around and there is nobody to stop him It will keep rotating. So that restoring It gives torque slowly. like this is very Take it easy, walk as much as you want and then stop. When it stops we take the reading. Restoring torque comes into play there. and one more Light Aluminum Pointer We Put It Here We give it. This is the pointer you are seeing Because of this, inside this, we will now talk about I have also added some soft iron. Now Inside this there is a horseshoe magnet Look, this is the meaning of this horseshoe It is cut in a concave shape. These so let's cut it and together we'll go here Soft: This is soft iron. inside this we are Put a soft iron sildicle in it. It is a bit square. Chakor is like this it is soft We took iron and made a square like this Let's put it inside it like this. Why Should I put it in? By adding this soft iron What is the benefit? Soft Iron Iron The magnetic material is ferromagnetic. So this creates a very strong magnetic field He gives it at the centre. Isn't it? and other help What does it do? Radial Magnetic Field In making. So this is concave type cutting It is also written in this that concave type cutting and The addition of cylindrical soft iron is due to It is done so that it is strong at the center a magnetic field is generated and the radial yes. This means that it is radial, look at the arrow It is going like this, right? So whenever this will rotate around some magnetic field It will come parallel. so look at this at this time It is almost parallel to the magnetic field. Is No? Do not understand from this that this Silidical means there is no such magnetic field To remove. Magnetic field never breaks down I don't do kattam. This will go wrong. Who The magnetic field is north-south This is how it is made here. The figure is very good. maybe we don't make it Got it. Suppose one is going straight. The second such will go. like this then like this very good The diagram will not be made but you will understand. So this magnetic field is very dense at the center It becomes strong but it does not get cut give because the magnetic field lines cut No, they do not intersect. So We would need a radial field such that it would rotate go into any position like turning around This frame goes here so it is parallel to this Let us take advantage of the magnetic field Let's pick it up. I hope you understood. these radial We need the field. and this work Who will do it? Soft Iron Core Plus These Concave Type of structure that has been cut. These Both help for the radial field. Now we will talk about its working MCG. So in working since the field is radial. Told you that the field is a radial field. Any There is no coil of this which is always in a field It will come parallel. So the plane of the coil Always remains parallel to the field. Now! Here it is. When it rotates like this then its parallel Will go. Now we have to calculate the torque that is applied I did the same thing and I have written it here. of torque the value is ni niba nib sin theta then You already know that this magnetic field 90° angle between the vector and the area vector It is made. So the torque is eliminated Formula. The Torque is now here at Work Tau deflects the coil through an angle. These Pay attention here. how did this 90 come that whenever it is exposed to this magnetic field will come parallel, its area vector will be 90° will give. I took this 90 from there. No Get confused. These are the magnetic fields The parallel has arrived. These coils and these magnetic Field. So its area vector is in this B What is the angle? Of 90°. so wherever it goes The magnetic field will become 90°. so this sin theta will run away. niba will be saved. watch now the torque that deflects the coil through an Angle. Now this torque that it was feeling Will try to rotate it. We have read it. Restoring in rotation will now rotate so this The spring will come. If she comes then she will provide restoring torque. So Restoring When it gives torque then how much restoring will it be will it give torque? So the restoring torque is Spring is providing that deflex Is proportional to the deflecting angle. The more you strain or the more you deflect The more you do this, the more twist will be felt inside the spring. So it became proportional to that, sir. Now Restoring a proportionality constant K We guys use it. and we will only say K are torsion constants or springs Constant. If we take out K, then You can also write "restoring upon alpha". i.e. what happened to the torsion constant Talking about defining torque Required to produce unit angular Twist. Brother, if we talk about K here I take white colour. If I call it ah K then this Torque/Alpha has arrived. So a unit angular The amount of torque needed to twist We speak of K as the torsion constant. These Torsion became constant. Now look at these equilibrium position these are the deflecting is the torque and that due to the spring The restoring torque is when both are equal When you go, this pointer or marker will remain in its place It will stop. i.e. in equilibrium condition Both of them will be equal. Restoring torque and deflecting torque. So K alpha Restoring torque and deflecting done torque was niba Now from here you can solve alpha key The value becomes nba / k * i, same formula In the beginning I showed you the proof here I have shown it to you by doing it and its full value It is constant. We have already said that when When you make a galvanometer, then set it up Let's take it. What will be n? What will be b? a How much will it be? k. If you open it, you will see a galvanometer it will open up and there will be a big ruin or something And if it happens then it gets fixed only. proportional to so here alpha angular deflection in linear relationship or becomes directly proportional to i This makes the linear scale possible as I mentioned that was a food if an amp shows So 10 sections will show 10 amperes in 20 sections 20 amperes so this scaling is very easy and This is the reason that a clear cut is made. I hope you can catch this. it There is important working and this derivation work It comes. I will remember this formula also. This is a very useful formula. alpha = NBA / K * I now have a terminology called figure of Merit. Figure of Merit basically i / alpha They call it. Meaning Unit current for one angular twist How much do you need? Just say it. Or the current which produces a deflection of one scale. One Diff for a Deflection The amount of current required to cause scale deflection That is called the figure of married. it is like No, this is here, assume it is a marker. One unit deflection has to be delivered here. You will need as much money for that. I will say figure of married. and from i / alpha Let us define it. So, this angular twist Say it and as much as i went. So, g is the figure of married. I / alpha current required for unit scale one scale deflection and corresponding If you take out I / alpha from it then it will become K /NBA should know this. Sometimes Let me write it in numerical. if it does not come then I won't be able to handle it. Ok? Now it comes Sensitivity of galvanometer. Sensitivity of galvanometer means that whenever you change the current or the voltage Make even a slight change in the galvanometer there is a thorn, pointer marker, that's fast Change. So they call him more sensitive Is. More shaking after slight change let's go. That is sensitivity. I also wrote It is given that high sensitivity means What? Large State Deflection on Small Change in I and V. Slight change of current or voltage More deflection pointer in change from Or if the marker shows, then it is called Highly sensitive galvanometer. these sensitive There are two types. a current sensitivity and a voltage sensitivity. Then the current sensitivity is called IS = Alpha / I This was the figure of merit On the contrary, it was I/Alpha. G did you see it Right now that was I/Alpha. and this is the opposite of that Current sensitivity. that is, what is being said Is? Deflection produced when a unit Current Flos. One unit current when you flow If you do this then how much deflection are you getting? This is the current sensitivity and NV/K is the same Removed it from the formula. and here comes the second Voltage sensitivity. It is said that a unit How much is the voltage change when you do it Does deflection occur? these voltages There is sensitivity. then we can write alpha V as ho IR then alpha / IR and alpha / I then right here Copy it from . So NBA / K So NBA / K and This R just remained sitting. this I Look, I have written the definition also. Deflection of Deflection produced when a unit Potential difference is applied. and these If we talk about the relation between the two then VS Look at the value IS / R formula. One R It is additional. Then VS = IS / R is sensitivity One slide alone can end the whole incident She gives it. So hold on to it. two kinds of There is sensitivity. what is the current voltage Is? What is the formula? All these things we I have told you. Now what is it that There is sensitivity, what are the factors By which you can increase sensitivity? so this Formula Current Sensitivity Voltage We are holding on to sensitivity. wrote By increasing the number of turns n. So Here you see, if you increase n then IS and Your VS will increase. what is n? How many turns of the coil did you wrap? Are. This is also an important thing here that you can't end it too much otherwise Your galvanometer will become bulky and By taking more turns the resistance increases Will go. So if the resistance increases then It is possible that the voltage sensitivity may decrease let's go. So we have to increase n but by one Only limited amount has to be made. with your mind To increase means to keep on wrapping it indiscriminately. Second by increasing the magnetic field. Look here, if B is increased then IS increases. B. extended So VS increased. then by increasing the magnetic field You can also increase the current sensitivity. Third by increasing the area of ​​the coil. If you increase this A then IS will increase. Will you increase A Then VS will increase. but again area if If you increase it, it will become bigger. Galvanometer It will become bulky. it is not easy to use you will find it. So there should be rational thinking there too How big should we make the balance approach? next thing by decreasing the value of Torsion Constant. If you reduce K then IS will increase. If you decrease K then VS increases Will go. Reducing the torsion constant means that's why phosphor bronze material We use it. His K would have been much less Is. The springs that are used. like this Sensitivity can be increased. here at Keep in mind that a question came on the boards In 2025. Is it always better to increase the IS But VS keeps increasing? i.e. always current If you increase the sensitivity then the voltage will always Sensitivity will increase. There is no answer to this. Because suppose here you are number off Turns started increasing. I always write this down I have not been there. I will have to write more. It is not necessary. Always on increasing IS VS does not increase. If you increase the number of turns So IS will increase for sure. But on increasing N, R If it increases too much then VS will decrease. so like this IS may increase but VS may decrease let's go. Then you will understand what we want to say have been. Increasing IS vs increasing any Not a sure deal. ok now convert off The galvanometer comes into an ammeter. Now this This is a very famous topic. It is very simple topic how to convert a galvanometer into an ammeter do you convert it? The first question that arises is That is why do we change? so changes because the galvanometer It would have been a highly sensitive device Is. If even a little more current comes It blows up. So how do we measure large current? That microcontroller can measure very small currents The one with amperes. so for that we do this we do this Let us convert it into ammeter. then we You can measure as much current as you want. We make the ammeter accordingly. 5 I want to measure amperes, I want to measure 25 amperes, 100 I have to measure amperes. as you like Make a galvanometer. so how to convert Are? Let us show you. so here is a It is a galvanometer. In parallel to that we are Let's put in a shunt. What is a shunt? Very low value resistance. somewhere here It must have been written. I will show you now what a shunt is Is? You will find it written here so that you can write Also get it. What is a shunt? very little Resistance to value. so a very small The resistance of the galvanometer is measured using the resistance of the We will install it in parallel. benefit from this We get that the current that was coming What is IGG? Full Scale Deflection Current. means the scale in the galvanometer If you send IG ji then the whole fork will run till the end Will go. If more current is given than this then it will blow up They. So what happened now? It can withstand up to IG g. next to that It cannot be cut. It will fly away. So we Here I will send current and the current will always be on that path follows the path of least resistance and its We have provided a path for this here Which is of least resistance. So out of this 99% of the current will pass through here because its The resistance is very low and its resistance Let G be the starting point. Let's take it. These The resistance is more than this, then it is less here There will be electric shock. At most IG then this It will not blow and you will also get the reading We. We are the ones who make these arrangements. Correct? well How do we convert a galvanometer into an ammeter? Should I change it? Putting Low Value Resistance which is known as a shunt in Parallel. Correct? now here how much if we What value of shunt should be installed? Now this I will also drive. So this is IG ji We explained the full scale deflection current. These The capital G written here is the symbol of resistance It is a galvanometer. What is written here and I It depends on the range of the ammeter you are making Are. Let's say you want the number from 0 to 25. If you want to measure upto ampere then measure from zero The 25 amperes after that is the value of i. Did you understand? If you want up to 50 amps If measurement is to be done then the value of I is 50. this that Is. So you will place the shunt accordingly. 2nd IG full scale deflection current tomorrow You may have to find it out in numerical terms. So s / g + s is the same value of shunt resistance g + Talking about s * I and total resistance of ammeter do it brother this is the complete ammeter setup so this Both are parallel resistances Parallel R1 R2 / R1 + R2 Formula Apply it. So look at this gss of this Resistance g is its s then g * s / g + s and You know that when in parallel combination If there are resistances then it is even smaller than the smallest If this happens then this total resistance is shunt will become smaller than R is the ammeter of I could understand the resistance issue and wrote this shunt that by the way ask what is shunt it happens you should know this very low Value resistance shunt has two-three functions We will tell you those too, so take the value Resistance connected in parallel to Protect galvanometer and ammeter. Understand so that you can either convert it or If you give it protection, it will blow away. Come We will do its derivation. which is the ideal ammeter what happens is the resistance that it should have Zero. You will know this, let me remind you that we put the ammeter in series in the circuit To measure the . So the resistance to this is the ideal ammeter of ammeter if it is There should be zero resistance. like that we I cannot make it zero, it would never have happened There is but the effort is as little as possible You will measure the correct reading otherwise your resistance because of this the reading will change isn't it good now Let's do this derivation here as you can see These two arms have to go from A to B. By the path SB or AB both are parallel So the voltage on both in parallel circuit If it is beans then it is written g meaning Resistance of galvanometer as you can see in Understand the meaning of the symbols, IG is full scale Deflection current. I is the required range 0 to 25 ampere, zero to 10 ampere, zero to 50 amperes. and I – IG is the current through shunt. This is current through shunt. Now consider the galvanometer and shunt is connected in parallel. as I told. so go across it this way or this way the voltage drop is same will get. Voltage drop same in parallel It happens. So here V = IR IG goes into it It has been happening. So what is its voltage? IG * G And what is the voltage here? I-IG * S then make both the voltages equal. IgG I - IG * S and take the S out from here. This Solve it. It's a 1 minute job. Then S = IG /I - IG * G This is the value of shunt. Depends on how much resistance you have want. This is the value of the shunt. Second By solving this formula we get IG * G = IS Took it. So this is written IG * G and this IS - IG * S is the same thing. Now what did we do here? Is? This IS was written as IGG + IGS Because what do we want to remove? IG then This IG and this IG taken together. Second We are deriving the formula. So IgG + S = The value of IS and IG is S/ G + S * I when You need to find the full scale deflection current Yes, this derivation has also come to you. Any There is no problem. and you will have total resistance Have to take it out. I said that both are in parallel. then two in parallel when If they are in parallel then R1 R2 / R1 + R2 You apply it. Put that one on. GS / G+S these The entire conversion was done within 2 minutes. Very simple. hope you liked it will be. Take note, you must have understood it. Let's go one Let's take a step further. Now uses of shunt Let's see. So what are the uses of the shunt? does it come in? This is the meaning of shunt brother. So This shunt prevents one thing Is. protects the galvanometer. Protection Gives. Otherwise the galvanometer will fly high From the current. The second emitter is To convert galvanometer into ammeter Does the work of. Number two. number three if a The ammeter is already made that from 0 to 10 You can measure up to amperes but you thought Bhaiya now we get 25 ampere instead of 10 ampere If you want to make an ammeter upto the range then a shunt and knock it down or change the shunt so that the ammeter Can also increase the range. So the three main There is work. First, by blowing the galvanometer To save or provide protection. Second converting the galvanometer into an ammeter and Third, increase the range of the ammeter. expect it I was able to grasp all three things. now comes the next topic how to convert galvanometer into voltmeter will you convert? You know that the one which A voltmeter is in parallel with a circuit It is applied in. so here we are Very high in series with galvanometer Let's apply resistance. so when we series If you apply very high resistance to This becomes a voltmeter. so how much now Do you apply it? I will understand now. because what is this This happens because of high resistance More current flows through the galvanometer Not there. So it stays safe from being blown up and Voltage also comes across it Is. So a galvanometer is converted to Voltmeter Buy putting high resistance in series. These The way to converge is to have a higher value You will put the resistance in series the galvanometer will change In the voltmeter. Now that IG full scale If the deflection current needs to be found out then It will also derive V/ R + JB and the R key The value is how much resistance you need to apply If it is there then it will come V/ IG - G brother which range Here also what is that V range that we can go from zero to If you want to measure up to 250 volts then 250 volts V arrived or zero to 500 volts Want to measure upto range of one volt meter If you are making it then 500 volts V is obtained. His R will be decided accordingly. Isn't it? Then, = V/ IG - G and the voltage of this voltmeter Because the resistance is in series, R1 + R2 then GR + G this is its voltmeter resistance is which is very very high than Galvanometer resistance. and the ideal voltmeter is its resistance It should be infinity. it is here which The ideal voltmeter will have a resistance of It should be infinity. You will know that Wherever we put a voltmeter, it is in parallel I use it for measurement. So its The resistance should be as high as possible so that So that they can take the correct reading. Isn't it? Now We can't do infinity. This is one It is a matter of idealism. The closer and The bigger you make it the better the situation It will be. So you must have understood this also. Now its Let us see the derivation. where is the formula from came out? High value resistance in series Have planted it. These are the parameters by which you can understand Get it. G means resistance of Galvanometer. IG is full scale Deflection. The current that pierces the thorn deep inside goes into the galvanometer. V is Required voltage range. zero to 250 Voltage required is from zero to 500 volts Do you want anything from zero to 1000 She became V. and R became high series Resistance connected in galvanometer In the series. so total resistance in the What is a circuit? R+G And apply Ohm's law. So what is the I current Will she go? You can't send more than IG. The galvanometer will not fly. Then IG = V/R So V/ R + G becomes the value of IG. Now From here you take out R + G = V/ IG and R From here. So R became V/ IG - G i.e. As much The amount of range you require: 250 volts Measure upto 500 volts, keep that and R Take it out. G Do you know about galvanometer? Resistance and IG full scale deflection of You already know that the work is done. And Here RV is the resistance of the voltmeter It is in the series. So it's R+G. Hope You can also understand that we do it. very simple Is. See, there is no confusion. By pausing you You can note it down. Very simple. Now There is a small numerical in it. We also They carry it out or they do it. These It is written in the question a galvanometer of Resistance 16 ohm 16 means value of G is 16 Is. Shows full scale deflection current IG 4 Millie Ampere. of full scale deflection Meaning of IG how will you convert it into a Voltmeter? a galvanometer can be connected to a voltmeter I have to convert it into . how to convert Are? By connecting high resistance in series. To measure a voltage up to 3 volts. These are V's The value is of range. Now do this a little bit Let's take it. Now here is the position of the galvanometer We installed high resistance in the series. Now it will be converted into a galvanometer. The formula is R = V/ IG - keep the G value Pick up everything and give it to me. This value of V is 3 volts. That range needs three. IG Full Scale Deflection 4 milliampere. So, the sum of 4 * 10 Power -3 amperes inside and one The resistance of the galvanometer given below is 16 ohms. How simple it is. solve this now Take it. 10 to the power of 3 was 1000 above that is 3000 up 4 - 16 3000 up 4 750 - 16 ie 734 ohms. If you install this of 734 ohm then This will be converted into a volt meter and 3 Can measure range up to volts. Now three of place if you want to measure up to 30 volts So there is nothing to do. just the value here Put 30 in place of 3, the amount you want to measure. So You can note this also. Big Simple But it becomes an interesting and important question goes. Now let us read the second conversion It seems as if the meter guy has clean hands too. Lets do it. Then a galvanometer coil has a Resistance of 15 ohm and it shows full scale Deflection current. Both of them came on board There have been questions. 4 milliamperes. convert it Into ammeter. what should we convert this into want to do it? In the ammeter. and gave its range Is 0 to 6 amperes. That means I give us 6 amperes I have given it. We know how we Let's convert from. a galvanometer In the ammeter. We are in parallel with the galvanometer Shunt is applied with low value resistance. Now How much will that shunt cost us to remove it? Is. So the value of shunt becomes IG/ I - IG * G You must have seen it. We have memorized this formula I have done it. The value of this IG has become full Scale deflection current which is 4 milliamps It was an empire. 410 to power of -3 and I Range 0 to 6 so value of I is 6 ampere. These 6 ampere minus IG written above 4 * 10 power-3 then 0.004 And * G means 15 ampere was given Resistance of the galvanometer. Now this You can calculate it. This is 2/3*10 power -3 * 15 approximately and this is almost The answer came as 0.01 ohm. I mean, this shunt You have installed this, if you install 0.0 ohm then it will Ammeter up to 6 amperes will change. Series Put it in and get it measured. so pause this too By doing this you can note down. this is complete I saw the lecture. in very simple language I finished it. I will remind you before I leave. Drona is a great course for you. Evening I take live classes. together with hee ncert exercise, ncert I have used all the video solutions for examples Recorded by myself in simple language. Last Recording of 10 years' PYQs also I have made it myself which you will get along with it. Apart from this there are MCQs, Assertion, Reasoning, Case You will also get study videos and assignments You will get it with full solution. all this together There is something that even telling it feels like enough I am telling you something. You can also get hand written notes You will get formula sheet for full revision With. So no matter how tough this paper is for you come if you are willing to read it Drona will give you a top notch performance You can do it if you study. So Drona You can do your studies regarding this. and right now This is, suppose the child joins now, then You must have five or six chapters in your mind Will be. There is no problem. you are with me Read it now. first week of august From here on out we start again from chapter one I will do it and complete the course by 10th December. Then you will get complete freedom To clear your confusion. so this Don't miss this opportunity at all. To Drona Please join. children who join drona He wants to use Arvind Academy app Download it. Store section below The link will be found in the description. Her Stores Go to the section. Drona will be visible there. You can take that Drona and study with me Are. thank you very much for watching this Video. I worked very hard Experience of 25 years I have experience and kept it in the simplest language Is. So Easy Physics with Arvind Sir I Let me tell you if you liked the video. If you liked Arvind Sir's hard work then watch the video Please like and comment Please give feedback on how you liked the video I can help you with whatever you want. Thank you very much. Wish you all the best.