Next topic is electrostatics. In electrostatics, we are going to study charges and their properties. And mostly electrostatic word means that charges should be on rest.
I think everyone has an idea about the basic properties of charges. There is no need to read the basic things in detail. For example, there are two types of charges, positive and negative. Charge is conserved, charge is quantized, charge has an additivity property. Additivity property means that when we add charges, when we say Qnet, Qnet means adding positive and negative with a sign.
If we take out the total charge of the universe, then the total charge is constant. So we can never create or destroy the charge. It can only shift from one body to another body.
And normally the shifting that happens through rubbing or induction, is the shifting of all the electrons. We have already studied an example. Let's say there is a glass rod.
If we rub this glass rod with silk cloth, does it charge? In childhood, we used to pick up paper pieces and scale and rub them on our hair. So, when we rub the scale on our hair, what happens?
The surface of the scale is charged. So, in the same way, if we rub the glass with silk cloth, In this case, we say that the surface of the glass, there is a positive charge on it and the silk load is a negative charge so tell me where the charge shifted from? tell me so we say that the shifting of electrons is done shifting of electrons from glass rod to silk load So the mass of the glass rod will decrease a little at the microscopic level. Is it clear?
In basic properties, tell me if there is any property or doubt, if you want to ask something, then we will discuss it in detail. And if you know all the basic things, then you can move a little forward. For example, the charge is quantized. Okay.
Charge is conserved. Okay. Then it follows additivity. Okay.
It follows additivity. Is it clear? Quantize means that charge on anyone will be equal to n times e.
And here, pick what you need. integer ho sakta hai integer kya natural number ho na chahiye aur e jo hai charge of one electron which is 1.6 10 power minus 19 coulomb toh kisi body ki upar charge ho ga electrons ke charge ke form me ho ga boliye what is called electroscope batao ki koi bataega koi what is Electroscope Electroscope is a word used What is the meaning of this What instrument is this Electroscope is basically Used to measure charge It will be used to measure charge How do we measure the charge? First, we connect a vacuum box to a metal rod. And this metal rod goes inside the box.
At the end of this metal rod, Gold leaves are used. Gold leaves or any metal can be used. and we can see the angle between these two gold leaves what will happen is that when we touch any charged body like this glass rod if we touch this glass rod with this metal rod then this charge will reach the gold leaf with metal rod and gold leaf will diverge so their divergence angle will tell us about the charge ok here we can remember that the divergence angle divergence angle will be proportional to magnitude of charge okay divergence angle is proportional to magnitude of charge And remember one more point, a body can be charged.
How can we charge the body? There are ways to charge the body using friction. Friction means by rubbing.
Simply rub, then also we can charge the body. Okay? Then it will come by touching. Okay? Then.
by induction and by earthing. So earthing we will read in detail. What is induction?
Is it clear? Induction means that any body, if it is a metal sphere, and if we bring this glass rod near this metal sphere, which had a positive charge on it, we are not touching it, we are just bringing it near it. So what will happen when we bring it near it?
Will the electrons of this metal sphere get attracted and the positive will come here? It will come, right? So this is also charged in a way. The left hand side of the metal sphere is negatively charged and the right hand side is positively charged. So the diagram I have made is for induction.
Induction but metal objects will not happen. See once what is written. If anyone has any doubt, ask. Next is Coulomb's law. Coulomb's law gives us value of attractive or repulsive force between two point charges.
Keep this in mind. The charges should be point charges. Let's assume that we have taken a charge on one side.
plus q1 and one side charge is taken plus q2 they are separated by distance r now if both are positive positive charge then the force applied on them look the force on this is called f21 and the force on this is called f12 means f21 means force acting on 2 by 1 and f12 means force acting on 1 by 2 so this force magnitude f12 or F21. So, if we want to find its magnitude, then it is simply 1 upon 4 pi epsilon 0 into Q1 Q2 upon R square. See, 1 upon 4 pi epsilon 0, Q1 Q2 upon R square. Okay. In which, this 1 upon 4 pi epsilon 0 is written.
We denote it with capital K and its value in SI unit is 9 into 10 to the power 9 Newton. meter square upon coulomb square. What do we call epsilon naught?
Epsilon naught is permittivity of free space. Epsilon naught is permittivity of free space. Is force repulsive or attractive? How will this be decided?
Right? Keep writing. Attractive if unlike charges. And it will be repulsive if it is light charged. Permittivity value is 8.85 x 10 to the power minus 12 Coulomb square upon Newton meter square.
Note down below. when charges are kept in some other medium. Okay. So, in that case, we replace epsilon naught with epsilon naught into epsilon r. Or we call it epsilon naught k.
If we are writing epsilon r, then it is called relative permittivity. And if K is written, then we can call it dielectric constant. At our level, both have the same meaning. Okay? Call it dielectric constant or relative permittivity.
So, the value of this force, net force acting on a charge, this will be modified. 1 upon 4 pi epsilon naught K and Q1 Q2 upon R square. So, this force is reducing by K times.
Look, if we put these charges in some other medium, then this force... k times is reduced. Okay. If we write it in vector form, suppose we need i cap, j cap, so how can we write i cap, j cap? Suppose here is y axis, this is q1, on r1 vector.
This is Q2. On R2 vector, the force applied on Q2 of Q1, let's say we are saying F21. So, this force will be applied along R21. R21 will become a vector. So, what will you write as F21?
If you write F21 in vector form, then it becomes 1 upon 4 pi epsilon naught into Q1. Q2 R21 upon mod of R2 minus R1 whole Q. R21 basically R2 minus R1. But this formula apply only when you are given in I cap J cap. Otherwise you will not need it.
Otherwise you will not need it. Okay? Do you want to tell a small question in this?
For example, there is a square of side a. And on all its corners, plus q, plus q, plus q, and plus q are kept. You have to take it out.
how much charge should be placed at center such that all charges are in equilibrium Hmm, you must have done it, Sabir. Tell me. Look, how much charge we have kept at the center.
So, first of all, understand that we have to keep a negative charge. We have to keep it negatively. Because the forces on Q.
From 1FQ. From 1FQ. And 1F.
It will not be F, but it will be F by 2. It will be F by 2. And this small Q. Minus Q. This on Q. If you apply this much force, then F resultant can be balanced.
So, if you take out the value of F resultant, then it will be root 2F plus F by 2. Look carefully. So, we will write F resultant as KQQ upon distance square. Distance will be A by root 2. And this is equal to root 2 plus 1 by 2 times F. F is because of one. So, because of some 1, KQ square by A square.
So, from here you will get Q value. Negative length, is this also clear to everyone? Yes, sir. Next, let's assume that one side charge is plus 4Q and one side charge is minus 9Q separated by a distance d.
The question is, where should a third charge be placed? such that all three charges all three charges are in equilibrium all three charges are in equilibrium also find nature and magnitude of third charge. Jai Bhushan, try.
We have to keep it on the left side. Okay? And should we keep it positive or negative charge? Positive. Negative.
Negative. Negative will come. Negative charge will have to be kept, only then balance will be possible.
All three charges are in equilibrium, right? So, suppose, how much distance should be kept from here? So, let's assume, x distance should be kept.
So, you see carefully, on this minus qq, force is due to 9q, and force is due to 4q. Force should be balanced. So, if we make an equation for this, then we will get the equation, kq, 9q.
upon d plus x's whole square is equal to kq4q upon x's square. So, if we solve this, we will get 3 upon d plus x is equal to 2 upon x. So, from here, you got the value of x first. dk equal. Are you getting this?
dk equal to 2dk equal. 2dk. This is what we got by balancing on this.
Now if you balance on 9Q, then on 9Q, because of minus Q, and on 9Q, because of 4Q, if you balance on 9Q, then we will write K4Q9Q upon D square is equal to K9Q into small q upon D plus X square. So, D plus X, you know, right? So, from here, the value of small q will come.
How much does it come? How much does the value of small q come? 9 q cancel, k cancel. It is coming near 36 q.
Look, tell me, are all three things clear or not? Where to keep distance, is that clear? To take positive or negative, is that clear?
Tell me if there is any doubt. No, sir. Hmm?
You were telling the wrong answer earlier. So, is it correct? Is it clear? What was the doubt?
Yes, sir. Sir, there can be a positive charge on the right side. Right side means 9Q's right side. Yes, sir. Positive charge.
Both attractions will be balanced. If we want to balance by keeping positive charge on 9Q's right side, then we will feel that it will be balanced. But tell me, if we have kept it on the right side of 9Q, then the force that will be applied due to 9Q and 4Q, which one will be bigger?
But sir, if we have adjusted the distance, then? Tell me, if 9Q is big and the distance is also small, then it will be like this, that the force of 9Q will always be big on it. Yes, sir.
Okay, I understood. What is the benefit of keeping it here? The benefit of keeping it here is that the distance is less than the small charge. And if the distance is more than the big charge, then the balance will be lost. Look, the next question is surface tension plus electrostatics.
Do it. Look, what is happening in this case? There is a square first of all.
And it says that on all four corners of the square, the charge of plus Q is kept. So if we take out the force on any one plus Q because of the rest of the sub, then you see, will this force come in this way? Just like we wrote, this F by 2 will come here.
In the same way, F will be applied here on this. F will be applied here on this. And the one applied from here, F by 2 will come here. Look. And the film which has become in between this.
Okay. Because of that film. Because of that film. Because of that film.
Because of that film. If we take out the force on any one. Then tell me how can we take it out. In fact, we can say that if we study this portion. Let's say we took this rod.
So on this rod. Because we do not take out the force of surface tension on any point. Let's take it out on length.
So, if we say that if we divide this system into two parts, this system should be divided into two parts, meaning left half and right half. So, we can say that the one which is applied on left half and right half, the one which is applied on right half and left half, should be balanced. So, you will know that how much force of surface tension will come out in this case. If we have given this length, this length is given as A.
So, what will be the force of surface tension? So, we can write force due to surface tension. This value will be surface tension S. Gamma is given. Come on.
Gamma into A. And will we have to do into 2 also? And this force, we will equalize it.
Whose will we equalize? Tell me in terms of F. This will be 2F plus 2 times F by 2 cos 45. Don't hurry, understand.
We have taken this force. On whom have we taken this force? We have taken combined on both of them.
So, how much force is applied on both of them combined? So, just remove this one. Which both of them are applying on each other. If you want, then don't show it. Now, what will be the resultant of this from the left half to the right half?
Will the resultant I have written come or not? Yes, sir. It will say 2 gamma a is equal to. So, how much will it be?
Tell me. If we take 2 common, 2 plus root 2 will be left. No, 2 plus 1 by root 2. And what will be the value of f?
So, the value of f will be k q square by. a square tell me tell me so from here you see what is the value of a cube a cube is q square upon gamma's inverse proportional so from here a will be proportional to q square upon gamma to the power 1 by 3 for now we just need power so it happened easily We didn't need to do all this to extract power. We know that due to surface tension, whatever force will happen, and whatever force of electrostatic will happen, if you balance it, you will get power. We didn't need a constant for now.
But if we have to extract, we can extract it. Is it clear? Let's assume that a simple pendulum is suspended from point O and it is Q charge.
We have to tell it how much minimum velocity is given. so that it completes the circle and there is a Q at the center of it ok, this is a string we have to find U minimum such that bob completes Vertical circle about O if A part. In A part, we will write KQ square by L square is greater than MG.
And in B part, KQ square by L square is less than MG. This is a good question. kq square by l square greater than mg kq square by l square if less than mg then what will happen try it and then we will increase it in next time ok in coulomb's law there are many formulas so it is a big chapter but we will see what are the things which are important for us we will focus on that and increase it ok