 We know that changing magnetic field induces changing electric fields and this is how they look like. In this video, we will explore the differences between induced electric fields and electrostatic fields. Alright, first of all, an induced electric field is an electric field at the end of the day. So by definition, f is equals to Qe is valid even for this field, just like it is valid for an electrostatic field. It's just that if we have an electric field due to a static charge and if we have one by changing magnetic field, they look different. But they are still both electric fields. If we see an isolated charge, if we see an isolated charge moving in an electric field, then if we just looked there, we can't really tell if it's moving because of an induced electric field or an electrostatic field. Okay, so one difference between them is that electrostatic fields, they start and stop on a charge. So if we have a positive charge and a negative charge, the electrostatic fields will look like this. There will be some more field lines, I've just not drawn them, but they always start from a positive charge and end on a negative charge. And if we draw uniform electrostatic field, we can say that it is implied that there must be a plane of charge over here. Now an induced electric field on the other hand, an induced electric field makes loops just like magnetic fields. Geometrically, it's more like a magnetic field and it has no charged source like an electrostatic field. It can only be created by a changing magnetic field. Now let's think about the work done by both these fields. Let's start with electrostatic fields. So let's say we have a unit positive charge and we try and move this charge horizontally and then we move it vertically and bring it to this point right over here. So the part taken by the charge would look somewhat like this. Now we can think about the work done by the electric field when the charge was moved from its original position to its final position. Now work done is force multiplied by the displacement. It's a dot product between force and the displacement vector. Now for the horizontal path, the displacement is opposite to the direction of electric field. So the electric field will do some negative work for this horizontal path. So that would be minus and because we are seeing a unit charge, so we need not worry about Q over here, that would just be one. So this will become electric field strength multiplied by the length of this path. And let's say that is L. Now there will be no work done in the vertical path because the angle between the displacement vector and the electric field will be 90 degrees. And because of the dot product, there will be a cos theta part, there will be a cos theta component and cos 90 will just be 0. So let's just write plus 0 over here. Now if we bring this charge back to its original position like this, the part taken would look like this and there will be again some work done by the electric fields. The work done by the field when it was moving horizontally. That will be in this case plus EL because now the electric field vector and the displacement is in the same direction. So it becomes plus E into L. And again in the vertical path, there will be no work done by the fields because the angle between the displacement and the electric field is 90 degrees. So we will add a 0 over here. Now we can see that in a closed path, in a closed path, the work done by the electric field comes out to be as 0. And it doesn't matter which path we take. We can take a very random path. We can move in this way right here and come to its final position. And then we can move this charge back to its original position, moving in a twisty and curly manner and bring it to its initial or original position. Even in that case, the work done would be 0. And we can actually see that. Let's move this charge in a curved path and take it to B. So the path in this case would look like this. Now we can make the same path with small horizontal and vertical steps. So that way it could look somewhat like this. And now we can see that for each horizontal displacement, there will be some work done by the electric field and there will be no work done in the vertical displacement. And a sum of the work done for all the horizontal displacements will come out to be as minus EL. And we can do the same when we take the charge back to its original position at A. Now there is a way to write this. If we take the charge from A to B, if we take it from A to B, the work done by the electric field is given by E dot, it's given by E dot DL. And if you bring back the charge from B to A, the work done in that case would be integral of E dot DL, that's the same. But now the limits are from B to A. The limits are from B to A. And we can look at these two integrals. They will be same in magnitude, but they will have opposite signs because the limits have been solved. So when you think about the total work done in a closed loop, this will always come out to be as, this will always come out to be as zero. So we can finally write that as integral of, closed loop integral of E dot DL. And that gives us, that is always equal to zero. So the work done in a closed loop by electrostatic fields is zero. Now let's think about the work done by the induced electric field in a closed loop. So we have the same positive test charge and we move the charge around the loop once. So when we do that, there will be some work done on this charge by the electric field. And if there is a loop of induced electric field, the direction of the electric field is always tangent to the loop. So at all these points, you have electric fields as tangents to the loop. And when we are moving it in the same direction, you will have displacement vectors, which will also be tangents to the loop. So if you think about the work done in this case, it will always be positive at each and every instant. At this point, it's some positive, some more work is done, now some more work is done, now more, more and more until it comes back to its original point. And if you think about the work done for a closed loop, in this case, it is not really equal to zero. There's always some positive work done on the test charge. In fact, this is equal to EMF. Now we can try and think about the idea of potential for both of these fields. In electromagnetism, we call it electric potential and that is electric potential energy per unit charge. Now for electrostatic fields, if we move from point A, let me bring this charge back to A, if we move from this point and let's say that the potential, that the potential of potential of this point is, let's say it is, let's say it is 10 joules per coulomb or 10 volts, which means one coulomb of charge will have a potential energy of 10 joules here. And if you move this to point B, then there is some work done by the electric field and that is negative over here. So let's say that the work done is minus 5 joules. So that means the potential at point B would be, it will be 10 minus 5, it will be 5 joules, 5 joules per coulomb. And if you move it back to the original position, to its initial original position, then there will be some positive work done on the charge, which will be plus 5 joules. And that will bring the potential back to 10 joules per coulomb. So overall, there is no energy lost or gained. The mechanical energy, and that is just potential energy here, assuming that the charge moves extremely slowly so that the kinetic energy is almost zero, the mechanical energy is conserved. And that is why we call electrostatic field as conservative fields. But for induced electric fields, if we move the test charge once around the loop, there is some network turn on it. So if we start from a potential of, let's say, if we start from a potential of 10 joules per coulomb or 10 volts, and the field, the electric field does a network of 5 joules around the loop, then when the charge comes back to this point, it will have a total potential energy of 15 joules. So that will make the total potential at this point to be as plus 5 joules per coulomb and that is 15 joules per coulomb. And if we move the charge once again around the loop, then this potential will increase further. So the idea of potential for induced electric field is meaningless. One point cannot have more than one potential. We see that the mechanical energy in this case is not conserved. As the charge returned to its original point, it can have more or less energy that it left with. And that is what makes induced electric fields as non-conservative. It's just like how friction is non-conservative. Let's say if there is a block which is moving on a rough surface and it is moving to the right, it is moving to the right with some velocity of let's say 3 meters per second. And when it moves, it presses against a spring and then comes back to its original position. Then when it comes back to its original position, it will have a speed which is less than 3 meters per second. That is because friction did some negative work and removed energy from the block. Some mechanical energy has been transformed into the thermal energy and therefore, even in this case, the mechanical energy is not conserved. All right, now let's summarize the differences between induced electric fields and electrostatic fields. So electrostatic fields, they start and stop on a charge, whereas induced electric fields, they make loops just like magnetic fields. The work done by an electrostatic field in a closed loop comes out to be as 0. If we move a positive test charge from point A to point B, there will be some negative work done on the charge by the electric field. And if the charge is moved back to A, equal amount of positive work is done on it. So the network done in a closed loop comes out to be 0. Whereas for induced electric fields, if a positive test charge leaves point A and goes around the loop, all the while some positive work will be done on it, considering if electric field and displacement are in the same direction. Now when the charge comes back to its initial position at A, there is some network done on it, which is not equal to 0. In fact, this is equal to the EMF. If there would have been a coil kept in the region of changing magnetic field, then some EMF would have been induced in it. And closed loop integral of E.dl is equal to that. Now because the work done in a closed loop by electrostatic fields is 0, we can talk about the idea of potential. Potential is potential energy per unit charge. So if some negative work is done on the positive test charge when it moves from point A to point B, that means its potential energy has decreased. Some energy is removed from it. So now the unit test charge has a different potential energy at point B. Which means the potential at point B will be different. And if the unit positive test charge is moved back to A, some positive work is done on it. So potential energy has been given to it, which will bring back the potential energy of the charge to its initial value. So in a closed loop, there is no energy lost or gained. We assume that the kinetic energy of the charge is 0 throughout because the charge was moving extremely slowly. So total mechanical energy at the point is just its potential energy. And since no energy was lost or gained when the charge completed a loop, that means its potential energy or mechanical energy is conserved. And that is what makes electrostatic fields conservative in nature. On the other hand, if a unit positive test charge left point A here and moved around the loop, there is some net positive work done on it. Which means some potential energy is given to it. So now when the charge comes back to its original position, it has more potential energy that it left with. Which means the potential of this point should now be more. If the charge completed one more loop, the potential should increase more. Which can't happen. So the idea of potential is meaningless. It is meaningless for induced electric fields. There is no well-defined potential. And since the potential energy increased when it went around the loop once, mechanical energy is not conserved. Which is what makes induced electric fields non-conservative in nature.