Free Physics NEET Video Lectures for Electromagnetic Induction

00:00:31 [Music] [Applause] A very good morning to all of you. Today we will start a a very important topic that is electromagnetic induction. Till now we have been studying magnetic fields produced by current carrying conductors, forces between current carrying conductors and so on. So remember I had shown you a demonstration which Hans Christian Oyster had done in 1820 to show that currents produce magnetic fields. Current carrying conductors produce magnetic fields and then we studied magnetic fields produced by a straight current

00:01:28 carrying conductor. Magnetic fields produced by a solenoid and so on. Now today what I'm going to discuss is a very very important topic in electromagnetics and that is electromagnetic induction. So when uh it was shown that electrical currents create magnetic fields the obvious question that arose is can magnetic field produce currents? Can magnetic fields produce current? That means can I use a magnetic field to generate current? So a lot of experiments were carried out by many scientists by placing very

00:02:06 strong magnetic fields magnets around conductors by passing current through conductors close to another conductor and they didn't find much successful results in generating currents until Michael Faraday in 1831 did a series of extraordinary experiments to show that to generate current I need a changing magnetic something should change and that change will result in an electrical current. Now Michael Faraday was a very famous scientist, British scientist and he has contributed significantly to

00:02:43 electromagnetics, electrochemistry and so on. He lived in the [Applause] period Michael Faraday 1791 to 1867. So he did some outstanding experiments in electromagnetics and also electrochemistry. He also introduced study diamagnetic properties. He was an excellent experimentalist. And in fact, Albert Einstein had a picture of Michael Faraday in a study room along with pictures of Sir Isaac Newton and also James Clerk Maxwell. We will study about Maxwell's equations later on. But Michael Faraday was a very very

00:04:05 important scientist in the in the development of electromagnetics. And today what I'm going to show you is some experiments similar to what Michael Faraday did at that time to show relationship between magnetic fields and currents. We have till now studied that currents produce magnetic fields. I will now show you that it is also possible to generate currents using magnetic fields but under certain situations. So let me first show you a solenoid which I have wound by taking a piece of copper

00:04:38 wire and here is a solenoid and these are the two ends and you can see here there are windings around the solenoid and this solenoid as you know can create an a magnetic field. So this is one solenoid. There's another solenoid here which is a smaller solenoid and that has a larger number of windings. And I want to show you that this solenoid will produce magnetic field. So what I do is here is a compass. Here is a compass which uh produces which is uh which contains the north and south poles and I connect this

00:05:10 solenoid to a a battery and you can see immediately the the magnetic coil is rotating. then this particular solenoid generates magnetic field. So this is essentially an experiment to show that currents generate magnetic fields. Now I want to show I want to see whether magnetic fields can generate currents. Now before that I want to show there are two permanent magnets here which I had shown in an earlier experiment. These are two permanent magnets. Very strong permanent magnets. And as you can see here, it has very

00:05:49 strong effect on uh the the needle. So this is a soft iron piece. A large number of pieces of soft iron. And uh this is formed into a a cylinder here. A large number of pieces. And this particular uh piece I connect to a magnet. The moment I put a magnet here, the magnetic field of the magnet actually gets concentrated into this and this soft iron piece gets magnetized and has a magnetic field associated with it. So this particular this is now becoming a it's a long magnet. So what I want to show see is whether this magnet

00:06:29 this magnetic field produced by this structure can generate electric currents. Now for this what I have done is here I show you a galvvinometer. You can see here in the other part there's a galvvinometer. There is another solenoid and this solenoid is connected to the galvvinometer. So this is one terminal of the solenoid. Another terminal of the solenoid. There is no source of current in the solenoid and so the galvvinometer is showing zero reading. The galvvinometer can shift to the right or to the left depending on

00:06:59 the direction of the current. For one direction of current, the needle will shift to the right. For a reverse direction of the current, the needle shifts to the left. So depending on the direction of the current, the needle of the galvvinometer will shift to the right or to the left. And so we will now investigate this. So this magnetic magnet. Now what I want to do is I want to put this inside this solenoid so that the magnetic field associated with the solenoid. So there is a magnetic field which is connected to the solenoid.

00:07:34 So now you see there is a strong magnet within this solenoid. There is a strong magnetic field but it does not generate any current. So a static magnetic field connect which is around a circuit or coil does not create any magnetic field any current in this in this coil. Now what I want to show you is if I change the magnetic field by pulling out or pushing in this soft ion piece I will generate a current in the galvvinometer which will be seen in the galvanometer. So what I'm going to do is the

00:08:08 following. I am going to pull the soft ion piece out of the solenoid or push it in. So what am I doing? Because there is a magnetic field associated with the soft ion piece which is connected to a magnet. there is a magnetic field associated with this soft ion pieces. And when I pull this soft ion piece, I'm changing the magnetic field encircled by the solenoid. So I'm changing the magnetic field whether I pull it or push it. I'm increasing or decreasing the magnetic field which is which is uh which is

00:08:41 encircled by the solenoid. So this was one of some of the experiments carried out by Michael Faraday. So let me show you. So here is the uh current in the uh in the in the gonometer. You can see now let me pull the solenoid the soft iron piece out of the solenoid. You see the needle shifted to the right and there was a short current generated when I was pulling it out. So when I pull the the soft iron piece out of the solenoid I'm changing the magnetic flux in the solenoid and that change in magnetic

00:09:10 flux generates a current. Now please note that when I pulled the soft iron piece out of the solenoid the current was generated where the needle shifted to the right of the zero. Now I want to do the same experiment but push the soft iron piece into the solenoid and to see what happens. Okay. Now let me push the solid let me push the soft into the solenoid. As you can see here when I push the soft iron piece into the solenoid the current generated is to the left. So when I pulled out so for example let me pull it out again. If I

00:09:44 pull it out the needle shifts to the right. And if I don't move the soft ion piece there is no current. So the current got generated only when I was moving the soft iron piece or when I was changing the magnetic field. So now if I push it here, the current is again generated as I'm moving and the current is now opposite to the direction of the current that I was produced before. Now let me pull it and push it very slowly. If I pull it out very slowly, the amount of current generated is very little. As

00:10:13 you can see here, there is a the needle shifts to the right. Very little, very little current. If I stop the current becomes zero. If I move it into the solenoid at a slow pace, there is a very small amount of current generated but it is to the left. So it's opposite direction current. So it looks like the current generated also depends on the speed at which I am moving the m moving the soft piece. So if I move it fast, it moves quite to the right. If I move it quickly here, then it moves to the left.

00:10:45 So two things I am observing that there is no current generated if the magnetic field remains constant. The magnetic field produced by the soft iron piece which is going through the solenoid is remaining constant if I don't move the magnet. And in that case there is no current generated. If I pull the soft iron piece I'm changing the magnetic field as a function of time. And as long as I'm moving, there's a current generated. And I have also shown you that the current generated depends on the rate at which I

00:11:20 am pulling it. Which means the current generated depends on the rate of change of magnetic field. Now we will quantify this through equations a little later. But it's important to notice that the current generated in the circuit depends on the rate of change of magnetic field. And the second observation which I've seen is if when I'm pulling the current is in one direction when I'm pushing the ion piece the current is in the reverse direction. So it also depends on the direction of the current in the circuit

00:11:54 depends on whether the magnetic field is increasing with time or decreasing with time. So again we will quantify this and understand this. So let me repeat once more. Here is my solenoid. Here is the galvanometer. I I pull it and it moves to the right. And if I stop pulling it, there is no movement. If I push it, it moves to the left. Again, as long as I'm pushing, it is moving. There is a current, but then it comes to zero. So, if I move it very slowly, there is some current generated but very little

00:12:24 current generated as compared to fast motion to the right here. And if I move to the left, then it's a small current generated. If I move very slowly, there's hardly any current generated. So the rate of change of magnetic field decides the amount of current generated. So that's one experiment. Now let me do another experiment with the same. So what I've done here is I have moved the magnetic I have moved the magnetic soft iron piece with the solenoid. Now let me fix the iron piece and move the solenoid. So

00:12:55 if I move the solenoid to the left, I'm not I'm not moving this iron piece but I'm moving the solenoid. If I move the solenoid to the left, there is current generated. If I move it to the right again current is generated. So you see if I move it like this there's a current to the right. If I move it like this there's a current to the left. Very interesting that the same kind of current is generated irrespective of whether I move the magnet with respect to the solenoid or the solenoid with

00:13:22 respect to magnet. This is a very very important concept that whether the magnet is moving with respect to the coil or the coil is moving with respect to the magnet I am generating a current in the coil. So again let me show you here. So I move the solenoid to the left and there's a current generated. If I move the solenoid to the to the other side then is opposite current generated. Very similar to exactly similar to what happens when I move the magnet rather than the coil. So that's another very

00:13:52 very important observation. The amount of current generated depends only on the relative motion between the magnet and the coil. That's a very very important consideration. Now now let me do another experiment which Michael Far did at that time. So I remove the permanent magnet and I take another solenoid. Here's another solenoid which I'm taking. I take the solenoid which has two wires here and I place the solenoid around this soft hand piece. So let me remind you that if I connect this to a current

00:14:22 source, if I current the solenoid, connect the solenoid to a current source, that current source will pass current through this small solenoid. That small solenoid will then generate a magnetic field. That magnetic field will then pass through this second solenoid. And then I will show you I will check whether there is a magnetic field generate current generated in the second coil or not. So for this I take a battery. This is a battery here 9V battery. So I connect this to this solenoid to one of the first solenoid

00:14:51 here. So you see if I when I connect there is a movement when I disconnect there is a movement but when there is no there is constant current for example here I'm constantly passing a current there is no current in the sec in the second transform in the second solenoid if I disconnect there is a current in the uh in the solenoid connect to the gamma if I connect again there is a current generated in the solenoid if I disconnect there's a current so I don't need a magnet to generate a

00:15:22 current. A current in the solenoid in the solenoid a current which is passing through the solenoid generates a magnetic field. That magnetic field is passing is encircling enthralled by the solenoid which is connected to galvanometer. So when I connect this first solenoid into the battery source, I pass a current through the solenoid and that current generates a magnetic field and only you can see here the current is there only when I connect at the point of connection or when I disconnect. If there is a constant

00:15:53 current flowing through the coil, there is no current generated in the gvanometer. As you can see here, moment I disconnect, there is a deflection. Moment I connect, there's a deflection. So in this case in the first case the magnetic field was produced by a permanent magnet a permanent magnet and through this soft piece. So irrespective of whether I move the magnet with respect to the coil or the coil with respect to magnet I am seeing an induced current generated in the in the coil. Secondly, the direction of the induced

00:16:30 current depends on whether the magnetic field is increasing with time or decreasing with time. Then I did an experiment in which I have a solenoid in which I pass the current this solenoid. So the current the this solenoid when I pass a current generates a magnetic field that magnetic field passes through this solenoid. And when I connect a battery to this solenoid, I'm changing the magnetic field generated by this solenoid and the change in magnetic field seems to induce a current in the solenoid. If I disconnect again, the

00:17:05 magnetic field goes from maximum to zero. In that process, I again generate a current in the solenoid. The direction of the current in the two cases are opposite to each other. That's a very very important consideration we must know. So as you can see here there is a magnetic field generated irrespective of whether I move the magnet with the SPTO coil or I move the coil with SPTO magnet or I have another coil which is producing a magnetic field and I change the current in that second other coil. So all these

00:17:34 are producing a ch a current in the in the solenoid and that current is called an induced current and that induced current seems to be appearing whenever the magnetic field changes. So when I move the magnet inside the solenoid, I'm changing a magnetic field through the solenoid and it induces a current. When I move the solenoid and fix the magnet, I'm changing a magnetic field through the solenoid which also induces a current. I put another coil near this coil and change the current in the mag in this

00:18:05 coil and I change I change the current passing through the coil which changes the magnetic field passing through this coil in which I'm measuring the current and that induces a current. So these were some observations which Michael Faraday did in 1831 and which uh which opened up the entire field of electromagnetic induction and which is today a very very important part of modern machinery including transformers, generators and so on which are all working on the principle of electromagnetic induction. So a current

00:18:36 produces a magnetic field a constant magnetic field does not generate a current. A changing magnetic field seems to be generating a current and this is called Faraday's law of induction and we will discuss the mathematical principles behind the far farad's laws of induction. So what all have I shown? Uh moving a magnet near a coil generates a current in the coil. moving the coil in front of a magnet. It generates a current in the coil. The direction of current depends on the movement the uh

00:20:03 movement towards or away. Uh placing Another coil nearby and changing current through that coil generates a current. So all these observations were essentially coming out of the experimental experiment you have performed. So we will quantify all this into what is called as Faraday's law of induction. a very very important part of electromagnetics. Okay. Now I want to show you another interesting experiment of magnetic levitation in which I will show you that using magnetic forces we can suspend an object

00:21:29 and some of these principles are today used in magnetic levitation trains mag trains. So I want to show you another experiment in which I will use another property of magnetic fields and induced currents to levitate a another object. Yeah. Now let me connect to the other circuit. So I want to show you some very interesting experiment uh which is an experiment which shows how magnetic effects can lead to levitation. So this is a variac which actually uh decreases the 220 volts which is coming on the main line to any voltage

00:22:04 which I want by rotating this knob here. This is connected to the same solenoid as before. And there is a soft ion inside and that soft ion piece is actually concentrated magnetic field and as we have seen before the magnetic field can become very strong inside the solenoid because of the presence of the soft iron piece because the soft ion gets magnetized and that magnetized material produces its own magnetic field adding to the magnetic field produces produced by the current and which results in a very very strong magnetic

00:22:35 field. So I want a strong magnetic field inside the solenoid. And I have put a piece of aluminium here. That's an aluminium piece. Uh no, please remember that aluminium is non-magnetic. It does not get attracted to magnets. As you can see here, it's not getting attracted to a magnet at all. This is nonmagnetic. And so this is an aluminium piece. And I'm going to place this inside the inside the soft piece. Now what I'm going to do is the following. So let me explain. I'm going to so it's just

00:23:06 connected to the to the variac. Right now the variac has zero voltage. So there is no current passing through the solenoid and I have connected this through a resistance here just to make sure that I have control on the current that is passing through the solenoid. So now what I'm going to do is I'm going to slowly increase the current in the solen in the solenoid and as I increase the current the magnetic field increases and please remember the current which is passing through the variac and through this is a alternating

00:23:35 current. The current is changing with time it's changing at the rate of 50 times per second and it's a 50 Hz current. So the current is continuously changing with time which implies that the magnetic field generated by the solenoid is changing with time at 50 Hz and so the flux passing through this the magnetic magnetic fields seen by this is changing with time at the at the rate at which the current is changing with time. So as we have seen in the earlier demonstrations, a changing magnetic

00:24:04 field induces a current in a in a material. And so what will happen is when I change my current here, I will induce a current in this aluminium piece. And we will see what happens now. So let me start to increase the current in the sol in the solid in the solenoid and I put a screen here so that it becomes very visible. So now let me start to increase my current here. And you can see here the the aluminium ring is floating in air. It's uh floating because of the magnetic repulsion between the solenoid and the

00:24:37 aluminium piece. Now let me reduce the current. As I reduce my current, the piece comes back to the original position. If I increase my current here again the aluminum co the aluminium piece lifts itself and I can raise it to quite a height here by changing the magnetic by inducing currents here. So what is actually happening is the current through the solenoid is changing with time. That changing current in the solenoid changes the magnetic field passing through this soft iron piece. That changing magnetic field which is

00:25:10 changing through this aluminium now ring is inducing a current in the ring. These are called eddiurrens. Those currents are in a direction so as to oppose the change as we will discuss. And so there is repulsion between the solenoid and the current that is passing through the aluminium leading to a repulsion and a levitation. So it's it's called magnetic levitation. As you can see here, you can have an iron piece floating up above the solenoid simply by having an oscillating magnetic field here. So that is a very

00:25:40 interesting demonstration of how changing magnetic fields can be used to lift up objects leading to what we call as levitation. magnetic levitation that means you can lift objects above the surface simply by using magnetic fields. So now we will move on to some discussion and try to understand what is actually happening in the case of uh the the what is actually happening in in terms of physics. We'll write write down some equations and try to discuss the mathematical structure behind uh what we

00:26:12 have been seeing. So let me recall now again. So this was in 1831. Michael Faraday demonstrated this uh experiment to show magnetic induction. So what we have seen is the following. If I have two coils, one coil for example here and another coil here. So this coil is closed and if I change the current changing current in this coil in coil let me call call it coil A induces a current in coil B. So there is a if I change the current through this coil coil a it produces a magnetic field which is changing on the circuit and this in this

00:27:22 coil there is a current generated it's I call call it coil B. Now if I also move this relative to each other either coil A towards coil B or coil B towards coil A I will have again induced currents in coil B because of the magnetic field generated by the coil A. I also showed that if I have a coil and if I bring a magnet Either I move the magnet like this or like this there is induced current. So current gets induced in this in this coil here whether I move the magnet towards the coil or away from the

00:28:12 coil. And I showed you that the amount of current generated here depends on the rate at which I am moving. If I move faster I generate more current. If I move slower I generate less current. What I did not show here is another interesting part. So if I for example take a region containing a uniform magnetic field pointing downwards into the page as I'm plotting here and if I take conductor like this for example and if I place another conductor here so there is a uniform magnetic field in this space and if I move this

00:28:55 conductor So this conductor this this is now a circuit and if I move this conductor I'm changing the area of the circuit. When I do that I find current is induced in the circuit. So if I move this faster the current is more. If I move it slowly the current is less. So there are multiple situations in which current gets induced in a coil. And all these observations have led us to what we call as Faraday's law law of induction. Now one thing that is uh significant and we need to understand

00:30:00 is the following that suppose I have a which I showed you if I have a magnet and if I have a coil whether I move the magnet towards the coil or the coil towards the magnet I showed you there is induced current. So I fix the coil here, move the magnet, I have induced current. If I move the magnet forward and backward, I fix the magnet. If I move the coil backward forward, I have induced current. Same induced current. Whether if I whether I move this or move this, I generate the same induced current in the

00:30:46 coil. And so it only depends on the relative motion between the coil and the magnet. But look here what is the physical explanation for this induced current in one case in which I have the magnet fixed but the coil moving towards the magnet. So for example if I if I fix the magnet and move the coil towards the magnet the coil the mag the the circuit here contains for example let me take a circuit like this. So this is this is a circuit for example. So if I have a circuit here and a magnet, if I move I

00:31:23 showed you that if I move the magnet towards the circuit, I generate magnetic field. Sorry, I generate a current in the circuit. If I move the circuit towards the magnetic magnet, I also generate the same current in the circuit. Now let me try to understand why there should be a current generated when I move the circuit towards the magnet. Now you see here the circuit this material contains electrons, free electrons, conductor. So when I move this coil towards the magnet, the electrons in the in the in

00:31:54 the wire gets velocity in this direction. There is a magnetic field generated by the magnet. And we know that there is a lawren force acting on the electrons. The magnetic field produced by the magnet is acted upon as acting on the electrons in the conductor which are moving when I move the coil. And that force I will show you leads to a current in this coil. Simple lawren force. So there is a lawren force acting on the electrons in the in this in this coil. And that lawrence force results in a current in

00:32:29 the coil. So I can have an explanation for the induced currents when I move the circuit towards the magnet or away from the magnet. So what happens if I move the magnet? Now when I move the magnet, the electrons in the conductor are not moving. and I still induce the same current in the coil. This is a completely different explanation. There is no explanation with the law force here because the electrons are I'm not moving the conductor. I'm moving the magnet. So as I move the magnet, I'm changing the

00:33:03 magnetic field acting on the electrons. And if I assume there is no current and there is no electron motion, then obviously there is no s force. But still there is an induced current. And this is the beauty of parad laws of induction. It only depends on the relative motion between the magnet and the coil. And in the second case, when I move the magnet towards the coil, actually the changing magnetic field induces an electric field. And that electric field generates a current in the circuit. Please

00:33:33 remember if charges will move when there is a magnetic field because of Laurens force, V cross B force or because of an electric field. So if I move the magnet there is no lens force but there is a force due to electric field generated by the changing magnetic field that's a parad law of induction. So it's a very very important law which we will discuss. So let me write down the parad law of induction. So let me consider a path like this. So for this I must define magnetic flux first. Remember we had in electrostatics we

00:34:18 were discussing Gauss's law at at that time we had defined an electro electric flux electrostatic flux and that was used to define the Gauss's law. So similarly we can define a magnetic flux. So if B is the magnetic field then we define the magnetic flux is equal to integral B do DA over surface. S is a surface. Remember E do DA was the electric flux and we had defined Gauss's law in terms of electrostatic flux. Here we define the magnetic magnetic flux which is integral B dot DA. Now remember we had also shown

00:35:12 that integral B do DA is equal to zero. If you integrate BDA over a closed surface, you get zero because there are no magnetic monopoles. Magnetic field lines form closed loops. So integral B dot da over a closed surface is zero. But so please remember this is not a closed surface. This is an open surface. So it could be a surface like this. So for example, if this is my uh this is the this is a line. This is the uh sorry for example circuit and this could be the surface the surface which is here on the surface. So this

00:35:54 could be the surface. So I define b da as the flux. This is the flux. So according to Faraday's law, changing magnetic flux induces an electromotive force. emf you must have studied electromotive force when we were discussing uh circuits. So according to Faraday's law any changing magnetic flu flux will induce an electromotive force. So retro uh the flux is defined as minus d by b by dt which is equal to minus p by dt of integral dot this is emf here. So a changing magnetic flux produces an electromotive

00:37:20 force. That electromotive force is responsible for the generation of current in the circuit. You've seen electromotive force because of battery for example earlier. A battery has chemical energy inside it. This battery has chemical energy. That chemical energy is is a a source of electromotive force. And when you current connect a wire outside, that electromotive force drives a current through the wire. The same current is flowing through the battery. So there is a complete circuit. Similarly, this is

00:37:47 another form of electromotive force and this is uh because of a changing magnetic flux and electromotive force is defined as integral over a path E dot E is the electric field. Please remember I'm calling an electric field not an electrostatic field. An electrostatic field for an electrostatic field we know that integral E dol path zero. So this is an electric field. And this uh induces an emf defined by. So this is not a electrostatic fields. This is an electric field. And so we differentiate between electric and

00:39:00 electrostatic field. Electric field electrostatic field generate generated satisfy this condition. electric field are not necessarily integral is not zero because there is a force which is driving the current through the circuit. So Faraday's law of induction essentially implies that the emf generated is minus of rate of change of magnetic flux. This minus comes in because of what is called as lenses law. So according to lenses law whenever a change produces an electric current. The direction of the

00:40:02 current of the induced current is so as to produce effects opposing the change. So that is contained in this negative sign here. If d5 by dt is positive, induced emf is negative. If d5 by dt is negative, induced electric field is positive. So this is a an important aspect of the induced electromagnetic induced current and that current according to lenses law is so as to oppose any change. So if you are for example if this is my if this is my coil and if I have a magnetic field passing through this

00:41:13 coil what this says is if I change the magnetic flux through this coil by either moving a magnet towards the coil or away from the coil or by placing another circuit nearby whose current is changing or by fixing a magnet and moving this up and down. Either way, whenever the flux through this changes, there's an induced current. If the flux is increasing with time, the induced emf will be such that there is a current generated in this circuit which opposes this change. That means it will try to oppose the change

00:41:51 in increase of flux. Similarly, if the flux is decreasing with time, the induced current will will adjust itself so that the it opposes any reduction in the flux through this through the circuit. Now, let me rewrite this law here. There are there's an important part here which we need to understand. So, this law is integral over to close path is equal to minus d by dt of integral dot So C is the path of integration and S is the surface with uh path C as boundary. Now again let me try to show you a

00:42:57 demonstration to help you to understand what is this what what is the meaning of this. So suppose this was my coil. So let me assume a planer coil. So I can have a coil which uh which is like this. So if I I could have a planer coil like this. So that's my coil. So I must be careful in choosing the path direction of integration for the path of integration and the corresponding surface. And here I must choose the right-handed rule. So if my path of integration is like this, then you see that the right-handed

00:43:40 screw implies that the surface area must be like this because the right-handed screw rotates like this. So if I rotate like this, if my path of integration is like this, the area must be pointing up. If my path of integration is like this, the area must be pointing down. So this da here is related to the direction in which I'm doing this line integral. So if I integrate from here like this if this path closed path is starting from here and going like this then because right-handed screw implies that this rotation must be

00:44:17 towards me area of integration da is pointing up. If I integrate like this in the other direction from here to this closed path the area is downward. So please keep track of this because that involves a sign here and we must be consistent between the chosen path of integration defined in the circuit C here and the surface S. Now I must make sure I must make clear that the surface need not be the surface which is flat here. All that we need is the surface of integration must have this as the boundary. So the same

00:44:57 surface for example I could have a surface which is like this. So I can have the same and this this will be DA here is DA the the circuit or the path of integration is only the boundary of the surface. So for example here I could have this flat surface as the surface and this is my path of integration. That's the flux. Or I could have for example the same the same path of integration from here to here. But that's my surface. So path of integration is like this but that's my surface. I can choose any surface which

00:45:46 which is such that this path of integration is the boundary of the surface. Please remember this is not a closed surface. This is an open surface. So this is the path of integration and that's my surface. So if I integrate like this, my path of integration, the area vector is pointing outward. If I integrate like this, the area integral here is pointing inward. So there has to be consistency between the path of integration in my line integral here and the surface integration here with DA. So let me show

00:46:16 you some examples here. [Applause] So for example I could have a path like this with so if I do an integration like this the area will be like this and suppose I had a magnetic field in this direction that's my area. So here uh so let me call number one magnetic flux 5 B is integral B do DA is greater than zero because B do DA is BA cos theta and cos theta is positive so the flux is greater than zero. So if if B increases with time then D5 by DB C5 by DT is greater than zero. So if the magnetic field is

00:47:40 increasing with time, the flux is positive and d5 by dt is greater than zero. This implies the induced dmf which is minus d5 by by dt is less than zero. Now this area is I'm plotting up upwards here. So the the curve of integration is like this. And because B is negative, because induced emf is negative, induced emf must be like this. Please note here. That's my area. So let me um look at the coil again. Yeah. So that's my that's my coil. And in this coil I have suppose I do this integration like this. The area

00:48:35 is pointing up. Let me assume the magnetic field is pointing like this. So, P do da integral is positive. If the magnetic field is increasing with time, then dy by dt is positive, which means induced emf is negative. So, if I integrate like this, I will get a negative value, which means that the induced emf must be in this direction, which will induce a current flowing in this direction. Now see in this circuit the current is flowing like this because of induction because the magnetic field is changing

00:49:07 with time. The flux through this is changing with time increasing with time actually. Because it is increasing with time it induces an emf in this direction which induces a current in this direction. Now what is the direction of the magnetic field produced by this current? This current produces a magnetic field opposite to the direction of the magnetic field that you are increasing. Magnetic field that you applied is in this direction. A current like this will produce a magnetic field in the downward direction which is

00:49:38 essentially opposing this increase in flux. So please note the current is induced which is trying to oppose the change in the magnetic flux. It is not opposing the magnetic field. It is opposing the change in the magnetic field. It is change it is opposing any change in magnetic flux. If you're trying to increase the flux the current is induced such that it tries to decrease the flux. If you're decreasing the flux the current induced tries to ensure that the flux does not decrease as fast as you are trying to decrease.

00:50:07 So it's a kind of an inertial effect inertia that is happening. So for example let me take another situation. So I have the same same coil and area is here magnetic field is this is again magnetic flux 5b is equal to integral p da is greater than zero If B decreases with time then D5 by DT is less than zero and induced D MF is greater than zero because that's minus D5 by DT And because of the area like this, this is my path of integration. So, emf will be so the direction of emf now is opposite to the earlier case because the

00:51:28 magnetic field is now decreasing with time rather than increasing with time. So, let me leave uh two problems for you. Try to work out what will happen if I have the same areas. This is area A here and magnetic field is downward. B increase. What is the direction of EMF and four the same? A B decreasing with time. What is the induced MF direction? And this will uh make you understand that the direction of integration for the line integral for the path of integration relationship between that and the flux. And we need to be very

00:52:43 careful of using the right signs in these cases. Also, for example, if I had a circuit like this, let me assume I have a magnet here with magnetic field lines coming like this. So, okay. So, that's a magnet. This is the north pole of the magnet. This is the south pole of the web. Now if I move the magnet towards this coil. Now remember uh if I define my area is like this pi b integral b do da is greater than zero. magnet moving towards coil implies 5B increases with time d5 by dt greater than

00:54:09 zero. So emf which is minus d5 by dt is less than zero. So if this is my path and I had defined my area here like this and my path of integration should have been this for this uh integral and this is less than zero. Sorry path of integration must be like this the other way around because the area is pointing downward. So the path of integration must be like this. So induced current will be like this. So when the magnet moves towards the coil towards the circuit here it will induce a current in this direction

00:55:00 and as you can work it out that that induced current is trying to oppose the increase in magnetic flux through the coil. Please work out the remaining situations. I'll leave it as a problem to you. What will happen if I had the same coil, the same coil here, north pole, south pole, and the magnet is moving like this. And if I have south pole, north pole, magnetic moving like this. And then south pole, north pole, I don't like this. Please find the direction of induced currents. Calc find out the flux. Choose

00:55:51 a direction of integration path of integration. You have a calculation of flux and from there you can find out the direction of induced currents. So please look at this problem. very interesting problem to understand and that will make you understand the relationship between the path of integration for the emf and the surface that I must choose for the integration and again I must point out the surface need not be the flat surface as long as the path of integration is the boundary of the surface that's fine

00:56:19 so I will stop here and in the next class we will continue with discussion of uh electromagnetic induction and we will consider some examples and I'll show you what kind of fields are in for currents are induced in circuit Thank you very much. [Music]