 In previous videos we looked at how changing magnetic flux through a closed loop or a coil induces a certain amount of emf or current. In this video let's predict if certain amount of emf is generated for a bunch of cases where magnetic flux is changing. Now magnetic flux is BA cos theta and we can change the magnetic flux through a closed loop if we change the magnetic field strength through it or the area of the coil or the angle between the magnetic field and the area vector and in this video we will be looking at examples for each of them. So let's begin. Let's look at the first case of changing magnetic field strength through a loop. Now for this we have a straight current carrying wire and a square loop with a lamp attached to it situated right next to it. Now in our previous videos we talked about how to figure out the magnetic field of a current carrying wire and for this we used the right hand grip rule. So for instance if the current is going in the upward direction my thumb should be pointing in that direction and the curl of my fingers it gives the direction of the magnetic field. So if the current is going upwards the magnetic field would be concentric circles just like this and also notice how as you go further away from the wire the density of the magnetic field lines decreases. That means the strength of the magnetic field is decreasing as you go further away. There is more strength near the wire and the strength decreases as you go further away. Now if we try and move this square loop with the lamp it will try and move this to the right. I am sure you can see that there will be some change in the magnetic flux. That is because at this moment there is some flux that is going through it but if we move it that flux would change because the strength of the magnetic field is changing as you go further away from the wire and if the flux is changing that should induce some EMF in the loop which should light up the lamp and that should look just like this. And notice how the bulb stops glowing when we stop moving the loop that is because then we are not changing the magnetic flux through the loop and if there is no change in magnetic flux there is no induced EMF and therefore we do not see the bulb glowing. Now there are some other ways to change the strength of the magnetic field through this loop. Let's say if we increase the current in this fire that would generate magnetic field lines with greater strength and in that case we won't even have to move the loop because if we kept on increasing the current in the wire that will keep on producing stronger and stronger magnetic field lines and that will keep on changing the flux through this loop. What would happen if we move this loop up or down? In that case first let's try and understand how the field lines look like for this straight fire. So we can see that they are concentric circles but they are also on top of each other. So if I add one more layer it would be somewhat like this. Of course there would be layer right next to it but we can't like it's difficult to draw that so you could imagine there's a layer right below it and we can draw one more layer which let's say it's even below that. Now if we move this loop down, if we move it down like this then notice something that is not changing is the strength of the magnetic field that is passing through the loop. That is not really changing even if you moved it above that strength is not really changing and like you could imagine some more field lines right in between these two they're right next to each other so you'll have, you continuously have field lines going through the square loop but the strength of them is not changing that is because the space between the magnetic field lines or the density of the magnetic field lines is not changing when you move the loop up or down. So if the strength of the magnetic field doesn't change through the loop that means the magnetic flux isn't changing and that means there won't be any induced GMF and we won't see the bulb glow just like how we aren't really seeing it glow when we move it up and down. Now let's look at the second case where we will change the area of the loop and for this one we have a region of magnetic field, a region of uniform magnetic field and there's a coil which is kept right at the center of it. Let's attach a lamp to it as well. Now we will try and increase the area of this coil and from what we know about magnetic flux which is phi equals to B multiplied by A the area multiplied by cos theta from what we can see over here if we can increase the area of the coil if we increase this area that will increase the number of magnetic field lines that are passing through that area. So that should increase the magnetic flux. So if the magnetic flux is changing then we should see some induced GMF in the form of the bulb glowing. So let's do that. Let's try and increase the area of this coil and yes we can see the bulb glowing in this one. Notice how when we stopped increasing the area of the coil the bulb also stopped glowing because then even though there's some magnetic flux that is going through the coil at this very instant there is no change in magnetic flux and that change only gives rise to some GMF and some current. Let's continue this example further. Let's keep on increasing the area of this coil and see what happens. Now if we further increase the area of this coil what do you think will happen? Will you see the bulb glow? Will there be any induced GMF for current? Why don't you pause the video and think about it? All right. So from what we know about magnetic flux which is BA cos theta if we increase the area if we increase the area of the loop we get more magnetic flux through that loop. So it seems that upon increasing the area we should get more magnetic flux and there should be some change in the magnetic flux. So we should eventually we should finally see the bulb glow. So let's see if that is happening over here. Now when we increase the area we do not really see anything happening. How can that be? Now for this let's go back to the very basic definition of flux. Flux is the amount of something that passes through a surface. Now this something could either be electric field lines if you're talking about electric flux. Over here they are magnetic field lines because we are talking about magnetic flux. Now notice even if we increase the area of the coil the number of magnetic field lines that are passing through this coil remain the same. They were 1, 2, 3, 4, 5, 6, they were 12 magnetic field lines to begin with and even after increasing the area of the coil further there are still 12 magnetic field lines that are passing through it. So the amount of magnetic field lines or the number of magnetic field lines passing through the surface remain the same. So this area in the magnetic flux relation is the area through which the magnetic field lines are passing through or the magnetic field lines are intersecting with or linked with. So even though the area of the coil is increasing the area in this equation is not increasing because the area in this equation is the area that the magnetic field lines are linked with or passing through and that is a small area over here. Therefore the flux is not changing. So now if the flux doesn't change there would be any induced DMF and we do not see the bulb glowing. Now let's look at the last case where we will change the angle. So for this one let's take a coil and three axis of rotation you have y, x and z and let's attach a lamp so that we know if there is some EMF generated or not and the magnetic field lines are vertically downwards. So now first let's try and rotate this coil about the z axis. Now in this case in order to figure out if the magnetic flux is changing let's try and visualize this. Let's try and visualize how the coil would look like when it starts rotating about the z axis. So let's say we are standing right over here. This is our eye and we are looking at the coil from the side. This is how we are viewing it. So from this direction the magnetic field lines would just be vertically downwards. They would remain vertically downwards and the coil. The coil would seem to be in a horizontal direction like this. So at this point you can see that the flux through the coil is like it's just simply equal to b multiplied by a, the magnitude of the magnetic field strength and the area of the coil whatever the area might be. And if you think about the angle between the magnetic field and the area vector over here that would either be 0 degrees or 180 degrees because if we look at the area vector we can take the area vector to be just like this vertically down or vertically up. In the first case the angle is 0 degrees the angle between the green, the magnetic field line and the yellow arrow vector and in the second case the angle is 180 degrees. In either case the magnitude of cos theta would be 1. So the flux in this case would just be b a. Now let's say the coil has rotated by 90 degrees and you are still looking at the coil from the side. So how will it look like then? Let's draw the magnetic field lines. When the coil is rotated by 90 degrees it would just be vertical. So I'm just drawing a straight line. That is what you will see. And to begin with the lamp was kind of like this. This is this was a lamp and at the end the lamp is at the top. This is a lamp. So now the flux would just be 0 because there are no magnetic field lines which are passing through the coil. There is no flux passing through the coil. So we saw that magnetic flux went from something like a maximum b a to 0. So there is some change in flux happening as the coil is rotating about the z axis. And if there is some change in flux there should be induced emf. There should be induced current and the bulb should be glowing. So let's see if that is happening. Yes, that is what happens. Now let's rotate the coil about the x axis. So we will adopt a similar approach. We will try and look at the coil from a side. So let's pick this side now. Let's say this is where we are standing and this is how we are seeing the coil from from the side. So the magnetic field lines would still be vertically down and to begin with the coil would seem to us to be in in a horizontal position. And if we look at the coil from this side we won't be able to see the bulb really because the bulb would be on the other side. So the flux at this moment similar to how it was with the case of that axis to begin with the flux over here would just be b multiplied by the area. And if we think about the angle the angle could either be 0 degrees or 180 degrees and in either case the magnitude would come out to be as one. So cos theta is just one. Now let's say that the coil has rotated by 90 degrees. So what will we see then? Again the magnetic field lines are vertically down and the coil would become vertical. So I'm drawing that I'm showing that by a vertical line like this. Now over here you can again see that there is no flux the flux would just be zero because there are no magnetic field lines passing through the coil. So there is no magnetic flux and over here we also saw that the flux went from something like a maximum B a to 0. So there is some change in magnetic flux that is occurring over here and when there is a change there will be some induced DMF and we should see the bulb light. So let's see how that looks like. Yes, this is how it looks like the bulb is glowing and there is some induced DMF. Now the last variation is if you rotate this coil about the y-axis and I'm sure you can see that if we do that if we rotate the coil about the y-axis there won't be any change in the magnetic flux through the coil because we are not changing any angle between the magnetic field and the area vector and we aren't changing the area that is linked with the magnetic field and of course we aren't changing the magnitude of the magnetic field itself. So none of the factors are really changing if we rotate the coil about the y-axis and you can try and visualize that as well. If we do rotate it about the y-axis this lamp would be in this position after some time then it would be over here then it would be over here then back again to its original position and you can see that at all those instance everything remained the same the magnetic field strength to the coil the area that is linked with the magnetic field and of course the angle between the magnetic field and the area vector didn't change at all. So we won't see the lamp lighting in this case because there is no change in magnetic flux no net change in magnetic flux and therefore no induced emf or current. In this video we looked at a bunch of situations where changing magnetic flux led to some induced emf and particularly we looked at three types of cases the first one was when we changed the magnetic field strength through a loop and we could either move the loop in that case or if we could increase the current to change the magnetic field strength through the loop then we looked at changing the area that is linked with magnetic field and finally rotating the coil about some axis which changes the angle between the magnetic field and the area vector of the loop.