Lenz's Law

Transcript

0:00Introduction

Hello everyone! Let's start with a small experiment. Hold a bar magnet above a horizontal copper ring, and let it go, so that it falls straight down the axis, through the ring. The ring is just a closed loop of copper, with no battery in it. So tell me, does the magnet simply fall freely, with acceleration g, the acceleration due to gravity? Hold on to your guess. By the end of this video, you will know the answer, and exactly why. The key is Lenz's law, which gives the direction of an induced current, and questions on it come up often in JEE, so let's begin.

0:38Lenz's law: the current opposes the change

So, here is Lenz's law in one line. The induced current flows in the direction that opposes the change in flux that produces it. Notice the words, the change in flux. We will come back to them, okay? Now look at the figure, the left half first. The bar magnet has its north pole, marked N, facing the coil, and its south pole, marked S, at the far end. The green arrow says the magnet moves in, towards the coil, so the flux through the coil is increasing. The coil must oppose this increase, and the orange label shows how it does that. With me? The induced current makes the near face of the coil a north pole. So a north pole faces a north pole, and the coil repels the magnet. The dashed grey arrow, marked repels, shows that push. The coil pushes back against the approach. Right? Now look at the right half. The magnet moves out, away from the coil; receding means moving away. So the flux through the coil is decreasing. The coil now tries to keep that flux, so its near face becomes a south pole, and the dashed arrow, marked attracts, shows it pulling the magnet back. Approaching or receding, the coil always opposes the motion that changes the flux. Clear? Now let us connect the face to the current. The little orange arrowheads on each coil show the induced current. So tell me, for the approaching north pole, the near face of the coil is a north pole. Seen from the magnet's side, is the induced current clockwise or anticlockwise? It is anticlockwise, yes, exactly! Here is the rule: a face is a north pole when the current in it looks anticlockwise, seen from outside. Our near face is a north pole, so, seen from the magnet, the induced current is anticlockwise. Got it?

2:29Why must it oppose? Conservation of energy

But why must it oppose? Why not help instead? Imagine the coil attracted the approaching magnet. What would happen next? That is correct, the magnet would be pulled in faster and faster! If the induced current helped the change, the motion would speed up by itself, and create energy from nothing. That is impossible, right? So the induced current must oppose the change. Then you have to push the magnet in, and work must be done against the opposition. Got it? And your work is not lost: it appears as electrical energy in the coil. So Lenz's law is simply the law of conservation of energy, applied to induction.

3:12Topper's trick: three steps to the direction

Okay? Now, here is a trick toppers use for every direction question, in just three steps. Step one: find the direction of the original field through the loop. Got it? Step two: decide whether the flux is increasing or decreasing. Just look at what is changing. Right? Step three: if the flux is increasing, the induced field points opposite to the original field, to fight the increase. Clear? Now, what if the flux is decreasing? Lenz's law means oppose, so the induced field is opposite to the original field again, isn't it? No, no, careful, this is the most common trap! When the flux is decreasing, the induced field is in the same direction as the original field. It tries to stop the flux from falling. With me? Because Lenz's law opposes the change in flux, not the flux itself. These are the words we noticed at the start, and now you can see why they matter. Got it? Then, once you know the induced field, the right-hand rule gives the current. Curl the fingers of your right hand along the current, and your thumb gives the field inside the loop. So point your thumb along the induced field, and your fingers show the current. Okay?

4:30Example 1: loop pulled out of a field into the page

Now our first example. Here, a rectangular loop is being pulled out of a region where the magnetic field points into the page. Find the direction of the induced current. Use the three steps, and pause the video and try it first. Are you done? Okay, let's check. Step one: the original field points into the page. On screen, the circle with a cross is the symbol for into the page. Right? Step two: as the loop comes out, less and less of its area is inside the field. So the flux into the page is decreasing. Clear? Now let's do step three. Lenz's law opposes, so the induced field must point out of the page, right? No, no, wait, this is the trap we just saw! The flux is decreasing, so the induced field points the same way as the original field, into the page, to keep the flux from falling. Got it? Finally, we use the right-hand rule. Point your right thumb into the page, and your fingers curl clockwise, as you look at the page. So the induced current is clockwise, and we are done. The three steps make it really quick. With me?

5:41Example 2: magnet falling through a copper ring, a vs g

Now, remember our falling magnet from the start? Let's settle it. Here, a bar magnet falls along the axis of a horizontal copper ring. How does its acceleration compare with g, the acceleration due to gravity, first while approaching the ring, and then just after passing through it? The letters in brackets mark the two parts, part A and part B, on screen. Pause the video and try it first. Are you done? Okay, let's check. In part A, the magnet approaches, so the flux through the ring increases. Just like the coil in our figure, the ring repels the approaching magnet. The magnet is above the ring, so this push on the magnet is upward. Okay? Now for part B, the magnet has passed through, and moves away below the ring, so the ring now attracts it. Attraction, so the magnet speeds up, and its acceleration is more than g, right? Oh no, careful, look where the ring is now. It is above the magnet! The flux through the ring is decreasing, so the ring attracts the magnet, and that pull is upward, back towards the ring. Clear? So the ring's force on the magnet is upward both times, and the acceleration is less than g in both cases. And that answers our puzzle from the start: the magnet does not fall freely, because the ring opposes its motion both times. Right?

7:10Quick revision: oppose the change in flux, not the flux

So, quick revision. First, the induced current opposes the change in flux, not the flux itself. Second, if the flux is increasing, the induced field is opposite to the original field; if it is decreasing, the induced field is in the same direction. And third, Lenz's law is conservation of energy: the work done against the opposition becomes electrical energy. Now go and try the four practice problems on this page. Use the three steps, and you will find them easy. All the best!