Video: Understanding Lenz’s Law

The diagram shows a bar magnet moving toward a solenoid. This induces an electric current in the solenoid, which creates its own magnetic field in turn. Which end of the solenoid is the north pole of the induced magnetic field?

03:57

Video Transcript

The diagram shows a bar magnet moving toward a solenoid. This induces an electric current in the solenoid which creates its only magnetic field in turn. Which end of the solenoid is the north pole of the induced magnetic field?

Okay, so, in this question, we can see that we’ve got a bar magnet being moved toward a solenoid, or a coil of wire. Now, at this point, it might be helpful to draw in the magnetic field lines from the bar magnet. So, here are the magnetic field lines from the bar magnet, drawn in green.

Now, let’s also recall that magnetic field lines flow from the north pole to the south pole of a magnet. Therefore, in our particular case, the magnetic field lines are flowing in this direction, both the top field lines and the bottom field lines. And near to the north pole, we can see that the magnetic field lines are flowing out of the north pole.

Now, we’ve also been told that the bar magnet itself is moving towards the solenoid, in other words, towards the right. And so, as a result of this motion, we can see that magnetic field lines pointing into the solenoid are entering the solenoid as the bar magnet moves. And therefore, the magnetic field through the area of the solenoid coils is changing with time. And more specifically, magnetic field lines pointing into the solenoid are moving into the area of the solenoid as the bar magnet moves.

Now, as the question tells us, this results in a current flow in the solenoid. And this happens because an emf, or electromotive force, aka a voltage, is induced across the solenoid because of the change of magnetic field through the area of the solenoid itself. This phenomenon is known as electromagnetic induction, where the changing magnetic field through an area of wire induces an emf across that wire. And if that wire forms a closed loop, then a current can flow through that wire as well.

And importantly, the current that starts to flow through the wire flows in a specific direction. In other words, in our solenoid, current could potentially flow this way, or it could flow the other way. And em induction tells us that it must flow in a very specific way. Not the direction of current itself, in this particular case, isn’t important. But what is important is that the current must flow in a specific direction so that the magnetic field due to this current flow opposes the change in magnetic field due to the motion of the bar magnet.

In other words, we’ve said earlier that magnetic field lines pointing in this direction from the north pole of the bar magnet are entering the solenoid. And so, the solenoid will have a current flowing through it. And that current will induce its own magnetic field. This induced magnetic field will oppose the direction of the changing magnetic field due to the bar magnet.

In other words, then, because rightward-pointing magnetic field lines are entering the solenoid, this means that the magnetic field strength is increasing in the rightward direction through the solenoid. And so, to counter this, the solenoid will generate its own magnetic field that points towards the left. But, of course, this is only true through the centre of the solenoid. The magnetic field through the rest of the solenoid actually looks very similar to that of the bar magnet. And so, we can sketch in the magnetic field from the solenoid, which actually points in this direction.

And we can actually sketch in a few more magnetic field lines to see that the magnetic field is pointing away from the part of the diagram labelled A and towards the part of the diagram labelled B. But then, as we saw from the bar magnet, magnetic field lines point away from the north pole and towards the south pole. And so, if we were to replace our solenoid with another bar magnet, then that bar magnet would have its north pole pointing towards the left, in other words, opposing the motion of the original bar magnet, which was towards the right.

And this make sense. Remember, the original bar magnet moving toward the right is resulting in an increase of rightward-pointing magnetic field through the solenoid. So, the current induced in the solenoid will try and resist this. And the way to resist this is to create a magnetic field of its own that points towards the left, in the opposite direction. And so, coming back to our original question, we can see that the end of the solenoid, which is the north pole, is the left end here. In other words, the answer to our question is A.

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