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Video: Understanding the Magnetic Field of Bar Magnets

Parth Gharfalkar

Which of the four diagrams correctly shows the field lines of the magnetic field produced by a bar magnet?

04:07

Video Transcript

Which of the four diagrams correctly shows the field lines of the magnetic field produced by a bar magnet?

So we’ve been given four diagrams. And we need to determine which one shows the correct field lines. In order to be able to work this out, we need to know what field lines actually tell us. Magnetic field lines represent the direction of force on a test magnet in the field. In other words, if we place a small compass, for example, a small magnet, inside the field, the field lines would tell us which direction that compass will point.

Specifically, magnetic field lines represent the direction of force on the north pole of that small test magnet. So we can go about placing a small test magnet in each one of these fields and seeing what happens.

The other piece of information that we need to know in order to be able to solve this problem properly is that opposites attract. The north pole of the bar magnet should be attracted to the south pole of the compass that we place in its field, and vice versa.

So let’s start by placing a compass in the magnetic field of the first diagram. Let’s say we place the compass here. Well, what’s gonna happen in that case? Well, the direction of the field lines basically show us the direction at which the compass will point. Therefore, the arrow in the compass will point this way.

And of course, we should remember that the arrow end — that’s this end over here — is the north pole of the compass. And the other end — that’s this end — is the south pole of the compass. So what we can do is to imagine taking this compass and following the magnetic field line.

Well, as we start moving in this direction, we can see that the north pole of the compass meets the north pole of the bar magnet. In other words, the two like poles are attracting, the north pole of the compass and the north pole of the bar magnet.

Now this goes against what we said earlier about opposites attracting. We want the north pole of the compass to be attracted to the south pole of the bar magnet. Therefore, this diagram is not a correct representation of the magnetic field of a bar magnet.

Let’s move swiftly on to number two then. Let’s place our compass here this time. Well, the compass basically follows the direction of the magnetic field lines. So this is what the compass arrow will show. And so far, this looks okay. The south pole is pointing away from the north pole. And the north pole seems to be pointing towards the south pole of the magnet.

However, if we were to place this compass over here now, once again the compass follows the direction of the magnetic field lines and the compass points this way. So now it looks like the south pole of the magnet is pointing towards the south pole of the compass. And this north pole of the compass seems to be pointing towards the north pole of the bar magnet. This makes no sense. Once again, it breaks the rule of opposites attract, because of course the opposite should attract anywhere in the magnetic field, not just in some places. Therefore, this diagram is also an incorrect representation of the magnetic field of a bar magnet.

Let’s then look at diagram number three. Let’s place the compass here this time. Well, once again, the compass follows the field lines and points in this direction, with the north pole and south pole being labeled as such. This looks okay. The north pole is pointing towards the south pole of the bar magnet. And the south pole is pointing towards the north.

However, let’s now place the compass here. Well, now it follows the field line again and points in this direction. This time, north is pointing to north and south is pointing to south. That again violates our rule of opposites attract. So this cannot be our correct diagram either, which means that number four must be right. So let’s give it a go.

Let’s say we place our compass here. Well, this is what the compass is gonna do. It will follow the field lines once again. And the north pole points to the south of the bar magnet and the south pole of the compass point to the north pole of the bar magnet. And this is true regardless of where we place the compass.

Let’s say we place it here instead. Well, once again, the compass arrow follows the field lines. And the north pole of the compass points to the south pole of the bar magnet, and vice versa. Therefore, this fourth diagram must be the correct description of the magnetic field produced by a bar magnet. And that is the final answer to our question.