### Video Transcript

Which of the following diagrams showing a direct-current motor correctly labels the terminals of the motor? The coil of the motor is simultaneously shown at four different angles to the magnetic field of the motor.

We’re shown two different diagrams, (A) and (B), and these diagrams are very nearly identical. Both diagrams show the north pole of the magnet on the left and the south pole on the right. So, the magnetic field of the motor on both diagrams is from left to right. Both diagrams also show that the coil is rotating clockwise. So, the left-hand side of the coil will move upwards and the right-hand side of the coil will move downwards. In fact, the only difference between these diagrams is that the left-hand diagram has its positive terminal on the left and its negative terminal on the right, whereas the diagram on the right has its positive terminal on the right and its negative terminal on the left.

And the question asked us which of these diagrams correctly labels the terminals. To answer this question, we will use the right-hand rule. The right-hand rule tells us that if we take our right hand and point our fingers in the direction of current in a wire and then we bend our fingers so that they point in the direction of magnetic field across the wire, then if we outstretch our thumb, then this will point in the direction that the wire moves.

In our case with the diagrams that we’re shown, we can consider the left-hand piece of wire of the coil when it is horizontal. As we know, the magnetic field is from left to right. And we also know that that side of the coil moves upward. And we can use the right-hand rule to work out the direction of current in that side of the coil. Now, this setup shown in the diagrams is very similar to the example that we did for the right-hand rule. The motion of the wire in both cases is upward. However, in our question, rather than the field being out of the diagram as it was in the example, the magnetic field is from left to right. And we can rotate our hand by 90 degrees around the thumb to match this, meaning our field is rotated by 90 degrees as well.

This is the same for the direction of current. So, if we rotate it from pointing right to left by 90 degrees, we see that the current is now pointing out of the diagram. So, the correctly labeled diagram will show that the direction of current from the left-hand side of the coil is out of the diagram. Let’s start by looking at diagram (A).

We can follow the route that current takes around the coil. Starting from the positive terminal of the motor, charge flows into the coil from the left, clockwise around the coil, and then out of the coil into the negative terminal on the right. Immediately, we can see that the direction of current in this left-hand side of the coil is into the diagram, which we know is incorrect. Therefore, we can rule out diagram (A).

Now, let’s take a look at diagram (B). Repeating the process, we see that charge flows into the coil from the right, flows counterclockwise around the coil, and then out of the coil to the negative terminal on the left. We can see that in diagram (B) the direction of current in the left-hand side of the coil is correctly out of the diagram. And therefore, the terminals are labeled correctly, with the positive terminal on the right and the negative terminal on the left.

So, we’ve ruled out diagram (A). And we’ve shown that diagram (B) has the correct direction of current in the coil. Therefore, the diagram that correctly labels the terminals of the motor is diagram (B).