# Video: Describing Optimisations in the Construction of an Electric Motor

Explain why rotating coils in an electric motor have small angles between their planes that are all equal

04:05

### Video Transcript

Explain why rotating coils in an electric motor have small angles between their planes that are all equal?

To start on our solution, let’s draw an electric motor that has just one rotating coil to it. We’ve sketched here a single conducting loop of wire or a coil that’s positioned between the poles of a permanent magnet. These are the only parts of an electric motor. But they’re the important ones for the purpose of our question. So we’ll focus on these.

We know that this permanent magnet will create a magnetic field in between its poles that points from the north pole to the south pole. And furthermore, we know that this rotating coil that we’ve drawn is a current-carrying coil. So we can draw a current, 𝐼, making its way around this loop.

What we have then is a current-carrying conductor in a magnetic field. And according to Fleming’s left-hand rule, this current-carrying wire experiences a force. This rule tells us that if we were to take our left hand and point our index finger in the direction of the magnetic field and then point our middle finger in the direction of current flow, where we consider current flow as conventional current, then this left-hand rule tells us our thumb will point in the direction of the resulting force on our current-carrying conductor.

We can apply this rule to our rotating coil to see which way the magnetic force on it acts. If we focus first on the left-hand part of the coil, the part here, then this left-hand rule tells us that the magnetic force on this particular segment of our rotating coil is downward. But if we switch over to the right-hand side of our coil, because the current in this site is moving in the opposite direction, the magnetic force is also in the opposite direction. It points up.

We see then that a rotational torque is applied to this rotating coil thanks to the fact that it’s a current-carrying conductor in a magnetic field. As this single coil rotates, the magnetic force on it remains the same so long as the current direction in the coil remains the same.

However, one thing that does not remain the same through all this is the torque applied to this rotating coil. For example, we can see that when our rotating coil is oriented vertically like this, the torque on it is actually zero because the forces are moving along the axis of rotation. This is in contrast to when our rotating coil was flat in a horizontal plane. In that orientation, the magnetic torque on the coil was at its maximum value.

In other words, in order to have this electric motor always supplying a nearly constant and maximum torque value, then we would always want to have a rotating coil that was oriented in a horizontal or nearly horizontal plane. So let’s say we add a coil at 90 degrees to our original coil.

So now our motor overall has two rotating coils set at 90 degrees apart from one another. That’s a good thing because now when one of the coils is arranged vertically, supplying no torque to the motor, the other coil is arranged horizontally, supplying maximum torque. And we can go even further than this because imagine that these coils were rotated 45 degrees from where they are now. In that case, both of our coils will be supplying some torque, not a minimum, but not the maximum either. That’s because neither of them is in a horizontal orientation. So we might want to add yet another rotating coil.

With more coils added to our electric motor, we’re more likely to have a single coil experiencing the maximum possible magnetic torque. Imagine looking at our set of rotating coils from the end on. Right now, it has three coils or loops in the magnetic field. And we’ve said that it’s the horizontally arranged coil that experiences the most torque.

As these coils rotate in a magnetic field, if we want to always or nearly always have a coil that’s in this horizontal orientation, a great way to do that is to add more coils. And notice that as we add more coils, they have the same angular separation one from another. They’re evenly spaced so that the overall torque supplied by our motor is near its maximum value and is nearly constant. And that’s what we can write in answer to this question.

We can say that it’s to keep the magnetic torque constant or nearly so at its maximum value. That’s why the rotating coils in an electric motor have small equal angles between their planes.