Homopolar Motor

Question

How does a homopolar motor work?

Answer 1

How do these work?

A homopolar motor is moved by Lorentz forces due to the magnetic field of a permanent magnet (or magnets) interacting with the current in a loop (or loops).

A cross-section of the magnetic field is shown on the diagram below (copied from this Wikipedia article).

In this particular implementation, we have one permanent magnet and two current loops, sharing one side, formed by the battery. Here we can see that magnetic field lines form various angles with various parts of the loops, but all Lorentz forces acting to the loops happen to push the wire frame in the same direction - clockwise, looking from the top.

Since the wire frame is spinning around the axis of the magnet, the relationship between the magnetic field lines and the current in the loops remains the same regardless of the position of the frame, so the Lorentz forces keep pushing the frame in the same direction.

If the second magnet is added on the top, its polarity would have to be opposite to the polarity of the magnet on the bottom, so that both magnets push the frame in the same direction.

If one of the loops is removed, the frame won't be well balanced, but, fundamentally, the operation of the motor wont't change.

What affects the speed of these homopolar motors?

The speed of the motor depends on the torque and friction.

The torque depends on the strength of the magnet, the current (limited by the internal resistance of the battery) and the shape of the wire frame: the narrower the frame, the stronger the torque, since the strength of the magnetic field decreases faster with the distance from the axis of the magnet than the lever increases. Of course, the frame should not be too narrow, since closer to the axis the field lines are pointing mostly up, so there must be some optimal width.

The friction is mostly affected by the sliding contacts, so there is a trade-off between the friction and the quality of the contacts. The weight of the wire frame also plays some role.

As the frame speeds up, the friction slightly increases until, at some speed, the counter torque caused by the friction balances out the torque caused by the Lorentz forces and the motor reaches its steady state speed.