Why Does Rotating a Magnet Below a Horizontal Coil Not Produce Voltage?

[Charlie_V]

Hello every, I have a question I've never found a good explanation for. Referring to the picture, imagine a coil that is horizontally situated. A magnet is placed below it with the poles perpendicular to the center of the coil. The magnet can be rotated as shown. Now my question is, why does this not produce a voltage? I have my own explanation as to why but I would like to compare and see what other people think.

Thanks,
Charlie

 

[CompuChip]

Hi Charlie, welcome to PF.

First of all, let me assume that by "why does this not produce a voltage" you mean "why does this not induce a current in the coil".

I'm not even quite sure that this is correct. If the magnet were rotated around the other axis (perpendicular to the coil, so the N-S axis of the magnet) then I would not expect a current to be induced in the coil, while for the rotation you indicate I would. The reason being that along the N-S axis, the field of the bar magnet is symmetric so rotating it around this axis would not produce any flux changes in the coil, which is not true for the rotation pictured.

 

[Dadface]

Think of it in terms of Lenzs law
1. Start by assuming that an emf is induced and that a current flows.
2. If the assumption is correct any unlike magnetic poles induced in the coil will be symmetrically situated relative to the poles of the magnet.
3.Because of the symmetry of the arrangement the work done against the repulsion from one of the induced poles will be balanced by the work done by the field due to attracton from the other pole.
4.Since no work is done when the magnet is rotated the original assumption is incorrect and so no voltage is induced.

I think this is called a reduction ad absurdum method.

 

[Charlie_V]

Thanks for replying CompuChip,

You are correct, if you rotated the magnet about the axis parallel to N-S, nothing would happen. But rotating it the way I have drawn does not induce a voltage either - as long as the magnet is rotating at the exact center of the coil (assuming the coil is uniformly constructed). If the magnet is moved just slightly left or right from the center point of the coil, voltage is induced. I've experimentally done this.

The only explanation I could come up with is that in the exact center of the coil, an equal amount of flux traverses each side the coil, so the voltage induced in each half of the coil is equal and opposite to the other half. The induced voltage then neutralizes itself and the result is zero potential across the coil.

I'd like to point out I'm only talking of voltage and not current because the coil is unloaded - so no in-phase current flows.

 

[Doc Al]

The only explanation I could come up with is that in the exact center of the coil, an equal amount of flux traverses each side the coil, so the voltage induced in each half of the coil is equal and opposite to the other half. The induced voltage then neutralizes itself and the result is zero potential across the coil.

Sounds good to me. It's as simple as that.

 

[Charlie_V]

@Dadface

That sounds like a pretty reasonable explanation. Is there really work done against an unloaded coil though?

 

[Dadface]

The work done would be very small when compared to that done with a loaded coil.If the magnet was off centre work would be done in driving the charge carriers to and fro along the coil.It may help to think of it in terms of the eddy currents that would be induced if the coil were replaced by a lump of metal.I think that your answer is simpler as Doc Al suggested.