# Magnet falling through a coil that does not form a circuit. Am I wrong or is the mark scheme?

So either this past paper is wrong or my ideas about induction have a problem.

The old exam I am doing asks what happens when you drop a magnet through a coil connected to an Amperemeter, and then how it might be different were the Amperemeter not properly connected (i.e. the circuit is incomplete).

My understanding is this: When you drop a magnet through a copper coil the acceleration is reduced as it enters (and leaves) the coil as these are the points where the flux linkage change occurs, and so EMF will be induced. This EMF will oppose the direction of motion (Lenz's Law) and thus it will slow the magnet.

Hopefully I'm right so far. I was under the impression that having an incomplete circuit wouldn't change a thing. But the mark scheme says this:

• Magnet now falls with acceleration g
• EMF induced
• No current
• So no energy lost from circuit [Or no opposing force on magnet, or no force from magnetic field, or no magnetic field produced]

I can sort of convince myself that a break in the circuit will stop electrons flowing round the coil which might stop the EMF being induced in the first place, but it certainly doesn't sit well with me. Also the fact that the MS says that EMF is induced, I thought Lenz's law stated that the induced EMF will always oppose the motion that caused it? If it's not opposing the motion, what the hell is it doing?? Also if the mark scheme is correct and I'm just way more misguided than I thought, can someone explain how a coil that doesn't form a complete circuit is different to a copper tube, because I'm pretty sure I've seen this done with a copper tube and the magnet definitely didn't fall at g.

• Real coils have a small capacitance, meaning that the establishment of the EMF $\mathcal{E}$ generates a minute current that charges the capacitance by moving electrons around in the wire. Given enough time the total charge would be $Q = \mathcal{E} C$. Aug 8 '17 at 17:36

The break in the circuit will stop electrons from flowing, but it does not stop the EMF from being induced. The EMF is simply canceled out by the electrostatic forces which prevent the electrons from "bunching up".

Without the flow of current, there is no generation of a secondary magnetic field, which is the thing which would normally slow the fall of the magnet. Therefore, the magnet remains in free fall. Because power loss is proportional to current, there is no power loss either, and energy conservation works out as expected.

In a copper tube, the electrons are perfectly free to flow in the azimuthal direction, because there would be no "bunching". In essence, each cross-sectional slice of the pipe forms a closed circuit. It is a topologically different system than a broken coil.

For reference - a more accurate (though wordy) transcription of Lenz's law might be

The induced EMF will generate a current which creates a secondary magnetic field which opposes the change in the original magnetic field

but this only applies to closed loops. If the loop is broken then current cannot flow, and the rest of the rule goes out the window.

Lenz is all about the induced current which flows in such a direction as to try and oppose the motion producing it.

Your reasoning in terms of energy is correct because if there is no (induced) current there is no dissipation of energy as heat and no force of opposition to the motion.

With the copper tube you have a complete circuit in the form of elements of the tube which are rings piled on top of one another.