Re: [Phys-L] Falling magnet and eddy currents

[Chuck Britton <britton@ncssm.edu>]

A good question, indeed. Feynman himself had to think (just a bit) before answering. 

For the short coil, just like for a short piece of pipe, we easily see that the current flows ‘one way’ as the magnet approaches and the ‘other way’ as it leaves. This is necessary in order for the current to act to keep the flux constant. 

So we see that the current MUST switch direction somewhere as it falls. 

For a long solenoid, while the magnet is fully enclosed, the magnet cannot add or subtract to the flux enclosed by the solenoid. There is still an emf below the magnet that is in the opposite direction to the emf that is above the magnet. The solenoid is formed of a single wire that is being subjected to opposing emf’s. These opposing emf’s cannot drive a current or establish a voltage in the wire. 

(When the magnet is at either end of the solenoid, the OTHER emf wins out.)

Someone posed the question of dropping a magnet through a superconducting pipe. Assuming that the magnet does not levitate over the open end, it will slowly enter the tube, but then fall freely to the other end since there is no restive force to damp the motion. There is no way to dissipate the gravitational energy of the magnet.)

A snarky way to address your student's question is to point out that the voltage doesn’t know which way to ‘point’, so it just becomes zero. 

In general, eddy currents form closed loops within a bulk conductor. This is what happens in a metal tube.

A solenoid is formed of a single insulated wire which prevents eddy currents from flowing. 

(There can be tiny eddy currents within small wires - but these won’r have much effect.) 
 
> On Sep 18, 2022, at 1:09 PM, Antti Savinainen via Phys-l <phys-l@mail.phys-l.org> wrote:
>
> Hi,
>
> Nowadays I seldom get a question that I cannot answer from my students. The reason is that after nearly 30 years of teaching physics, I've heard a lot of questions.
>
> The recent question I couldn't anwer is about a falling magnet, induced emf, and eddy currents. If a solenoid is long, zero voltage is observed when the magnet is fully inside the solenoid:
>
> https://mammothmemory.net/physics/magnets-and-electromagnetism/electromagnetism/drop-a-magnet-through-a-solenoid.html
>
> On the other hand, the effect of eddy currents is clearly observable with naked eye if a neodymium magnet and an aluminium tube is used.  This is easy to explain using Faraday's law.
>
> So far, so good?
>
> A student asked why there are no eddy currents in the long solenoid when the magnet is fully inside, since the situation looks quite similar to the aluminium tube case. Of course, one clear difference is that the long coil has a much larger resistance than the aluminium tube which would limit the effect of eddy currents on the falling magnet if there were an induced emf in the first place. However, there is a change in magnetic flux through an individual coil turn in the solenoid (quite similarly to the aluminium tube) when the magnet passes by, although there is no net change of magnetic flux through the solenoid as a whole.
>
> Perhaps I'm missing something important here. How would you answer the student?
>
> Regards,
>
> Antti Savinainen, PhD
>
> Kuopio Lyseo HS
>
> Finland
>
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