EMF induced by Bar Magnet falling through a Coil

[neilparker62]

TL;DR

Induction, Lenz's law

What should a graph of induced emf look like if you have a relatively short bar magnet falling through a long coil ? Let's say the north pole is first to enter. So as it approaches a North pole will be induced in the coil which then looks like a N-S bar magnet. When the magnet exits , the south pole leaves last so at that point a North pole will be induced at the other end of the coil which now ends up like a S-N bar magnet. So overall the emf should have a positive peak and then a negative peak or vv. I'm not quite sure what happens in between. Are the two peaks symmetric or does the graph have some asymmetry due to the bar magnet slowing down on entry and speeding up on exit ? Is there a constant emf for the time during which the bar magnet is totally surrounded by the coil ?

Edit: found an answer here:


for anyone else who might have wondered.

 

[kuruman]

I explored the magnet falling through a solenoid in the limit of a very short bar magnet, i.e. a point dipole, in this article. Your conjectures are correct. In between the emf is zero and yes, there is an asymmetry in the peaks due to the increased speed of the dipole. The difference in peak amplitude is (theoretically) proportional to the transit time of the dipole through the solenoid (equation (5) in the article.) I do not know if this asymmetry has been investigated experimentally.

 

[neilparker62]

I explored the magnet falling through a solenoid in the limit of a very short bar magnet, i.e. a point dipole, in this article. Your conjectures are correct. In between the emf is zero and yes, there is an asymmetry in the peaks due to the increased speed of the dipole. The difference in peak amplitude is (theoretically) proportional to the transit time of the dipole through the solenoid (equation (5) in the article.) I do not know if this asymmetry has been investigated experimentally.

Great article - it will take me some time to digest the Maths but the graphs show clearly what is happening 'in transit'.

 

[kuruman]

Thank you for your interest. You might also consider reading the related article of how to model a magnet falling through a conducting pipe, a well known classroom demonstration.