# Lenz's law and magnetic force

## Main Question or Discussion Point

I've read a lot and watched a lot about lenz's law , about how a magnet moving towards a solenoid will experience an opposing force. But I tried to search how to calculate this force , found nothing .
So i tried to find how to calculate force between 2 magnets . Found on wikipedia how to calculate force between 2 magnetized areas, 2 cylindrical magnets and 2 dipoles ( very basic , resembling coulombs law). So , which one should i use when calculating force between solenoid and the cylindrical magnet moving towards it ?

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marcusl
Gold Member
I assume you are speaking of a shorted solenoid? If yes, then the answer is neither because this is not a magnetostatics question. The opposing force depends on the dynamics--the relative speed of magnet and solenoid, the rate of change of magnetic flux in the solenoid, and the R/L time constant of the solenoid. These are more complicated calculations than your statics case.

I assume you are speaking of a shorted solenoid? If yes, then the answer is neither because this is not a magnetostatics question. The opposing force depends on the dynamics--the relative speed of magnet and solenoid, the rate of change of magnetic flux in the solenoid, and the R/L time constant of the solenoid. These are more complicated calculations than your statics case.
Lets say it's a wire loop , is there a webpage or a book where i can find those calculations?

marcusl
Gold Member
I took a quick look at webpages and didn't find this problem worked out. It's not simple due to the difficulty of finding the inhomogenous field from a bar magnet and integrating it to find the flux in the loop as the magnet approaches. You will end up solving it numerically (e.g., Matlab).

This link solves similar problems and shows how force depends on motion for a simpler geometry:
One of the problems asks for qualitative solutions to your scenario--but as I indicated, there is no closed-form analytical solution.

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I took a quick look at webpages and didn't find this problem worked out. It's not simple due to the difficulty of finding the inhomogenous field from a bar magnet and integrating it to find the flux in the loop as the magnet approaches. You will end up solving it numerically (e.g., Matlab).

This link solves similar problems and shows how force depends on motion for a simpler geometry:
One of the problems asks for qualitative solutions to your scenario--but as I indicated, there is no closed-form analytical solution.
the link doesn't work, is there another one ?
So you're saying that i won't find those calculation because they are so complicated?

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marcusl
Gold Member
the link doesn't work, is there another one ?
Hmm. Try cutting and pasting the following line into Google

Course notes: Faraday's law of induction- mit ocw

The first link listed should be the one.
So you're saying that i won't find those calculation because they are so complicated?
Yes. It has no closed form solution, so you'll need to simulate the answer numerically. Solutions to problems with simpler geometry (typically involving a uniform magnetic field) can be written down analytically.

quoting from notes 21 :" Therefore, as the bar magnet approaches the loop, it experiences a repulsive force due to the induced emf. Since like poles repel, the loop must behave as
if it were a bar magnet with its north pole pointing up"
Can we calculate the opposing force at a certain moment?

marcusl