Where Can I Find a Free Electromagnetic Field Simulator?

Astrum
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Is there any program (preferably free) that simulates electromagnetic fields and their interactions with charged particles?

I've found a couple gravity simulators, but none for EM, which isn't any fun, because I reckon it would be great to play with a realistic EM program.
 
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Try looking up particle-in-cell programs.
 
Thread 'Motional EMF in Faraday disc, co-rotating magnet axial mean flux'
So here is the motional EMF formula. Now I understand the standard Faraday paradox that an axis symmetric field source (like a speaker motor ring magnet) has a magnetic field that is frame invariant under rotation around axis of symmetry. The field is static whether you rotate the magnet or not. So far so good. What puzzles me is this , there is a term average magnetic flux or "azimuthal mean" , this term describes the average magnetic field through the area swept by the rotating Faraday...
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