Induced voltage and current in an odd scenario

[FilipLand]

Hi! I have a question about induces volatge and current in an odd scenario.

Suppose we have a leader in a homogeneous magnetic field caused by two strong magnets (btw, which causes the strongest magnetic field?). Assume now that a charged ion travels through the magnetic field. It will mean a change in the magnetic field (although the change is small). How can you calculate the voltage will be induced in the conductor?

 

[anorlunda]

You use Maxwells Equations and you need to do triple integrals in 3D space. The answers depend on the exact 3D geometry of the fields and wires and the path of the Ion.

Saying that was easy, but doing the calculations is pretty difficult. How are your calculus skills?

 

[FilipLand]

Thanks for your answer!

Well I am pretty familliar with Maxwells equations indirectly. (On my first year in Theoretical physics batchelor program).

But I guess it will be an intergral of some sort since the charged particle will come closer the conductor because of Lorenz force. Mabye something like the integral of -dPHI/dt. And use the area of the particle or the conductor. But it seems wrong and not to be all.

Do you know how to approach the problem?

Thanks in advance! :)

 

[anorlunda]

Do you know how to approach the problem?

Off the top of my head, I would say finite element analysis.