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[Void123]

Homework Statement

https://www.physicsforums.com/showthread.php?p=2484733&posted=1#post2484733

Homework Equations

The Attempt at a Solution

 

[kuruman]

You use spherical coordinates, but without boundary conditions, you will not be able to find the potential, so you need to specify them.

Barring time-dependent boundary conditions, "conducting" means that the entire sphere is an equipotential.

 

[Void123]

So, my solution will satisfy:

$$\nabla^{2}\Psi = 0$$

$$\Psi = \sum a \Psi$$

Should I assume there will be no potential outside the spheroid (or whatever)? And do the boundary conditions determine what particular solution (there is a table of different ones) it will be?

 

[kuruman]

I am not sure exactly what you are looking for. Check this reference. It is pretty good and comes with examples.

http://www.luc.edu/faculty/dslavsk/courses/phys301/classnotes/laplacesequation.pdf