How Does the Shape of a Conductor Affect Electrostatic Behavior?

[ghery]

I hace read in Electrodynamics from griffiths chapter 2, that, whenever acavity is inside an spherical conductor, for the outside it acts as if there was a point cherge at the center...

But what if thew conductor has another shape, for example a revolution ellipsoid...?? how do you deal with that...??

 

[maimonides]

In electrostatics, it doesn´t matter what is inside a conductor.
You can use the point charge approximation, if you´re far away from your charged conductor, no matter what its shape. (distance much greater than size of conductor).
Otherwise you´ll have to integrate over the shape, or do a multipole expansion.

 

[Born2bwire]

I hace read in Electrodynamics from griffiths chapter 2, that, whenever acavity is inside an spherical conductor, for the outside it acts as if there was a point cherge at the center...

But what if thew conductor has another shape, for example a revolution ellipsoid...?? how do you deal with that...??

I assume to mean that if you were to place a charge inside a spherical shell made out of a conductor then the field outside of the shell would be the same as if the shell was not there at all.

It behaves the same but the math to calculate the charge distributions and show this explicitly becomes a lot more difficult. It can be more readily justified by looking at Gauss' Law for the electric field. Gauss' Law only regards itself with the net enclosed charge of a Gaussian surface. Since any conductor that you use to enclose your charge was neutral to begin with, then it will remain neutral regardless of the induced charge distributions. So for the purpose of Gauss' Law, our neutral conductor that was inserted has no consequences. As long as you choose a surface to fully enclose the conductor it will not matter and then you can use Gauss' Law in the same manner as you would to find the electric field for a point charge.