A question about Shell Theorem and a question about center of charge

Question

I have 2 questions about Newton's Shell Theorem.

Is it valid when mass is distributed arbitrarily in 3D space? not like sphere?
When it comes to electrostatic force, can we define "Center of Charge" like "Center of Mass" used in Gravitation's shell theorem? As if all of those charges distributed along the space are concentrated in one point inside the space.

General tip: Unrelated subquestions should be asked in different posts. — Qmechanic, Sep 13 '18 at 11:29
Subquestion 2 is related to https://physics.stackexchange.com/q/49745/2451 and links therein. — Qmechanic, Sep 13 '18 at 11:32

score 2 · Accepted Answer · answered Sep 13 '18 at 10:07

For the first question: no, it only applies to spherically-symmetric distributions. There are generalisations to some other distributions I think, but it is certainly not true for arbitrary distributions.

For the second, yes, you can do that: if you're dealing with a spherically-symmetric distribution of charge you can treat it as a point charge at the centre of the distribution.

A question about Shell Theorem and a question about center of charge

1 Answers1