- #1

Potatochip911

- 318

- 3

## Homework Statement

(Problem 2.38 From Griffth's Electrodynamics): A metal sphere of radius

*R*, carrying charge

*q*, is surrounded by a thick concentric metal shell (inner radius

*a*, outer radius

*b*). The shell carries no net charge.

Find the surface charge density ##\sigma## at

*R*,

*a*, and

*b*.

## Homework Equations

##\sigma = \frac{\mbox{Charge}}{\mbox{Surface Area}}##

## The Attempt at a Solution

Since the metal sphere of radius

*R*contains charge

*q,*in order for the electric field to be 0 inside the conducting shell there must be charge -

*q*at radius a which implies charge +

*q*at radius b as the shell carries no net charge which gives $$\sigma_a=-\frac{q}{4\pi a^2}\\\sigma_b=\frac{q}{4\pi b^2}$$

Now what I'm confused about is that it just mentions that the metal sphere of radius R carries charge q and not whether it is a surface charge distribution or volume charge distribution. In the solutions manual they just give ##\sigma_R=\frac{q}{4\pi R^2}## as if all the charge is on the surface although I'm not sure this makes sense.