# Pressure on uniformly charge spherical shell

1. Dec 19, 2009

### timhunderwood

1. The problem statement, all variables and given/known data

First part of the problem was to work out E-field of uniformly charged spherical shell with charge Q and Radius R.

This was fine : E = 0 for r<R
and E = Q/(4*Pi*eps*r2) for r>R

QUESTION:
Find the pressure exerted on the shell due to the charges on its surface.

2. Relevant equations

3. The attempt at a solution

I tried to do it using the principle of virtual work, I get an answer and was hoping someone could confirm it is right?

I did this:
u_s, Energy stored in Electric field = $$\int$$eps*E2/2 (integrate over all space)

I did this in spherical polar coordinates and get U_s = Q2/(8*Pi*eps*R)

I then said (principle of virtual work:)

F, Force*dR = $$\partial$$U_s/$$\partial$$R *dR
and solved this to get:
F = -Q2/(8*Pi*eps*R2)

dividing by area of shell then gives

pressure = Q2/(32*Pi2*eps*R2)

is this right? If there's a mistake I think I may have not used the principle of virtual work correctly....

Thanks very much.

2. Dec 19, 2009

### jdwood983

I do believe you are making this a little more complicated than necessary. The electrostatic pressure on the surface is given by the formula

$$P=\frac{\varepsilon_0}{2}E^2$$

(cf. Griffiths Equation 2.52)

3. Dec 19, 2009

### diazona

You're missing a factor of R^2 in the denominator, but otherwise, yes, that is fine.

4. Dec 20, 2009

### timhunderwood

Thats good,

I mistyped my last equation- it should have read R^4.

Thanks for the help