- #1

timhunderwood

- 12

- 0

## Homework Statement

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*r

^{2}) for r>R

QUESTION:

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

## Homework Equations

## 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 = [tex]\int[/tex]eps*E

^{2}/2 (integrate over all space)

I did this in spherical polar coordinates and get U_s = Q

^{2}/(8*Pi*eps*R)

I then said (principle of virtual work:)

F, Force*dR = [tex]\partial[/tex]U_s/[tex]\partial[/tex]R *dR

and solved this to get:

F = -Q

^{2}/(8*Pi*eps*R

^{2})

dividing by area of shell then gives

pressure = Q

^{2}/(32*Pi

^{2}*eps*R

^{2})

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

Thanks very much.