(adsbygoogle = window.adsbygoogle || []).push({}); 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*r^{2}) 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 = [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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Pressure on uniformly charge spherical shell

**Physics Forums | Science Articles, Homework Help, Discussion**