- #1
timhunderwood
- 12
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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*r2) 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*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 = [tex]\partial[/tex]U_s/[tex]\partial[/tex]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.