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Pressure on uniformly charge spherical shell

  1. Dec 19, 2009 #1
    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 = [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.
     
  2. jcsd
  3. Dec 19, 2009 #2
    I do believe you are making this a little more complicated than necessary. The electrostatic pressure on the surface is given by the formula

    [tex]P=\frac{\varepsilon_0}{2}E^2[/tex]

    (cf. Griffiths Equation 2.52)
     
  4. Dec 19, 2009 #3

    diazona

    User Avatar
    Homework Helper

    You're missing a factor of R^2 in the denominator, but otherwise, yes, that is fine.
     
  5. Dec 20, 2009 #4
    Thats good,

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

    Thanks for the help
     
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