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Homework Help: What is the work done by the electrostatic force

  1. Feb 20, 2010 #1
    1. The problem statement, all variables and given/known data
    A spherical shell of radius 'a' and charge Q is expanded to radius 'b'. What is the work done by the electrostatic force in this process?

    2. Relevant equations
    Method 1

    Work done = initial energy - final energy

    Method 2

    Work done = Q (potential difference between the two positions)
    3. The attempt at a solution

    Method 1

    Initial energy of the spherical capacitor = Q*Q / 2C
    = Q*Q / 2*4*pi*E*a (E= permittivity of the medium)
    Final energy = Q*Q / 2*4*pi*b

    Work done = Q*Q / 2*4*pi*E [ 1/a - 1/b]

    Method 2

    Initial potential = Q / 4*pi*E*a

    Final potential = Q / 4*pi*E*b

    Work done = Q*Q / 4 *pi* E* [1/a - 1/b]

    The two methods do not lead to the same answer. I need to understand why this is so. Would appreciate some tips. Thanks.
  2. jcsd
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