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Homework Help: Work done moving a test charge into conducting shell

  1. Feb 12, 2015 #1
    1. The problem statement, all variables and given/known data

    Ok, so I've read many of the threads on here and they all say the same thing. I think I understand the Gauss Law and the theory behind the spherical shell.

    The question is this:

    Find the WORK done bringing a test charge q from infinity to the center of a spherical shell of thickness T, radius R, and surface charge [itex]\sigma[/itex]. Assume the charge passes through an infinitesimal hole in the shell.

    2. Relevant equations

    [itex]W = q[\phi(inf)-\phi(r)] [/itex]

    3. The attempt at a solution

    [itex]W_{\infty, R+T} = q[\phi(\infty)-\phi(R+T)] = -\phi(R+T) [/itex]
    [itex]W_{R+T,0} = q[\phi(R+T)-\phi(0)] = \phi(R+T) [/itex]

    My second equation takes the 'fact' that [itex]E(r) = 0[/itex] inside the shell, resulting in a zero potential.
    The final result is that the total WORK = 0
    This is for a graduate class, and this result seems somewhat trivial. My other assumption is that the test charge induces an electric field inside the shell, but I do not think work can be done by moving the test charge through its own electric field? I could be totally wrong, and that's why I'm asking this question.

    Any help clarifying my result would be greatly appreciated.
  2. jcsd
  3. Feb 12, 2015 #2
    The electric field being zero inside the shell does not mean the potential is zero. Recall that electric field is the negative gradient of potential.
    Last edited: Feb 12, 2015
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