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Homework Help: The force between two conductors (Duffin)

  1. Apr 1, 2010 #1
    1. The problem statement, all variables and given/known data
    I have been reading electricity and magnetism by Duffin in order to understand my first year EM course. So far it has been straightforward- however, I've hit a wall when it derives the force between 2 conductors (p.117 section 5.7 if you have the book!). The book says:

    2. Relevant equations
    Force along x = - dU/dx with Q held constant, where U=electrical energy stored(I accept this)

    Elementary increment dU= 0.5QdV (i accept)
    =0.5 Q^2 * d(1/c) (I accept)
    =-0.5 V^2 * dC.

    This I do not accept, as in the first equality, it implies V is changing (dV) yet in the last equality V is constant? I'm also unsure as to where the minus sign cam from but I assume it was a misprint.

    3. The attempt at a solution

    The only answer I can come up with is that the equation was meant to be
    dU= 0.5 d[ V^2 * C]. But if I use this for the example of a parallel plate capacitor I get a sign error.

    Please help!!
  2. jcsd
  3. Apr 1, 2010 #2
    I think I solved the problem- when you consider dU as 0.5 *d(V^2 * C), this is equal to

    0.5 * (V + dV)^2 * (C + dC) - 0.5*V^2 * C, which by using dv/dc= -Q/(C^2) leaads to the answer given. And pleasingly it gave me that annoying negative sign :)

    I would still like a pat on the back though.
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