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Homework Help: Force on parallel plates at a given voltage

  1. Apr 19, 2012 #1
    Hello All,

    I have noticed that a similar question have been asked many times here, but I still have doubts how to solve the parallel plates problem defined below:

    1. The problem statement, all variables and given/known data

    We have two freely moving parallel plates of area A, separated by distance d, one is grounded and the other is supplied with voltage from a regulated power supply which can also have its polarity reversed.
    1. What is going to happen to the plates at a given voltage V?
    2. What will happen to the plates when changing the voltage with constant speed dV/dt?
    3. What will happen to the plates at voltage V when the polarity is suddenly changed?
    4. How the problem will change when the plates are replaced with grids?

    2. Relevant equations

    See below.

    3. The attempt at a solution

    1. The plates will attract each other with force F(V,d) = V^2 * e_0 * A / (2 * d^2)
    2. As above, but the equation gets more complicated and becomes a function of time. They should meet sooner than in #1.
    3. Nothing should happen because of V^2, so sign doesn't play a role. Perhaps I'm underestimating some switching effects here?
    4. Again, everything should be the same - to first approximation, ignoring the edge effects and fringe fields near the surface/edges.

    Could anyone comment on my answers? Thanks.
  2. jcsd
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