# Homework Help: Force on parallel plates at a given voltage

1. Apr 19, 2012

### physiker12

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.