Question about distribution of electric charges on two parallel plates

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Main Question or Discussion Point

Here is a problem I made up, in order to try to understand electrostatics of conductors better. Suppose two large square parallel conducting plates, are in space. One has a charge of Q, and another has a charge of -q. They are put close together, from a separation of L, to a separation of l (l < L). (abs(Q) different of abs(q))

1. Describe both the inital charge distribution of both plates, and, the electric field between and on the outer sides of both plates, once equilibrium is reached.

2. After waiting, you "inject" an extra amount of charge m to the plate with inital charge -q. What happens to the charge distribution? and to the electric field?

It would be really nice if you guys could provide explanations for your answers, as I am still trying to understand electrostatics.


PS: My idea of solving this is setting E=0 inside the conductor. Considering charges can only be on the surface, I set up surface charge densities so that the E field contribution of both plates end up cancelling each other within each plates. My difficulty lies in the fact that how do I know if my distribution is unique? And also, how do I find the possible polarization of the plates due to the other plate?


Thanks so much.
 

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