Figure shows three large metallic plates with charges -Q, 3Q and Q respectively. Determine the final charges on all the surfaces.

Explanation

We assume that charge on surface `2` is x. Following conservation of charge, we see that surfaces `1` has charge `(-Q-x)`. The electric field inside the metal plate is zero so field at P is zero.

Resultant field at O : `E_(p)=0 rArr (-Q-x)/(2A epsilon_(0))=(x+3Q+Q)/(2A epsilon_(0))rArr -Q-x=x+4QrArr x=(-5Q)/2`
Note : We see that charges on the facing surfaces of the plates are of equal magnitude and opposite sign. This can be general proved by gauss theorem also. Remember this it is important result.
Thus the final charge distribution on all the surfaces is :