Two identical metal plates each having surface area A, having charges `q_1 and q_2`, are placed facing each other at a separation d. Find the charge appearing on
surface (1),(2),(3), and (4). Assume the size of the plate is much larger than the separation between the plates.

Explanation

Facing surfaces have equal and opposite charge (by Gauss's theorem). Let
the facing surfaces have charges x and -x
[surfaces (2) and (3), respectively].
Then the charge on surfaces (1) and (2)
should be `(q_1 - x) and x`, respectively (by
conservation of charge). Facing metallic
surfaces always have equal and opposite
charge. Hence, charge appearing on
surfaces (3) and (4) will be -x and `(q_2 + x)`, respectively.
Let us consider a point P inside the left plate. The net
electric field at P should be zero.



The net electric field at P will be due to the resultant of
electric fields due to the charges appearing on all four surfaces.
Thus,
`E_1 + E_3 = E_2 + E_4`
` rArr (sigma_1/(2epsilon_0) + (sigma_3)/(2epsilon_0) = (sigma_2)/(2epsilon_0) + (sigma_4)/(2epsilon_0)`
`rArr q_1 - x + x = q_2 + x + x or x = (q_1 - q_2)/2`
Hence, charge appearing on different surfaces are as shown
in figure