Figure shows three metallic plates with charges Q, 4Q, and -Q, respectively. Determine the final charges on all the surfaces.

Explanation

Method 1: We assume that the charge
on surface 2 is x. Following conservation
of charge, we see that surface 1 has charge (Q-x). The electric
field inside the metal plate is zero, so field at P is zero.
So the resultant field at P is `-E_(P) = `
`rArr ((Q-x)/(2Aepsilon_0)) = (x+4Q-Q)/(2Aepsilon_0)`
or `Q-x = x+3Q`
or `x = -Q`
The charges on the facing
surfaces of the plates are of
equal magnitude and opposite
sign. This can be proved by
Gauss's theorem also. It is an
important result.
Thus, the final charge
distribution on all the surfaces
is shown in figure.

Method 2: The electric field
due to an infinite sheet of charge
is independent of distance. We
can take plates (ii) and (iii) as
one system or one plate having
charge `4Q - Q = 3Q`.


The charge appearing on surface (2) is
`q_2 = (Q-3Q)/2 = -Q`
Hence, final charge distribution is same as we calculated in
method 1.