An isolated conducting sheet of area A and carrying a charge Q is placed in a uniform electric field E, such that the electric field is perpendicular to the sheet and covers all the sheet. Find out the charges appearing on its two surfaces.

Explanation

Let there be x charge on the left
side of the plate and Q -x charge on the
right side of the plate. Then
`E_(P) = 0`
`rArr x/(2Aepsilon_0) + E = (Q-x)/(2Aepsilon_0)`
or `x/(Aepsilon_0) = Q/(2Aepsilon_0)-E`
or `x = Q/2 - EAepsilon_0`
and `Q-x = Q/2 + E Aepsilon_0`
So the charge on one side is `(Q/2-EAepsilon_0)`and the other side
is `(Q/2 + E A epsilon_0)`