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 is x charge on left side of plate and Q - x charge on right side of plate
`E_(P) = 0 (x)/(2A epsilon_(0)) + E = (Q-x)/(2A epsilon_(0))`

`rArr (x)/(A epsilon_(0)) = (Q)/(2 A epsilon_(0)) - E`
`rArr x = (Q)/(2) - E A epsilon_(0)` and `Q - x = (Q)/(2) + EA epsilon_(0)`
So charge on side is `(Q)/(2) - E A epsilon_(0)` and other side `(Q)/(2) + E A epsilon_(0)`
Note : Solve this question for Q = 0 without using the above answer and match that answers with the answers that you will get by putting Q = 0 in the above answer.