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 cgarge on right side of plate

`E_(P)=0 rArr (x)/(2A epsilon_(0))+E=(Q-x)/(2A epsilon_(0))rArr (x)/(A epsilon_(0))=(Q)/(2A epsilon_(0))-ErArr x=Q/2-EAepsilon_(0)`
So charge on one side is `Q/2-EA epsilon_(0)` and other side `Q/2+EA epsilon_(0)`
The resutlant electric field on the left and right side of the plate.
On right side `E=(Q)/(2 A epsilon_(0))+E` towards right and on left side `(Q)/(2 A epsilon_(0))-E` towards left.