A positive charge q is placed in front of a conducting solid cube at a distance d from its centre. Find the electric field at the centre of the cube due to the charges appearing on its surface. 

Explanation

Charges will induce on the surface of the cube due to the charge q. The net electric field at the centre of the cube due to all the charges must be zero. Let `E_1` be the electric field due to the charges appearing on the surface of the cube. If `E_2` is the electric field due to charge q, then 
`vec(E_1) + vec(E_2) = 0 ` or
`vec(E_1) = -vec(E_2)` or `E_1 = E_2`
The electric field due to charge q at the centre of the cube
`E_1 = ((1)/(4 pi in_0)) q/(d^2) implies E_1 (1/(4 pi in_0))q/(d^2)`