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 charge appearing on its surface.

Explanation

Charges will be induced 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 charge must be zero . Let `E_(1)` be the electric field due to charge 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 vec(E_(1)) = vec(E_(2))`
The electric field at the centre of the cube , due to charge q.
`E_(2) = ((1)/(4 pi in_(0))) (q)/(d^(2))`
`rArr E_(1) = ((1)/(4pi in_(0))) (q)/(d^(2))`