Two uniformly charged large plane sheets `S_1` and `S_2` having charge densities `sigma_1` and `sigma_2` (`sigma_1gtsigma_2`) are placed at a distance d parallel to each other. A charge `q_0` is moved along a line of length a(altd) at an angle `45^@` with the normal to `S_1`. Calculate the work done by the electric field

Answer

`W = (q_0 E a)/sqrt(2)`

Explanation

As we see `E_1 = (sigma_1)/(2 epsilon_0), E_2 = (sigma_2)/(2 epsilon_0)`
`E = E_1 - E_2 = (sigma_1 - sigma_2)/(2 epsilon_0)`

`W = q_0 E xx a/(sqrt(2)) = (q_0 a)/(2 sqrt(2 epsilon_0)) (sigma_1 - sigma_2)`.