Two uniformly charged large plane sheets `S_1` and `S_2` having charge densities `sigma_1` and `sigma_2 (sigma_1 gt sigma_2)` are placed at a distance d parallel to each other. A charge `q_0` is moved along a line of length `a (a lt d)` at an angle `45^(@)` with the normal to `S_1`. Calculate the work done by the electric field.
(##BMS_V03_C03_E01_060_Q01##).

Answer

2

Explanation

Electric field near a large metallic plate is given by `E = sigma // epsi_(0)`. In between the plates two fields will be in opposite directions. Hence
`E_("net") = (sigma_(1) - sigma_(2))/(epsi_(0)) = E_(0)` (say) , Now (potential difference )
` = q ( E_(0) a cos 45^(@) ) = (q) ((sigma_(1) - sigma_(2))/(epsi_(0))) (a)/(sqrt(2)) = ((sigma_(1) - simga_(2)) qa)/(sqrt(2) epsi_(0))`.