(a) Obtain the expression for the energy stored per unit volume in a charged parallel plate capacitor.

(b) The electric field inside a parallel plate capacitor is E. Find the amount of work done in moving a charge q over a closed loop a b c d a. 

(a) Consider a parallel-plate capacitor of plate area A.

Let us say, charge Q is given to the capacitor. Now, in order to increase the separation between the plates, plate b is slowly pulled away from plate a.

Distance between the two capacitor plates = d

Force on plate b due to plate a is given by, 
Work done inorder to displace the plate from its fixed position is, W=Fd 
      ; where  is the capacitance of the capacitor.
Work done is equal to increase in energy of the system.

Electric field is created in a volume which is given by, V = Ad

So, Energy stored per unit volume is given by, 


where, E is the intensity of the electric field. 

(b) Work done, W= F.d ;

where, F is the force exerted on electrical charge and d is the displacement.

Since, the charge is moved along a closed path, net displacement is zero.

Therefore, work done= 0