Question

Each plate of a parallel-plate air capacitor has an area *. What amount of work has to be performed to slowly increase the distance between the plates from x1 to x2 if (a) the capacitance of the capacitor, which is equal to q, or

(b) the voltage across the capacitor, which is equal to V, is kept constant in the process?

Answer 1

(a) Sought work is equivalent to the work performed against the electric field created by one plate, holding at rest and to bring the other plate away. Therefore the required work,

is the intensity of the field created by one plate at the location of other.

(b) When voltage is kept const., the force acing on each plate of capacitor will depend on the distance between the plates.

So, elementary work done by agent, in its displacement over a distance dx, relative to the other,

Alternate : From energy Conservation,