(i) If the plates of a charged capacitor are moved farther apart after the battery is disconnected, the energy stored increases by the amount of work done by the external agent in pulling the plates apart against the force of attraction between the opposite charges on the plates.
(ii) With the battery still connected, increasing the separation between the plates decreases the energy stored in the charged capacitor.
[Notes : (1) The charge on the capacitor does not change after the battery is disconnected. Because the electric field of a large plate is independent of the distance from the plate, the electric field between the plates also remains the same. Therefore, since E = V/d, the p.d. between the plates (V) changes in the same proportion as d. Since the energy stored,
U = \(\cfrac 12CV^2\) = \(\cfrac12\)\(\left(\cfrac{A_ɛ}d \right)\)(Ed)2 = \(\cfrac12\) (AɛD)E2
U also changes in the same proportion as d. The addi-tional energy is transferred to the system from the work done by the external agent.
(2) With the battery still connected, the p.d. between the plates remains the same. Since the energy stored,
U = \(\cfrac 12CV^2\) = \(\cfrac12\)\(\left(\cfrac{A_ɛ}d \right)\)V2.
U is inversely proportional to d. With decrease in capacitance, the charge on the plates decreases.]
