Suppose the plates of a parallel-plate capacitor move

QUESTION:

Problem 44P

Suppose the plates of a parallel-plate capacitor move closer together by an infinitesimal distance ?, as a result of their mutual attraction.

(a) Use Eq. 2.52 to express the work done by electrostatic forces, in terms of the field E, and the area of the plates, A.

(b) Use Eq. 2.46 to express the energy lost by the field in this process. (This problem is supposed to be easy, but it contains the embryo of an alternative derivation of Eq. 2.52, using conservation of energy.)

Reference equation 2.52

Reference equation 2.46

Reference equation