Electrodes of area A are spaced distance d apart to form a parallel-plate capaci

Question

Electrodes of area A are spaced distance d apart to form a parallel-plate capacitor. The electrodes are charged to ±q. Part A) What is the infinitesimal increase in electric potential energy dU if an infinitesimal amount of charge dq is moved from the negative electrode to the positive electrode? Express your answer in terms of A, d, dq, and appropriate constants. Part B) An uncharged capacitor can be charged to ±Q by transferring charge dq over and over and over. Use this idea to find an expression for the potential energy of a capacitor charged to ±Q. Express your answer in terms of A, d, Q, and appropriate constants.

Explanation / Answer

A) energy stored in capacitor is U = q^2/2C

dU = d(q^2/2C) = 2*q*dq/2C =q*dq/C = q*dq/(eo*A/d) = q*dq*d/(eo*A)

B) U = Q^2/(2*C) = Q^2/(2*eo*A/d) = (Q^2*d)/(2*eo*A)

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