3-A capacitor consists of two parallel plates, each of area A. It is charged usi

Question

3-A capacitor consists of two parallel plates, each of area A. It is charged using a battery of potential Vo. which is then disconnect- ed. (a) How much does the energy of the capacitor change if the separation of the plates is changed from do to di? (b) How mach work is done by the external force used to move the plates? (c) Suppose that the plates of the capacitor remain connected to the battery as they are moved. How much does the energy stored in the capacitor change under these conditions? (d) Is this change related to the work done by the force moving the plates?

Explanation / Answer

3. (A) C0 = e0 A/ d0

Q = C0 V0 = e0 A v0 / d0

battery is dissconncted so charge will not change.

U = Q^2 /2 C

Ui = (e0 A V0 / d0)^2 / (2 e0 A / d0)

Ui = e0 A V0^2 / 2 d0

UF = (e0 A V0 / d0)^2 / (2 e0 A / d1)

Uf = e0 A d1 V0^2 / 2 d0^2

Uf - Ui = (e0 A V0^2 / 2 d0^2) (d1 - d0)

(b) Work done = change in energy

= (e0 A V0^2 / 2 d0^2) (d1 - d0)

(C) now V0 will not change,

Ui = e0 A V0^2 / 2 d0 and Uf = e0 A V0^2 / 2 d1

delta(u) = (e0 A V0^2 / 2) (1 /d1 - 1/d0)

(D) yes, work done = change in energy

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