A metallic circular plate with radius r is fixed to a tabletop.An identical circular plate supported from above by a cable isfixed in place a distance dd above the first plate. Assume that ddis much smaller than r. The two plates are attached by wires to abattery that supplies voltage V.

1) What is the tension in the cable? Neglect the weight of theplate.

Express your answer in terms of the variables d, r, V, andconstants ϵ0, pi.

F=

2)

The upper plate is slowly raised to a new height 2d. Determinethe work done by the cable by integrating ∫d to 2d F(z)dz, whereF(z) is the cable tension when the plates are separated by adistance z.

Express your answer in terms of the variables d, r, V, andconstants ϵ0,pi.

W=

3) Compute the energy stored in the electric field before thetop plate was raised.

Express your answer in terms of the variables d, r, V, andconstants ϵ0, pi.

U=

4) Compute the energy stored in the electric field after the topplate was raised.

Express your answer in terms of the variables d, r, V, andconstants ϵ0, pi.

U=

5)

is the work done by the cable equal to the change in the storedelectrical energy? If not, why not?

The work done in separating the plates is equal to energychange in the plates.

The work done in separating the plates is equal to themagnitude of the energy change in the plates. This does not meanthat the work done is equal to the change in the energy stored inthe plates. The work done on the plates is positive but the plateslose energy. The plates are connected to the battery, so thepotential difference across them remains constant as they areseparated. Therefore charge is forced off of the plates through thebattery, which does work on the battery.