Each plate of a parallel plate air capacitor has an area S and are separated by

Question

Each plate of a parallel plate air capacitor has an area S and are separated by a distance x1. A charge +q is given to one plate and -q to another plate. What is the amount of work that has to be done to slowly increase the distance between the plates from x1 to x2 is
a) the charge on the plates are kept constant (i.e. the capacitor is not connected to any circuit or battery while increasing the distance between the plates)
b) the voltage V across the capacitor is kept constant (i.e. the capacitor is connected across a battery or constant voltage source while increasing the distance)

Explanation / Answer

initial capacitance C1 = 0S/x1

final capacitance C2 = 0S/x2

a) charge = q

initial energy = q2/(2C1), final energy = q2/(2C2)

work W = q2/(2C2) - q2/(2C1) = q2(x2 - x1)/(20S)

b)

initial energy = C1V2/2, final energy = C2V2/2

work W = C2V2/2 - C1V2/2 = 0.50SV2(1/x2 - 1/x1)

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