Question

Suppose that a small spherical conductor is placed inside a hollow spherical conductor. The inner conductor has a charge +q, which induces a charge −q on the inner surface of the hollow conductor, which in turn induces a +q charge on the outer surface of the hollow conductor. I want to calculate the total electrostatic potential energy of the system.

My observation is that the system can be seen as a capacitor with two spherical plates. My question is: is correct to assume that the total electrostatic potential energy of the system is equal to the energy stored between the two plates of the capacitor?

Answer 1

Yes, it is correct to assume that the total electrostatic potential energy of the system is equal to the energy stored between the two plates of the capacitor.

Step-by-step explanation:

Yes, it is correct to assume that the total electrostatic potential energy of the system is equal to the energy stored between the two plates of the capacitor. In this case, the two conductors can be seen as the plates of a capacitor, with the inner conductor carrying a positive charge (+q) and the outer surface of the hollow conductor carrying a positive charge (+q) as induced charge.

The electric potential energy of a capacitor is given by the equation U = 1/2 C V², where U is the potential energy, C is the capacitance, and V is the potential difference between the two plates. In this system, the potential difference (V) between the inner conductor and the outer surface is equal to the potential difference between the two plates of a capacitor, and the energy stored is equal to the total electrostatic potential energy of the system.