What work must be done to charge a conductor with a capacity of c = 2 * 10-12 f to a voltage of 100 V?

The required work can be calculated as the difference between the potential energies of the electric field of the conductor:

A = W2 – W1, since the initial voltage is zero, then W1 = 0 and A = W2.

W2 = (C * U ^ 2) / 2, where C is the electrical capacity of the conductor (C = 2 * 10 ^ -12 F), U is the voltage, the potential difference (U = 100 V).

Let’s perform the calculation:

A = W2 = (C * U ^ 2) / 2 = (2 * 10 ^ -12 * 100 ^ 2) / 2 = 1 * 10 ^ -8 J = 10 nJ.

Answer: You need to do 10 nJ work.