Two isolated conducting spheres, each of radius 14.0 cm, are charged to potentials of 240 and 440 V and are then connected by a fine wire. We have to calculate the internal energy developed in the wire.

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Potential difference with respect to infinity of a conducting sphere of radius r and total charge q on its surface is given by

Therefore, the capacitance of a conductor of radius r is

The other fact that we will use in answering this problem is that energy associated with a condenser of capacitance C and charge q is

Therefore, charge on the conductor at 240 V potential will be

Similarly, the charge on the conductor at 440 V potential will be

After the two charged conductors have been connected by a fine wire, they will have equal charge as they are of equal radius. So the charge on each conductor after they have been connected will be

The common potential on the two conductors will be

The change in energy of the two conductors after they are connected by a fine wire will be

From the conservation of energy, we note that the energy developed in the wire will be 156 nJ.