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Two spherical conductors, each of capacitance $C$, are charged to potentials $V$ and $-V$. They are then connected by means of a fine wire. The loss of energy will be

1. Zero
2. $\frac{1}{2}CV^2$
3. $CV^2$
4. $2CV^2$

Correct answer: $CV^2$

Solution

Initially, each conductor stores energy $\tfrac{1}{2}CV^2$, so total energy is $CV^2$. After connecting a conductor at $V$ with one at $-V$, the common final potential becomes zero, so final stored energy is zero. Hence the entire initial energy is lost.

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