Define electric potential in terms of work done per unit charge.
An isolated conducting sphere in vacuum has radius $r$ and starts off uncharged. It is then charged by friction so that its final charge is $Q$. This charge may be treated as if it were concentrated at the centre of the sphere. By using the electric potential at the surface, show that the capacitance $C$ of the sphere is given by $C = 4\pi\varepsilon_0 r$, where $\varepsilon_0$ is the permittivity of free space.
The dome of an electrostatic generator is a spherical conductor with radius $13\,\text{cm}$. It is first charged so that the electric potential at its surface is $4.5\,\text{kV}$. A smaller isolated sphere of radius $5.2\,\text{cm}$, which is initially uncharged, is then brought near the dome. Sparking produces a current between the two spheres until they are at the same potential. Assume that any charge on a sphere may be treated as though it were concentrated at its centre. Calculate the charge transferred between the two spheres.