(a(i))[1]
State an expression, in terms of $R$ and $q$, for the surface potential $V$ of the sphere.
(a(ii))[1]
Define capacitance and hence show that the capacitance $C$ of the sphere is given by $C = 4\pi\varepsilon_0 R$.
(b(i))[2]
An isolated metal sphere has a radius of $45\,\text{cm}$. Using the expression from (a)(ii), calculate the capacitance of the sphere, in picofarad.
(b(ii))[3]
The sphere is charged to a potential of $9.0 \times 10^5\,\text{V}$. A spark takes place, partly discharging the sphere so that its potential falls to $3.6 \times 10^5\,\text{V}$. Determine the energy of the spark.