(a)[2]
Define electric potential at a point in space.
(b(i))[2]
An isolated metal sphere is charged to a potential $V$. Let the sphere carry charge $q$. The sphere’s charge may be treated as a point charge at the centre of the sphere. Fig. 5.1 shows how the charge $q$ on the sphere varies with potential $V$. Use Fig. 5.1 to work out the sphere’s radius.
(b(ii))[3]
Use Fig. 5.1 to determine the energy needed to raise the sphere’s potential from zero to $24\,\text{kV}$.
(c)[3]
The sphere in (b) loses charge by sparks whenever the electric field strength at its surface exceeds $2.0 \times 10^6\,\text{V m}^{-1}$. Use your answer to (b)(i) to calculate the highest potential to which the sphere can be charged.