Define the term gravitational field.
Define the term electric field.
State one similarity and one difference between the gravitational potential produced by a point mass and the electric potential produced by a point charge.
An isolated uniform conducting sphere has mass $M$ and charge $Q$. The gravitational field strength at the sphere’s surface is $g$. The electric field strength at the sphere’s surface is $E$. Show that $\frac{M}{Q} = \alpha \frac{g}{E}$, where $\alpha$ is a constant.
Show that $\alpha$ has the numerical value $1.35 \times 10^{20}\,\text{kg}^2\,\text{C}^{-2}$.
Treat the Earth as a uniform conducting sphere with mass $5.98 \times 10^{24}\,\text{kg}$. Its surface carries a charge of $-4.80 \times 10^{5}\,\text{C}$, evenly spread over the surface. Use the result in (b) to find the electric field strength at the Earth’s surface. State a unit in your answer.
State how the direction of the electric field at the Earth’s surface compares with the direction of the gravitational field.