Past exam of the mathematics course of the University of Oxford / 2015 / Prelims / Mathematics V resit / Question 7 / a / ii

For the surface, a source element has mass $dm=\sigma d{S}^{\prime }$. Superposing its Newtonian gravitational potential gives the surface integralHere $d{S}^{\prime }$ is the source surface area element, ${\mathbf{r}}^{\prime }$ the source position vector, and $G$ the gravitational constant. The same zero-at-infinity convention applies.