 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/2015/prelims/mathematics-v-resit/question-7/a/ii/solution

For the surface, a source element has mass

d m = σ d S^{'}

ϕ (r) = - G σ \iint_{S} \frac{d S ^{'}}{∣ r - r ^{'} ∣} .

Here

d S^{'}

r^{'}

the source position vector, and

G

the gravitational constant. The same zero-at-infinity convention applies.

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