 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2020/paper-1/19/d/solution

a

, the outward unit normal is

n = (x, y, z) / a

. Thus

F \cdot n = a

everywhere. Multiplying by the surface area

4 π a^{2}

gives

Φ = \int F \cdot n d S = 4 π a^{3} .

d S = a^{2} sin ϑ d ϑ d φ

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