 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2016/paper-2/6/b/solution

ϕ = 0

. At the final point

z = 0

, so the exponential factor is one, and

\int_{C} F \cdot d r = ϕ (C_{end}) - ϕ (C_{start}) = sin \frac{π}{8} cos \frac{π}{4} = \frac{2}{2} sin \frac{π}{8} .

The detailed shape of the path does not affect this line integral.

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