 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ib/paper-1/15c/ii/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

s

and width

d s

has charge

d Q = 2 π s σ d s

, current

d I = \frac{ω}{2 π} d Q = σω s d s,

and dipole moment

d m = π s^{2} d I \overset{n}{^}

m = πσω \int_{0}^{R} s^{3} d s \overset{n}{^} = \frac{πσω R ^{4}}{4} \overset{n}{^} .

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