 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ii/paper-3/36b/b/solution

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

A^{μ} (x, t) = \frac{μ _{0}}{4 π} \int_{R^{3}} \frac{J ^{μ} ( x ^{'} , t ^{'} )}{∣ x - x ^{'} ∣} d^{3} x^{'},

where the source is evaluated at the retarded time

t^{'} = t - \frac{∣ x - x ^{'} ∣}{c} .

This is the causal solution with no incoming radiation.

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