 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/ii/paper-2/14e/b/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

p = m \dot{r} + q A

H = p \cdot \dot{r} - L = \frac{∣ p - q A ∣ ^{2}}{2 m} + qϕ .

\dot{r} = \frac{\partial H}{\partial p} = \frac{p - q A}{m}

and, componentwise,

\overset{p}{˙}_{i} = - \frac{\partial H}{\partial r _{i}} = q \overset{r}{˙}_{j} \partial_{i} A_{j} - q \partial_{i} ϕ .

Combining the second equation with

p = m \dot{r} + q A

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