 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2020/ii/paper-4/34c/a/solution

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

For a particle of mass

m

and charge

q

H (x, p, t) = \frac{1}{2 m} [p - q A (x, t)]^{2} + qϕ (x, t) .

p = m \dot{x} + q A

m \ddot{x} = q (E + \dot{x} \times B), E = - \nabla ϕ - \partial_{t} A, B = \nabla \times A .

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