 Solution

ID: past-exam-of-the-short-options-paper-shared-by-prelims-and-parts-a-and-b-of-the-physics-course-of-the-university-of-oxford/2017/s7/1/c/solution

The Legendre transform cancels the velocity-linear magnetic term. Expressing velocities in terms of momenta gives

H = \frac{p _{r}^{2}}{2 m} + \frac{p _{θ}^{2}}{2 m r ^{2}} + \frac{[ p _{z} - q A ( r ) ] ^{2}}{2 m} .

The Hamiltonian is time independent and hence conserved. It equals kinetic energy because a static magnetic field does no work; its dependence on

A

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