 Solution

ID: past-exam-of-the-theoretical-physics-i-course-of-the-university-of-cambridge/2012/paper-1/3/c/solution

The coordinate

θ

is cyclic. Its conjugate momentum is therefore a second conserved quantity,

p_{θ} = m r^{2} \dot{θ} + e μ r^{2} = constant .

It differs from mechanical angular momentum

m r^{2} \dot{θ}

. The magnetic contribution is essential to the rotational Noether charge in this axisymmetric gauge.

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