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Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2024

Paper 4

With $H=p_jp_j/(2m)$, the stated brackets give
$$
\dot q_i=\{q_i,H\}=\frac{p_i}{m},
$$
and
$$
\dot p_i=\{p_i,H\}
=\frac em\epsilon_{ijk}p_jB_k
=e(\dot{\mathbf q}\times\mathbf B)_i.
$$
\b[Thus $m\ddot{\mathbf q}=e\dot{\mathbf q}\times\mathbf B$, the Lorentz-force equation with zero <electric field>. The magnetic interaction has been moved from the <Hamiltonian> into the noncanonical symplectic structure.]

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 4 / 8E / c / Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 4 / 8E / c / Solution

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Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 4 / 8E / c / Solution

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