9 The equations of motion for a particle of mass $m$ and charge $e$ moving in a uniform magnetic field $B$,
which points in the $x_3$-direction, can be obtained from a Lagrangian
$\frac{1}{2}m\dot{r} + \frac{eB}{2}(x_1\dot{x}_2 - x_2\dot{x}_1)$.
(a) Find the momenta $p_i$ conjugate to $x_i$.
(b) Find the Hamiltonian, expressing your answer first in terms of {$x_i$, $\dot{x}_i$} and then in terms of {$x_i$, $p_i$}.
2 + 2 points
