Brief layout of strategy:

1. Write down [Lorentz force](http://en.wikipedia.org/wiki/Lorentz_force) ${\bf F}$.

2. Find (velocity-dependent) potential $U$ for ${\bf F}$.

3. Write down [Lagrangian](http://en.wikipedia.org/wiki/Lagrangian) $L=T-U$.

4. Define the canonical (as opposed to kinetic/mechanical) [momentum](http://en.wikipedia.org/wiki/Momentum) ${\bf p}:=\frac{\partial L}{\partial{\bf v}}$.

4. Perform [Legendre transformation](http://en.wikipedia.org/wiki/Legendre_transformation) ${\bf v}\to {\bf p}$.

5. Write down Hamiltonian $H={\bf v}\cdot{\bf p}-L$.