  We determine the Hofer-Zehnder capacity for twisted tangent bundles over
closed surfaces for (i) arbitrary constant magnetic fields on the two-sphere
and (ii) strong constant magnetic fields for higher genus surfaces. On $S^2$ we
further give an explicit $\text{SO}(3)$-equivariant compactification of the
twisted tangent bundle to $S^2\times S^2$ with split symplectic form. The
former is the phase space of a charged particle moving on the two-sphere in a
constant magnetic field, the latter is the configuration space of two massless
coupled angular momenta.
