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

On the Hofer-Zehnder capacity for twisted tangent bundles over closed surfaces