Paramagnetism in spherically confined charged active matter

The celebrated theorem of Bohr and van Leeuwen guarantees that a classical charged system cannot have a magnetization in thermal equilibrium. Quantum mechanically, however, a response is obtained. In contrast, we show here that a classical charged active system, consisting of a motile particle confined to the surface of a sphere, has a nonzero magnetization and a response. We numerically sample Langevin trajectories of this system and compare with limiting analytical solutions of the Fokker-Planck equation, at small and large temperatures, to find excellent agreement in the magnetic response. Our Letter suggests experimental routes to controlling and extracting work from charged active matter.