Maxwell's equations in flat spacetime are solved for an isolated uniformly rotating magnetised sphere that can sustain convective and vorticity currents in the infinite conductivity limit. The study is motivated by the problem of accounting for the radiation from rapidly spinning compact stellar objects. Two types of magnetic interiors are considered to determine how the resultant radiation field departs from traditional point dipole magnetisation models. The torque reaction produced by the emitted radiation is calculated and the result compared with simpler models that have featured in the dynamics of pulsars.