@johncarlosbaez Technical details: This follows from Lorentz invariance and the electromagnetic field tensor F_ab, which has N(N-1)/2 independent components in N spacetime dimensions (F_ab is anti symmetric). The electric field is the inner product of the unit timelike basis vector with F, which has N-1 components, and the magnetic field is “the rest” (simplifiable as the inner product of the dual of the unit timelike basis vector with F), which has (N-1)(N-2)/2 components: a spinning vortex.