I find an approximate axially symmetric stationary solution of the Einstein-Maxwell equations for a pair of charged, spinning, massive particles with a magnetic dipole moment. For general values of the particle parameters there are two singularities on the axis between the particles. One is the well known stress singularity representing a force holding the particles apart. The other I believe to be a torsion singularity representing a couple maintaining the spins at the prescribed values. Among the effects demonstrated which might conceivably be experimentally tested are: (a) a magnet in the presence of an electric charge needs a couple to stop it turning; (b) a charged particle in the presence of an uncharged one produces a ghost charge at the position of the latter. This work provides a physical explanation of a puzzling singularity in the Perjes-Israel-Walker exact solution.