The behaviour of an insulating particle suspended in a liquid metal and subject to the influence of locally uniform electric and magnetic fields (E, B) is considered. The electric field drives a current J which is perturbed by the presence of the particle, and the resulting Lorentz force drives a flow. It is assumed that both the Reynolds number and the Hartmann number based on particle size are small. If the particle is fixed, it experiences a force and couple that are each bilinear in J and B; if it is freely suspended, then it moves with translational velocity U and angular velocity Ω each similarly bilinear in J and B. The general form of these bilinear relationships is determined, with particular attention to three types of particle symmetry: (i) isotropy; (ii) axisymmetry; and (iii) orthotropy.