Exact expressions for the electromagnetic fields of a charged particle through a dispersive and dissipative medium have been used to calculate exact expressions for the energy loss due to distant collisions. These are evaluated using Fermi's one-oscillator approximation to the dielectric constant. For particle velocities with beta < epsilon _o^-1/2 the results are identical to those of Fermi for an electric charge and to those of Ahlen (1980) for a magnetic monopole. For beta > epsilon ₀^-1/2 the present results differ from those of these authors. It is shown that this is due to their incomplete treatment of the conditions imposed by the model for the dielectric constant. The relevance of these results to the detection of magnetic monopoles and of dyons is also discussed.