In analogy with the free‐space solution of Maxwell's equations, the excitations which are set up in an anisotropic, macroscopically neutral plasma by an arbitrary current can be described by potentials. The equations which the one vector and two scalar potentials must satisfy are first obtained for a relatively general physical situation. Due to the complexity of the mathematics, however, one cannot expect to obtain analytic solutions to this set of coupled equations without first making some realistic simplifications. One particular case that can be solved without an inordinate amount of difficulty is that of the point charge moving with uniform velocity parallel to a strong magnetic field. It is shown that the propagating waves which arise in this situation are electroacoustic in nature but very different from those created by a moving charge in an isotropic plasma.