The dyadic Green's function for hydromagnetic waves in a uniform, fully ionized, perfectly conducting, pressureless fluid is obtained. The electromagnetic field consists of two modes, one that propagates isotropically and one that propagates along the field lines. The radiation rate from some simple model current distributions is derived from the Green's functions. If the source contains a current along the constant static field, then the radiation along the field lines through the source is very intense. This last result also holds in the nonuniform static field of an infinitely long straight wire.