  We consider the three-dimensional Dirac equation in spherical coordinates
with coupling to static electromagnetic potential. The space components of the
potential have angular (non-central) dependence such that the Dirac equation is
separable in all coordinates. We obtain exact solutions for the case where the
potential satisfies the Lorentz gauge fixing condition and its time component
is the Coulomb potential. The relativistic energy spectrum and corresponding
spinor wavefunctions are obtained. The Aharonov-Bohm and magnetic monopole
potentials are included in these solutions.
