Effective dipole potentials after angle averaging

The problems of a freely rotating dipole interacting with a charge, and of a freely rotating dipole interacting with a polarizable surface (dielectric discontinuity), are solved here. Fully analytic expressions for angle-independent, i.e., radially symmetric, effective interaction potentials are derived and analyzed for their asymptotic forms. For the charge-dipole case the exact result takes a simple enough form to permit direct implementation in statistical mechanical calculations, and displays the appropriate limiting forms at large and small separations. The dipole-surface interaction potential is slightly more involved analytically but is nevertheless amenable for application in statistical thermodynamic study of bulk systems. Order parameter analyses demonstrate the orientational behavior of the dipole at small, large, and intermediate distances.