A point particle approximation to the classical dynamics of well separated vortices of the abelian Higgs model is developed. A static vortex is asymptotically identical to a solution of the linearized eld theory (a Klein-Gordon/Proca theory) in the presence of a singular point source at the vortex centre. It is shown that this source is a composite scalar monopole and magnetic dipole, and the respective charges are determined numerically for various values of the coupling constant. The interaction potential of two well separated vortices is computed by calculating the interaction Lagrangian of two such point sources in the linear theory. The potential is used to model type II vortex scattering.