  We consider a moving vortex in a two dimensional superconductor located at a
distance $d$ from a metallic overlayer. Starting from the microscopic imaginary
time action we integrate out the electronic degrees of freedom to obtain a low
energy, long wavelength effective action for the vortex. We focus our attention
on the vortex kinetic energy and derive a general expression for the vortex
mass. We find that in the limit $d\to \infty$ the Coulomb screening of the
density fluctuations, associated with vortex motion, results in a very small
vortex mass as has been obtained in earlier studies. In the opposite limit of
$d\ll \xi $ where $\xi$ is the coherence length of the superconductor we find
that the vortex mass diverges logarithmically with the size of the system as
the proximity to the metal makes the screening processes, that usually make the
mass small, ineffective. We comment on the relevance of our results to recent
experiments which show a dramatic fall in resistance when a metallic gate is
placed near a supeconducting film in a magnetic field at low temperature.
