We study the heavy charge potential in the Coulomb phase of pure gauge
compact U(1) theory on the lattice. We calculate the static potential
V-W(T,(R) over right arrow) from Wilson loops on a 16(3)x32 lattice a
nd compare with the predictions of lattice perturbation theory. We inv
estigate finite size effects and, in particular, the importance of non
-Coulomb contributions to the potential. We also comment on the existe
nce of a maximal coupling in the Coulomb phase of pure gauge U(1) theo
ry.