We present numerical calculations using the magnetic monopoles of four-dimensional U(1) lattice gauge theory to obtain the heavy quark potential. Using the cosine action we perform a conventional gauge field simulation on a 16 4 lattice. We then use the DeGrand-Toussaint scheme for locating magnetic current in the lattice gauge field configurations to obtain our monopole configurations. In addition to the heavy quark potential we also calculate the potential between heavy external monopoles. In the confined phase of quarks, we observe total screening between external monopoles. In the Coulomb phase of the quarks we find a partially screened Coulomb potential between external monopoles. Under the assumptions used to obtain the potential between external monopoles, we verify that the Dirac quantization condition holds for the product of renormalized electric and magnetic charges.