Beam-generated magnetic fields strongly influence the behavior of relativistic electron guns. Existing methods used in ray-tracing codes have limited accuracy and may not correctly represent nonlaminar beams. We describe a technique for the magnetic field calculation in a two-dimensional code based on the assignment of particle currents to the faces of elements in the mesh used for the electrostatic calculation. The balanced calculation of electric and magnetic forces in the same iteration cycle reduces the possibility of numerical filamentation instabilities. With simple rules of assignment on boundary faces, the method also handles field contributions of electrode currents. Several benchmark calculations performed on conformal meshes illustrate the versatility of the technique.