In this paper we derive the surface-current distribution on a perfectly conducting circular disc. The current is obtained by calculating the limit of the surface currents on an oblate spheroid as the thickness goes to zero. The null-field approach is used. We show that it is possible to calculate all quantities in terms of the spherical basis functions, thus avoiding the cumbersome spheroidal basis functions. Furthermore, it is shown that the correct edge behaviour appears very naturally within the formulation. We compute the surface field on the disc for a plane incident wave, the surface current (eigencurrents) at the complex resonances of the disc, and the induced current on a subterranean disc excited by a circular antenna loop on the ground.