Debye superpotential for charged rings or circular currents on Kerr black hole

We provide an explicit, closed and compact expression for the Debye superpotential of a circular source. This superpotential is obtained by integrating the Green function of Teukolsky Master Equation (TME). The Debye potential itself is then, for a particular configuration, calculated in the same manner as the ${\phi }_0$ field component is calculated from the Green function of the TME – by convolution of the Green function with sources. This way we provide an exact field of charged ring and circular current on the Kerr background, finalizing thus the work of Linet.