The internal and external electric fields for a resistive toroidal conductor carrying a steady poloidal current

Abstract

We consider the case of a resistive toroidal conductor carrying a steady current in the poloidal direction. We obtain algebraic expressions for the electric potential, the electric field and the surface charges inside and outside the toroidal shell. We use toroidal coordinates, in which Laplace's equation is R-separable. We analyze the limiting case of a thin toroid, which can be compared with the solution for the ideal straight solenoid.