Computational physics in action: the problem of a charged conducting toroid

Abstract

We present a comprehensive numerical analysis of the peculiarities of the electric field, equipotential surfaces, capacitance, and surface charge density at different thickness of a charged conducting ring. First, we review the filamentary ring case and prove that, unlike a sphere, there is a non-zero electric force inside it. We find that at relatively large values of the ring thickness the electric field has a local maximum inside the hole of the toroid. We also show the existence of a region of space, where the electric field is substantially homogeneous.