Poynting Vector Flow in a Circular Circuit

摘要

A circuit is considered in the shape of a ring, with a battery of negligiblesize and a wire of uniform resistance. A linear charge distribution along thewire maintains an electrostatic field and a steady current, which produces aconstant magnetic field. Earlier studies of the Poynting vector and the rate offlow of energy considered only idealized geometries in which the Poyntingvector was confined to the space within the circuit. But in more realisticcases the Poynting vector is nonzero outside as well as inside the circuit. Anexpression is obtained for the Poynting vector in terms of products ofintegrals, which are evaluated numerically to show the energy flow. Limitingexpressions are obtained analytically. It is shown that the total powergenerated by the battery equals the energy flowing into the wire per unit time.