Magnetic-Field Effects in High-Power Batteries .1. the Penetration of An Electric-Field Into A Cylindrical Conductor

Abstract

The penetration of the axial component of an electric field into a cylindrical conductor is described by an asymptotic solution method for long and short times. The development of the respective current distributions allows for a mathematical comparison of the solution schemes and indicates that the current initially increases at a rate proportional to time until a time of order epsilon/sigma, subsequently at a rate proportional to the square root of time, and finally levels off exponentially to the steady-state value. Numerical estimates of these time frames for a bipolar lead-acid battery with porous lead electrodes of 0.10 m radius give values of 1 x 10(-18) s for the inner time regime and 0.1 s for the diffusion time regime. Criteria for the proper omission of the displacement current also are given