Eddy current calculations for thin cylinders of finite length with driving fields of ramp time dependence

Eddy current density for a thin cylinder of finite length is calculated for the case of a driving field of ramp time dependence and dipole spatial dependence, the dipole being at the center of the cylinder. The calculations are made by using a perturbation expansion of the eddy current integral equations with a polynomial approximation to the time factor of the driving term. The steady state solution, presented as an arrow plot, shows the effects of edge charges forcing currents to remain within the conductor. The transient solutions show that the entire geometrical pattern of the steady state eddy currents is approached uniformly in the typical exponential manner of diffusion equations. Typical transient curves are given. All calculations are in normalized coordinates to allow maximum flexibility in applications.