On the validity of characterizing eddy current phenomena by parabolic partial differential equations

Eddy current problems are commonly solved by neglecting displacement current. This assumption reduces Maxwell's equations to a parabolic partial differential equation [1]. It is shown that neglecting displacement currents entirely may reduce the space dimension of the problem and yields the magnetic and electric fields in the conducting regions accurately. However, the electric fields in the air regions are very inaccurate, and the charge distribution resulting on the conducting surfaces is absent in the standard solution, which neglects displacement currents and longitudinal field variations. The standard solution is found to yield the proper value of skin depth over a very wide range of conductivity, permeability, and frequency.