Inductance of a coil on a thick ferromagnetic metal plate

We study the frequency-dependent inductance of a small air-cored coil of wire placed flat upon various ferromagnetic metal plates. The change in the complex inductance of the coil, measured with an HP 4193A impedance analyzer, is reported for frequencies between 1 kHz and 1 MHz. The metal plates consisted of commercially pure (99.7% and 99.9%) Ni, commercially pure (99.9%) Fe, and a suite of medium carbon steels. For the steel plates, inductance changes were consistent with a simple half-space model that treats the metal as a continuum defined by a conductivity σ and a relative initial-permeability μ where these material parameters are isotropic, local, and uniform throughout the plate. The inductance changes for Ni and Fe could not be fit to the half-space model for any values of σ and μ, but were consistent with a model that assumes a thin (~10 μm) surface layer with a significantly reduced permeability-a dead layer. We tested the existence of the hypothetical dead layer in several ways. We found that the inductance increased when the surface was chemically etched (presumably eroding the dead layer) and decreased when the surface was mechanically polished (presumably increasing the dead layer). We also found that the inductance of the Fe and Ni samples decreased substantially over the course of days and months when exposed to air