Scaling Relation for the Inductance of a Coil on a Ferromagnetic Half-Space

Abstract

<p>Quantitative measurements have been made recently for the inductance of a coil placed next to flat ferromagnetic metal plates [1–3]. Results for a suite of low carbon steels were in good agreement with the analytic solutions of Cheng [4] and Dodd and Deeds [5], which describe the metal as a structureless half-space defined by an isotropic and uniform conductivity, σ, and initial relative permeability, μ. However, Refs. 1–3 reported poor agreement between the same halfspace model and inductance measurements made on commercially pure iron and nickel. Our desire to understand these results prompted us to more completely analyze the rather complicated analytic solution for the half-space model. [6] Somewhat to our surprise, we found that the solution simplifies for highly permeable metals and that above a characteristic frequency, the inductance change can be approximated by a simple expression.</p>