Scaling relation for the inductance of a coil on a ferromagnetic half-space

The calculated change in inductance when an air-core coil is placed next to a uniform ferromagnetic half-space is found to be well described by a simple two parameter scaling relation for a broad class of coils. The scaling relation is ΔL(ω) = ΔL₀L*(ω/ω₀). Here, ΔL₀ is a constant that determines the overall strength of the inductance change, while the frequency scale is set by ω₀, the frequency for which Re ΔL(ω) is zero. We test the hypothesis that the inductance change of a coil next to a uniform ferromagnetic plate can be described by the scaling relation with measurements made on a suite of medium carbon steels.