Transient electromagnetic response of an inhomogeneous conducting sphere

Abstract

Analytic expressions for the quasi-static electromagnetic response of a sphere in presence of unit-step and ramp-type time varying magnetic fields are derived. The conductivity inside the sphere is assumed to vary linearly with radius, i.e. σ(ρ)=σ₀(ρ/a), where ρ is radial coordinate, σ₀ is a constant and a is the radius of sphere. Curves showing the decay of the magnetic field for both types of fields are presented. In the case of ramp-type applied magnetic field, the magnitudes of maxima of the induced magnetic field are found to decrease with increase in the rise time of the applied field and, hence, exciting pulses having small values of rise time should be used. It is believed that the analysis will be useful in the geoelectric exploration for highly conducting mineral deposits.