An electrically conducting sphere in a three‐dimensional, alternating magnetic field

The electrical vector and scalar potential as well as the underlying induced eddy current density of a conducting sphere exposed to an external, time‐varying magnetic field are calculated. The external magnetic field is assumed to be generated by sinusoidally alternating current density distributions. Admitting arbitrary three‐dimensional current density fields, this paper extends previous results on this subject. Among other things, these calculations prove that in a sphere there is no radial component of the induced eddy current density field. As an application of these results the impedance and power absorption of the sphere are derived. The impedance is the key for the contactless, inductive measurement of the electrical conductivity of metallic melts.