Revisit: derivation of induction heating power equation for a conductive metal sphere

Currently, we are in the research of magnetic induction heating by using conductive metal particles. The technology (comes from a phenomenon known as the “skin effect”) generates heat produced by electrical eddy currents on metal particle’s surfaces. However, till now, the power equation to describe the energy consumption of the eddy current on a single particle surface still remains ambiguous. William R. Smythe derived this equation for metal ball. A minor error was clearly located in his derivation result. Today, similar ambiguous power equation is still adopted by researchers. In order to clarify this ambiguous situation and make our further deep study on particle-based induction heating process, in this paper, I revisit the derivation of the power equation with richful results.