Induced Eddy Currents in Simple Conductive Geometries: Mathematical Formalism Describes the Excitation of Electrical Eddy Currents in a Time-Varying Magnetic Field

A complete mathematical formalism is introduced to describe the excitation of electrical eddy currents due to a time-varying magnetic field. The process works by applying a quasistatic approximation to Ampere's law and then segregating the magnetic field into impressed and induced terms. The result is a nonhomogeneous vector Helmholtz equation that can be analytically solved for many practical geometries. Four demonstration cases are then solved under a constant excitation field over all space.