Formulations via vector potentials

Abstract

Motivated by the fact that the magnetic induction B=μH is divergence-free in Ω, a classical approach to the Maxwell equations and to eddy current problems is based on the introduction of a vector magnetic potential A such that curl A=μH. Often, this is also accompanied by the use of a scalar electric potential VC in the conductor Ω _C , satisfying iwA _C +grad V _C =−E _C (see Silvester and Ferrari [227]; for the engineering literature, see, e.g., Chari et al. [79], Biddlecombe et al. [47], Morisue [180], Bíró and Preis [49]).