Introduction:
Maxwell’s equation in differential form ## \nabla \times \vec{B}=\mu_o \vec{J}_{total}+\mu_o \epsilon_o \dot{\vec{E}} ## with ## \dot{\vec{E}}=0 ## comes up quite frequently in magnetostatic problems. In addition, the equation from the magnetic pole model ## \vec{B}=\mu_o \vec{H}+ \mu_o \vec{M} ## comes up quite often as well. It seems the textbooks are somewhat lacking in a thorough treatment of the use of these two equations, and the mathematical operations that can be used to generate solutions. In this Insights article, we will attempt to fill that gap.
In this paper, we will consider two rather different problems, which both employ the vector ## \vec{H} ##. The first involves an integral expression for ## \vec{H} ##. The second involves a derivation of the magnetomotive force (MMF) equation. The EE’s often use this equation in working with transformers. Here we will show that this MMF equation arises from an alternate form of Maxwell’s/Ampere’s...