Maxwell’s Equations in Magnetostatics and Solving with the Curl Operator

Thread starter Charles Link
Start date Aug 12, 2019
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Curl Curl operator Magnetostatics Operator

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Maxwell's equations in magnetostatics, particularly the equation involving the curl operator, are crucial for solving magnetostatic problems, especially when the time derivative of the electric field is zero. The discussion highlights the importance of the magnetic pole model equation, which relates magnetic field strength to magnetization and magnetic field intensity. It emphasizes the need for a more comprehensive treatment of these equations, as current textbooks often lack depth in this area. Two distinct problems are explored: one involving an integral expression for the magnetic field intensity vector and another focused on deriving the magnetomotive force (MMF) equation, commonly used in transformer applications. This exploration aims to bridge the gap in understanding and applying these fundamental concepts in electromagnetism.

Aug 12, 2019

Charles Link

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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...

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