A Novel Simple Format of Maxwell’s Equations in SI Units

Abstract

In the International System of Units (SI), distinct physical dimensions were assigned to the electric ( $E$ ) and magnetic ( $H$ ) fields as volt-per-meter and ampere-per-meter, respectively. To save the dimensional balance in the standard Maxwell’s equations (MEs) in SI units, a pair of free-space constants, $\epsilon _{0}$ and ${\mu } _{0}$ , with their dimensions of farad-per-meter and henry-per-meter were installed heuristically. Eventually, every quantity that participated in each ME in SI units has an individual physical dimension distinct from the other terms therein. This situation hampers the control of the dimensional balance in the processes of analytical manipulations with the MEs during the theoretical studies. Reformatting the free-space constants is performed in this article so that one new constant is obtained with its dimension of volt, and the other one has its dimension of ampere. These gave a handle to scale the electric and magnetic fields appropriately. Ultimately, the new fields are obtained with their common dimension of inverse-meter. Meanwhile, the standard differential procedures $\epsilon _{0}\frac {\partial }{\partial t}$ and ${\mu } _{0}\frac {\partial }{\partial t}$ from MEs are obtained in their simple common format of $\frac {\partial }{c\,\partial t}$ , where $c$ is the speed of light. The MEs in the novel format are exhibited for the fields in the free space, plasma, and dielectrics. The content of this article is destined for the researchers who deal with theoretical studies in electrodynamics, and the level of content is appropriate for and realizable by recent graduates, M.Sc. and Ph.D. students, and professionals.

Keywords

• Maxwell’s equations
• electrodynamics
• time domain analysis