A Pedagogical MKS-based Electromagnetic Unit Convention with $\epsilon_0 = \mu_0 = 1/c$

TL;DR

This paper introduces a pedagogical MKS-based electromagnetic unit system with vacuum constants set to 1/c, simplifying equations and units for undergraduate teaching, supported by student surveys showing improved clarity.

Contribution

It proposes a new rationalized unit convention that reduces cognitive load and enhances understanding in electromagnetism education, with empirical student support.

Findings

Students showed improved understanding of the wave equation derivation.

Majority preferred the dimensionless resistance feature.

The system simplifies dimensional analysis in electromagnetism.

Abstract

We propose a pedagogical, rationalized MKS-based convention for electromagnetic quantities designed to reduce cognitive load in undergraduate undergraduate electromagnetism. By setting vacuum constants to $\varepsilon_0 = \mu_0 = 1/c$, we preserve the familiar structure of Maxwell's equations while making the role of the speed of light explicit. In this convention, electrical units are expressed directly in terms of mechanical units (e.g.\ $[\mathrm{nuA}] = \sqrt{\mathrm{J/s}}$), effectively reducing the number of independent base units. A striking pedagogical consequence is that electrical resistance becomes dimensionless, capacitance and inductance acquire units of time, and radiation pressure reduces to $|\mathbf{E}\times \mathbf{B}|$, greatly simplifying dimensional analysis for circuits and fields. We introduce corresponding non-SI units (\textit{nu}-units), provide conversion relations to SI, and demonstrate the potential utility of this system through comparative ``before/after'' derivations of the wave equation, electromagnetic energy density, radiation pressure, and the Bohr atom. Preliminary empirical support is provided by student attitude surveys administered to $N_1 = 46$ and $N_2 = 39$ students in an undergraduate physics course, which showed a statistically significant improvement in the perceived clarity of the wave equation derivation after exposure to the nu-system ($p = 0.005$, Mann--Whitney $U$ test), and a majority preference for the dimensionless-resistance feature.