Electromagnetism · undergrad

Ampere-Maxwell Law

Magnetic circulation is sourced by current and changing electric flux.

Published Apr 26, 2026 · 1 min

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Differential Form

\nabla\times\mathbf B =\mu_0\mathbf J+\mu_0\varepsilon_0\frac{\partial\mathbf E}{\partial t}.

The term

\mu_0\varepsilon_0\frac{\partial\mathbf E}{\partial t}

is Maxwell’s correction. It makes charge conservation compatible with the field equations and permits electromagnetic waves.

A changing magnetic field induces a circulating electric field.

The four pillars of electromagnetism — differential, integral, and covariant forms in one view.

The differential equation describing fields that propagate at fixed speed.