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A free current is the part of the macroscopic electric current assigned to mobile or externally supplied electric charges, rather than to the bound motion represented by polarization and magnetization. In a conductor, drifting conduction electrons provide a familiar example.

In macroscopic Maxwell's equations, the free-current density appears as $\nabla \times \mathbf{H}={\mathbf{J}}_{\mathrm{f}}+\partial \mathbf{D}/\partial t$. Here $\mathbf{H}$ is the magnetic field strength and $\mathbf{D}$ the electric displacement field. The separation depends on the material model; the total microscopic charge motion remains the source of the electromagnetic field.

A surface current density $\mathbf{K}$ concentrated on an interface creates a discontinuity of tangential magnetic field. Let the unit normal $\mathbf{n}$ point from side $-$ to side $+$. In SI units, the microscopic Ampere-Maxwell law givesHere the surface current includes both free current and bound current. An infinitesimal rectangular integration loop straddling the sheet derives the tangential jump. The no-monopole equation separately gives $\mathbf{n}\cdot ({\mathbf{B}}_{+}-{\mathbf{B}}_{-})=0$.

In a macroscopic material description, the magnetic field intensity instead satisfiesWriting a jump in $\mathbf{B}$ using only free current without accounting for magnetization would mix these two descriptions. In Gaussian units, the total-current magnetic-field jump is $4\pi {\mathbf{K}}_{\mathrm{total}}/c$.

For an isolated uniform sheet in vacuum, reflection symmetry givesFor example, current along $+x$ on $z=0$ gives a field along $-y$ above the sheet and $+y$ below it. The directions agree with the right-hand rule.

In macroscopic electromagnetism, magnetic field strength is $\mathbf{H}=\mathbf{B}/{\mu }_0-\mathbf{M}$, where $\mathbf{B}$ is magnetic flux density and $\mathbf{M}$ is magnetization. In SI units $\mathbf{H}$ is measured in $\mathrm{A}{\mathrm{m}}^{-1}$, while $\mathbf{B}$ is measured in tesla units. In a linear isotropic medium $\mathbf{B}=\mu \mathbf{H}$, where $\mu$ is magnetic permeability. The macroscopic Ampère-Maxwell equation writes its curl in terms of free current and displacement current. The electromagnetic Poynting vector is $\mathbf{E}\times \mathbf{H}$ in this convention.

A rod of magnetic path length $l$ and tangential magnetization $M$ closed by a gap of width $a$ has constant flux in the one-dimensional magnetic circuit approximation. Equal cross sections and negligible leakage give $H_g=H_r+M$, while absence of free current gives $l{H}_r+a{H}_g=0$. Their solution is the displayed pair. Gap fringing or an unspecified cross-section change requires a more detailed field model.