Result

Field of a long straight wire

B = \frac{μ _{0} I}{2 π r}

Statement

The magnetic field at perpendicular distance r from a long, straight current-carrying wire.

Symbols and units

$B$	field magnitude	T
$I$	current	A
$r$	perpendicular distance from the wire	m
$μ_{0}$	permeability of free space	4π×10⁻⁷ T·m/A

When it applies

An infinitely long, straight wire — a good approximation near a wire far from its ends.

Don't use when

An idealization for an infinitely long wire — a good approximation only near a wire far from its ends.

Derivation

Integrate the Biot-Savart law along an infinite straight wire; the result falls off as 1/r, exactly like the electric field of an infinite line of charge.

B = \frac{μ _{0} I}{2 π r}

Watch out for

Field lines circle the wire — thumb along the current, fingers curling in the direction of B — never pointing radially outward the way an electric field does.

Connects to

Long line of charge