Field of a straight wire

Moving charges do not just experience magnetic forces, they create them. A wire carrying a current is a source of magnetic field: this is Ørsted’s discovery, made quantitative.

Law — Field of an infinite straight wire

A straight wire carrying current $i$ generates a magnetic field of magnitude: $\ev{|\vec{B}| = \frac{\mu_0\,i}{2\pi\,r}}$ where $r$ is the perpendicular distance from the wire.

The field decreases as $1/r$ moving away from the wire (more slowly than the electric field of a point charge, which goes as $1/r^2$). The field lines are concentric circles around the wire, lying in planes perpendicular to it. The direction is found with the right-hand rule: thumb along the direction of the current, the curling fingers indicate the direction of $\vec{B}$.

Field of a straight wire: concentric circles whose direction follows the right-hand rule (thumb along $i$).

Two parallel wires carrying current therefore exert forces on each other at a distance through their respective fields: currents in the same direction attract, currents in opposite directions repel. This phenomenon underlies the old definition of the ampere.

Collegamenti

Argomenti: Magnetismo Concetti: Campo magnetico

Esercizi collegati: Field of a wire at 3 mm · Force between two parallel wires with currents in the same direction · Field of a household cable and compass