Magnetic moment of a loop

A current loop immersed in a magnetic field experiences a torque: it behaves like a small magnet, that is, a magnetic dipole. The quantity that characterises it is the magnetic moment.

Principle — Magnetic moment of a loop

A closed loop of area $A$ carrying current $i$ has a magnetic moment: $\ev{\vec{\mu} = i\,A\,\hat{n}}$ where $\hat{n}$ is the unit vector normal to the loop, oriented according to the right-hand rule: the fingers follow the current, the thumb indicates $\hat{n}$.

The magnetic moment summarises in a single vector everything needed to predict the loop’s behaviour in an external field: how large it is ($iA$) and how it is oriented ($\hat{n}$). The direction of $\hat{n}$ is given by the “hitchhiker’s” rule applied to the current: curling the right-hand fingers in the direction of $i$, the thumb points along $\vec{\mu}$.

For a coil of $N$ stacked loops the moment is multiplied by $N$: $|\vec{\mu}| = N\,i\,A$. This is the quantity that appears in every torque and energy formula for the dipole, and it is what manufacturers maximise (many loops, large area, high current) to obtain sensitive motors and instruments.

Collegamenti

Argomenti: Magnetismo Concetti: Dipolo magnetico

Esercizi collegati: Torque on a square loop · Which field gives maximum torque · Motor and dynamo