Q.A circular coil of radius 5 cm and 50 turns carries a current of 3 ampere. The magnetic dipole moment of the coil is nearly

Magnetic Moment of a Current Loop

Think of a tiny compass needle. It has a north pole and a south pole, and when you put it in a magnetic field, it feels a torque — a twist that tries to align it with the field. A current-carrying loop behaves exactly the same way. It's not a permanent magnet, but it acts like one: it has its own magnetic "strength" and a preferred direction, and an external field will try to rotate it.

That "magnetic strength" of the loop is called its magnetic moment. The bigger the current, the stronger the effect. The larger the area enclosed by the loop, the stronger the effect. And if you stack many loops together (N turns), each turn contributes, so the effect multiplies.

The Precise Definition

For a flat loop of wire carrying a steady current, the magnetic moment $\vec{m}$ is defined as:

Here:

• $N$ is the number of turns of wire (if it's a single loop, $N=1$).
• $I$ is the current flowing through the loop.
• $\vec{A}$ is a vector whose magnitude equals the area enclosed by the loop, and whose direction is perpendicular to the plane of the loop.

The direction of $\vec{A}$ — and therefore of $\vec{m}$ — is given by the right-hand rule: curl the fingers of your right hand in the direction of the current; your thumb points along the magnetic moment.

Why This Makes Sense

A single moving charge produces a magnetic field. A current is a stream of moving charges. When those charges go around a loop, their individual magnetic fields add up. The net effect far away from the loop is identical to that of a tiny bar magnet placed at the centre of the loop, with its north pole pointing along $\vec{m}$.

The torque this loop experiences in a uniform external magnetic field $\vec{B}$ is:

The magnitude of the torque is $mB\sin\theta$, where $\theta$ is the angle between $\vec{m}$ and $\vec{B}$. This is exactly the same formula as for a bar magnet. The loop tries to align its magnetic moment with the field — just like a compass needle.

A Common Exam Point …