Current Loop as a Magnetic Dipole : Magnetic Dipole Moment of Current Loop

A current-carrying planar loop behaves like a tiny bar magnet. It has two magnetic faces and, when placed in an external magnetic field, it tends to rotate until it aligns with that field.

Analogy: A current loop behaves like a compass needle. Both turn in a magnetic field until their magnetic moment points along the field.

A coil is a set of current loops. A solenoid contains many loops and also shows magnetic behaviour similar to a bar magnet.

When a current-carrying loop is placed in a uniform magnetic field, magnetic forces act on opposite sides of the loop. These forces form a couple, producing rotation but no net translational force.

If the area vector of the loop makes an angle θ with the external magnetic field \[vec B\], then

A magnetic dipole in a magnetic field experiences torque: τ = mB sin⁡ θ

For a current loop: τ = IAB sin ⁡θ

Comparing the two equations: m = IA

Thus, the magnetic dipole moment of a current loop is the product of the current flowing through it and the area enclosed by it.

Vector Form: \[\vec m\] = I\[\vec A\]​

Here, \[\vec A\] is the area vector, perpendicular to the plane of the loop.

For a Coil of N Turns

The direction of \[\vec m\] is perpendicular to the plane of the loop.

Right-Hand Grip Rule

• Curl the fingers of your right hand in the direction of conventional current in the loop.
• The extended thumb gives the direction of \[\vec A\] and hence \[\vec m\].