Current loop as a magnetic dipole

Magnetic dipole:

An arrangement of two equal and opposite magnetic poles separated by a small distance is called a magnetic dipole.

Magnetic dipole moment:

The magnetic dipole moment of a magnetic dipole is defined as the product of its pole strength and magnetic length. It is a vector quantity, directed from S-pole to N-pole.

Ampere found that the distribution of magnetic lines of force around a finite current carrying solenoid is similar to that produced by a bar magnet.

The magnetic induction at a point along the axis of a circular coil carrying current is

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The direction of this magnetic field is along the axis and is given by right hand rule. For points which are far away from the centre of the coil, x>>a, a2 is small and it is neglected. Hence for such points,

If we consider a circular loop, n = 1, its area A = πa2

The magnetic induction at a point along the axial line of a short bar magnet is

Comparing equations (1) and (2), we find that

Hence a current loop is equivalent to a magnetic dipole of moment M = IA

The magnetic moment of a current loop is defined as the product of the current and the loop area. Its direction is perpendicular to the plane of the loop.

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