**Current loop as a magnetic dipole:**

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. This is evident from the fact that a compass needle when moved around these two bodies show similar deflections. After noting the close resemblance between these two, Ampere demonstrated that a simple current loop behaves like a bar magnet and put forward that all the magnetic phenomena is due to circulating electric current. This is Ampere’s hypothesis.

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

**B = [μ _{0} nLa^{2} / 2(a^{2}+x^{2})^{3/2}]**

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, a^{2} is small and it is neglected. Hence for such points,

**B = B = [μ _{0} nLa^{2} / 3x^{3}]**

If we consider a circular loop, n = 1, its area A = π a^{2}

B = **[μ _{0}IA/2πx^{3}] … … (1)**

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

**B = (μ _{0}/4π) . (2M/x^{3})**

so, B = **(μ _{0}/2π) . (M/x^{3}) … … (2)**

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

**M = IA … … (3)**

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.