consider a current loop where the circulating

Question

 

Consider a current loop where the circulating current is I. This may be for an example of a coil carrying a current. We will assume that the current loop lies within a single plane. The area enclosed by the current by the current is A suppose that μ_n is a unit vector coming out from the area A. The direction of μ_{n is} such that looking along it, the current circulates clockwise. Then the magnetic dipole moment or simply the magnetic moment μ_{m is} defined as

                                                  μ_{m  =} I A μ_n

Magnetic dipole moment measures the strength of the magnetic field created by a current loop and also the extent of interaction of the current loop with an extremely applied magnetic field. When a magnetic moment is positioned in a magnetic field, it experiences a force torque that tries to rotate magnetic current to align its axis with the magnetic field. Since a magnetic moment is a current loop, it gives rise to a magnetic field B around it. Which is similar to a magnetic field around the bar magnet. The field B at a point P at a distance r along the axis of the coil from the centre is directly propositional to the magnitude of the magnetic moment but inversely propositional to the r³ that is

                                                                      B α μ_m/r³