Show that a current carrying loop acts as a magnetic dipole. Derive an expression for its magnetic dipole moment?

Explanation

When current flows through the circular loop in clockwise direction, the direction of magnetic field is such that the lower face of the loop acts as north pole and the upper face will act as south pole. This shows that current carrying circular loop behaves as a magnetic dipole.
Magnetic dipole moment of current carrying loop When current carrying loop is placed in a magnetic field
`vec B,` torque acting on it is given by `tau = lAB sin theta " "...(i)`
Torque which acts on a magnetic dipole placed in the magnetic field is given by
`tau = MB sin theta " "...(ii)`
From equation (i) and (ii) M = IA For loop having n turns `M = n l A `