If r > > l, then B = μ o / 4 π 2M / r 3 Torque Acting on a Magnetic Dipole
When a Magnetic Dipole( M) is placed in a uniform magnetic field( B), then a Torque acts on it, Which is given by
τ = M * B or τ = MB sin θ Where θ is angle between the dipole axis and magnetic field. Potential Energy of a Magnetic Dipole in a Uniform Magnetic Field
The work done in rotating the dipole against the action of the torque is stored as potential energy of the dipole.
Potential Energy, U = W = – MB cos θ = – M. B Current Carrying Loop
A current carrying loop behaves as a magnetic dipole. If we look the upper face of the loop and current is flowing anti-clockwise, then it has a north polarity and if current is flowing clockwise. then it has a south polarity.
Magnetic dipole moment of a current carrying loop is given by M = IA For N such turns M = NIA Where I = current and A = area of cross-section of the coil.