Magnetic Dipole MomentFrom the expression for the torque on a current loop, the characteristics of the current loop are summarized in its magnetic moment
The magnetic moment can be considered to be a vector quantity with direction perpendicular to the current loop in the righthandrule direction. The torque is given by As seen in the geometry of a current loop, this torque tends to line up the magnetic moment with the magnetic field B, so this represents its lowest energy configuration. The potential energy associated with the magnetic moment is so that the difference in energy between aligned and antialigned is These relationships for a finite current loop extend to the magnetic dipoles of electron orbits and to the intrinsic magnetic moment associated with electron spin. Also important are nuclear magnetic moments. 
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Torque on a Current LoopThe torque on a currentcarrying coil, as in a DC motor, can be related to the characteristics of the coil by the "magnetic moment" or "magnetic dipole moment". The torque exerted by the magnetic force (including both sides of the coil) is given by
Since this torque acts perpendicular to the magnetic moment, then it can cause the magnetic moment to precess around the magnetic field at a characteristic frequency called the Larmor frequency. If you exerted the necessary torque to overcome the magnetic torque and rotate the loop from angle zero to 180 degrees, you would do an amount of rotational work given by the integral The position where the magnetic moment is opposite to the magnetic field is said to have a higher magnetic potential energy. 
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