A current carrying circular loop is located in a uniform external magnetic field. If the loop if free to turn, what is its orientation of stable equilibrium? Show that in this orientation, the flux of the total field (external field + field produced by the loop) is maximum.

Explanation

The current carrying circular loop behaves as a magnetic dipole of magnetic moment `vecM` acting perpendicular to its plane. The torque on the current loop of magnetic dipole moment M in the magnetic field B is
`tau=MB sin alpha=IAxxB sin alpha, ( :' M=AI)`
where `alpha` is the angle between `vecM` and `vecB`. The system will be in stable equilibrium if torque is zero, which is so if `alpha=0^@`. This is possible if `vecB` is parallel to `vecA` i.e. `vecB` is perpendicular to the plane of the loop. In this orientation, the magnetic field produced by the loop is in the same direction as that of external field, both normal to the plane of loop. It is due to this fact, the magnetic flux due to total field is maximum.