(a) A current-carrying circular loop lies on a smooth horizontal plane. Can a uniform magnetic field be set up in such a manner that the loop turns around itself (i.e., turns about the vertical axis). (b) A current-carrying circular loop is located in a uniform external magnetic field. If the loop is 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. (c) A loop of irregular shape carrying current is located in an external magnetic field. If the wire is flexible, why does it change to a circular shape?

Explanation

(a) In order to rotate a current carrying horizontal circular ring about its vertical axis, we need to exert torque on it along vertical direction. For this, we need to have area vector `vecA` of this coil and applied magnetic field `vecB`, both in horizontal plane because `vectau=NIvecAxxvecB`.
`rArr` Direction of `vectau` will be perpendicular to plane passing through `vecAandvecB`. But in the present arrangement since the ring is placed on horizontal surface, its area vector `vecA` will be vertical. Hence, here we can not make this ring (or loop) rotating about its vertical axis by setting up uniform magnetic field in any direction.
(b) For a stationary current carrying planar coil, when induced magnetic field and applied magnetic field both are in the direction of area vector of that coil, we get maximum magnetic flux linked with the coil. Here since `vecAandvecB` are parallel, angle between them is `theta=0^(@)` and so torque exerted on the coil will be `tau=NIABsintheta=NIABsin0^(@)=0`. At this time coil remains stationary without any linear or rotational motion and so it is said to be in stable equilibrium.
( c) Every system has a natural tendency to attain a state of minimum potential energy to ensure maximum stability. That is why when any current carrying flexible coil with irregular shape is subjected to an external uniform magnetic field, assumes circular shape and becomes planar with its plane becoming perpendicular to external uniform magnetic field. Here, `vecA|\|vecB` and so angle between them becomes `theta=0^(@)` and so `tau=NIABsintheta=0` and ultimately that coil attains stable equilibrium.