A wire of length L carries a current i . If the wire is turned into a circular coil and kept in a uniform magnetic field B , the maximum magnitude of torque in the given magnetic field will be

Step-by-step solution

The torque on the current loop is =N I A B ---(1) If there are N turns of the circular coil, each of radius r , then L=2 r N r= L 2 N Area of the coil, A= r^2= ( L 2 N )^2= L^2 4 N^2 Putting this value in (1), we get, =N I ( L^2 4 N^2 ) B = L^2 I B 4 N --(2) From (2), it is clear that is maximum if N is minimum. Torque is maximum if =1 and N=1 _ =L^2 I B / 4