A wire of length L is bent in the form of a circular coil and current ' i ' is passed through it. This coil is kept in magnetic field. The torque acting on the coil will be maximum, when the number of turns is ___

Step-by-step solution

The torque acting on a circular coil of N turns in a magnetic field is given by = N i A B . For maximum torque, = 1 , giving = N i A B . Let r be the radius of the coil. The total length of the wire is L = N(2 r) , which gives r = L 2 N . The area of the coil is A = r^2 = ( L 2 N )^2 = L^2 4 N^2 . Substituting the area into the torque expression, we get = N i ( L^2 4 N^2 ) B = i L^2 B 4 N . For the torque to be maximum, the number of turns N must be minimum. Since N is a positive integer, the minimum possible value