The magnetic moments associated with two closely wound circular coils a and b of radius r and 2r respectively are equal if (where N_a , I_a and N_b , I_b are number of turns and current in A and B respectively)

Step-by-step solution

The magnetic moment of a circular coil is given by M = NIA , where N is the number of turns, I is the current, and A is the area of the coil. For coil A, the area is A_a = r^2 . The magnetic moment of coil A is M_a = N_a I_a ( r^2) . For coil B, the area is A_b = (2r)^2 = 4 r^2 . The magnetic moment of coil B is M_b = N_b I_b (4 r^2) . Given that the magnetic moments are equal, M_a = M_b . N_a I_a ( r^2) = N_b I_b (4 r^2) N_a I_a = 4N_b I_b Answer: N_a I_a = 4N_b I_b