A circular coil with a radius of 2.0 cm consists of 500 turns and carries a current of 1.0 A . The axis of the coil forms an angle of 30^ with a uniform magnetic field of magnitude 0.40 T present in the region. Determine the torque acting on the coil.

Step-by-step solution

Given: Radius of the coil, r = 2.0 cm = 0.02 m Number of turns, N = 500 Current, I = 1.0 A Magnetic field, B = 0.40 T Angle between the axis of the coil and the magnetic field, = 30^ The magnetic moment of the coil is given by: M = N I A = N I ( r^2) Substituting the values: M = 500 1.0 (0.02)^2 = 500 0.0004 = 0.2 A m ^2 The torque acting on the coil is: = M B Substituting the values: = 0.2 0.40 30^ = 0.08 0.5 = 0.04 N m Using 3.14 : 0.04 3.14 = 0.1256 N m 0.13 N m