A circular coil of 100 turns has an effective radius of 0.05 m and carries a current of 0.1 A . How much work is required to turn it in an external magnetic field of 1.5 ~Wb / m ^2 through 180^ about its axis perpendicular to the magnetic field? The plane of the coil is initially perpendicular to the magnetic field.

Step-by-step solution

The potential energy of circular loop in the magnetic field =-M B , where is the angle between normal to plane of coil and magnetic field B . Initial potential energy, U_i=-N i A B 0^ =-N i A B When coil is turned through 180^ , therefore final potential energy, U_f=-N i A B 180^ =N i A B Required work, W= gain in potential energy =U_f-U_i=N i A B-(-N i A B)=2NiAB Here, N=100, i=0.1 ~A , B=1.5 ~Wb / m ^2 and radius r=0.05 ~m A= r^2=3.14 (0.05)^2=7.85 10⁻³ ~m ^2 Work, W=2 100 0.1 7.85 10⁻³ 1.5 W=0.2355 ~J