Question

The magnetic moment of an iron bar is M. It is now bent in such a way that it forms an arc section of a circle subtending an angle of 60° at the centre. The magnetic moment of this arc section is

(1) \(\frac{3M}\pi\)

(2) \(\frac{4M}\pi\)

(3) \(\frac M\pi\)

(4) \(\frac{2M}\pi\)

Answer 1

Correct option is (1) \(\frac{3M}\pi\)

\(M = m.L\)

\(R\theta = L\)

\(\frac{R\pi} 3 = L\)

\(R = \frac{3 L}\pi\)

\(M' = m(2R) \sin 30^\circ\)

\(= m(2) \frac{3L} \pi \times \frac 12\)

\( = \frac{3} \pi mL\)

\( = \frac{3 M} \pi\)