A magnetised wire of moment M is bent into an arc of a circle subtending an angle 60° at the centre, then the new magnetic moment is

Question

A magnetised wire of moment M is bent into an arc of a circle subtending an angle 60° at the centre, then the new magnetic moment is (A) (2 M / π) (B) (M / π) (C) (3 √2 M / π) (D) (3 M / π)

Tardigrade Admin · Accepted Answer

New magnetic moment, M'=(2 M sin (θ / 2)/θ)=(2 M sin (π / 6)/θ / 3) =(2 M × (1/2)/π / 3)=(3 M/π)

Q. A magnetised wire of moment $M$ is bent into an arc of a circle subtending an angle $6 0^{\circ}$ at the centre, then the new magnetic moment is

$(2 M / π)$

$(M / π)$

$(32 M / π)$

$(3 M / π)$

New magnetic moment,
$M^{'} = \frac{2 M s i n ( θ /2 )}{θ} = \frac{2 M s i n ( π /6 )}{θ /3}$
$= \frac{2 M \times \frac{1}{2}}{π /3} = \frac{3 M}{π}$

Q. A magnetised wire of moment M is bent into an arc of a circle subtending an angle 60∘ at the centre, then the new magnetic moment is

(2M/π)

(M/π)

(32​M/π)

(3M/π)