Question

A bar magnet of length l and magnetic dipolemoment M is bent in the form of an arc as shown in figure. The new magnetic dipole
moment will be :-​

Answer 1

new dipole moment is 3M/π

we know, magnetic dipole moment = magnetic moment × minimum seperation between two poles.

let magnetic moment is m.

so, initial magnetic moment, M =ml.....(1)

A bar of length l is bent into arc, angle made by arc in centre is 60°.

so, length of bar = arc length

⇒l = π/3 × r

⇒r = 3l/π .......(2)

now, new magnetic dipole moment = m × r

= m × 3l/π [ from equation (2) ]

= 3ml/π

= 3M/π [ from equation (1)..]

hence, new dipole moment is 3M/π

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Answer 2

Answer:

Let m be the strength of each pole of bar magnet of length l.

M=m\times l

when bar magnet bent in the form of an arc.

l=\frac{\pi }{3}\times r=\frac{\pi r}{3}

r=\frac{3l}{\pi }

new magnetic dipole moment

M^{'}=m\times 2r\sin 30^{\circ}

=m\times2\frac{3l}{\pi }\frac{1}{2}

M^{'}=\frac{3ml}{\pi }

=\frac{3M}{\pi }

Option 1)

\frac{\text{M}}{2}

Option is incorrect

Option 2)

M

Option is incorrect

Option 3)

\frac{3}{\pi}\text{M}

Option is correct