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

Question

A bar magnet of length 'l' and magnetic dipole moment 'M' is bent in the form of an arc as shown in figure. The new magnetic dipole moment will be (A)  (M/2) (B) M (C)  (3/π) M (D)  (2/π) M

Tardigrade Admin · Accepted Answer

Let magnetic pole strength be m then M = m ℓ In new situation M' = (m) (2r sin (60°/2)) where r ( (π/3)) = ℓ M' = 2m ( (2 ℓ/π)) ((1/2)) = (3mℓ/π) = (3M/π)

Q. A bar magnet of length ' $l$ ' and magnetic dipole moment 'M' is bent in the form of an arc as shown in figure. The new magnetic dipole moment will be

$\frac{M}{2}$

$M$

$\frac{3}{π} M$

$\frac{2}{π} M$

Let magnetic pole strength be m then
M $= m ℓ$
In new situation
$M^{'} = (m) (2 r s in \frac{6 0 ^{\circ}}{2}) w h ere r (\frac{π}{3}) = ℓ$
$M^{'} = 2 m (\frac{2 ℓ}{π}) (\frac{1}{2}) = \frac{3 m ℓ}{π} = \frac{3 M}{π}$

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

2M​

M

π3​M

π2​M

Let magnetic pole strength be m then M=mℓ In new situation M′=(m)(2rsin260∘​)wherer(3π​)=ℓ M′=2m(π2ℓ​)(21​)=π3mℓ​=π3M​

Q. A bar magnet of length ' $l$ ' and magnetic dipole moment 'M' is bent in the form of an arc as shown in figure. The new magnetic dipole moment will be

$\frac{M}{2}$

$M$

$\frac{3}{π} M$

$\frac{2}{π} M$

Let magnetic pole strength be m then
M $= m ℓ$
In new situation
$M^{'} = (m) (2 r s in \frac{6 0 ^{\circ}}{2}) w h ere r (\frac{π}{3}) = ℓ$
$M^{'} = 2 m (\frac{2 ℓ}{π}) (\frac{1}{2}) = \frac{3 m ℓ}{π} = \frac{3 M}{π}$