A magnetic dipole experiences a torque of when placed in uniform magnetic field in such a way that dipole moment makes angle of 60° with magnetic field. The potential energy of the dipole is: [2025]

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Solution

Q.
A magnetic dipole experiences a torque of $80 \sqrt{3} Nm$ when placed in uniform magnetic field in such a way that dipole moment makes angle of 60° with magnetic field. The potential energy of the dipole is: [2025]

1 80 J

2 $- 40 \sqrt{3} J$

3 –60 J

4 –80 J

Ans.
(4)

$| \vec{τ} |$ $=$ $| \vec{M} \times \vec{B} |$ $= M B \sin 60 °$

$80 \sqrt{3} = \frac{\sqrt{3}}{2} M B \Rightarrow M B = 160$

$U = - \vec{M} \cdot \vec{B} = - M B \cos 60 °$

$U = - 160 \times \frac{1}{2} = - 80 J$

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