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Question
A short bar magnet of magnetic moment 0.9 J/T is placed with its axis at 30° to a uniform magnetic field. It experiences a torque of 0.063 J.
(i) Calculate the magnitude of the magnetic field.
(ii) In which orientation will the bar magnet be in stable equilibrium in the magnetic field?
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Solution
(i) Magnetic moment M = 0.9 J/T
τ = 0.063 J, θ = 30°
We know τ = M × B
= MB sin θ
0.063 = 0.9 × B × sin 30°
`B = (2 xx 0.063)/0.9 = 0.14T`
(ii) Stable equilibrium is position of minimum energy. Since `U = -vecM.vecB`
U = − M B cos θ
Where, U is the energy stored or P.E. of the magnet inside magnetic field B.
So, when θ = 0, U = − MB is the minimum energy.
Thus, when `vecM` and `vecB` are parallel to each other bar magnet is in stable equilibrium.
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