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JEE Main 2016 · 9 Apr · Shift 1, Physics question 15

A magnetic dipole is acted upon by two magnetic fields which are inclined to each other at an angle of 75°. One of the fields has a magnitude of 15 mT. The dipole attains stable equilibrium at an angle of 30° with this field. The magnitude of the other field (in mT) is close to :

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Answer and worked solution

Official answer: A

At equilibrium the torques from the two fields cancel. The dipole is at 30° to the 15 mT field and 75∘−30∘=45∘75^\circ-30^\circ=45^\circ to the other:
15sin⁡30∘=Bsin⁡45∘  ⟹  B=7.50.707≈10.6≈11 mT.15\sin30^\circ=B\sin45^\circ\implies B=\frac{7.5}{0.707}\approx10.6\approx11\text{ mT}.

Topics:Magnetic dipole and bar magnet
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