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JEE Main 2016 (9 Apr, Shift 1) · Current Loop as a Magnetic Dipole

Current Loop as a Magnetic Dipole question from JEE Main 2016 (9 Apr, Shift 1)

Q80JEE Main 2016 · 9 APR · SHIFT 1Difficult

Current Loop as a Magnetic Dipole

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: (a)

  1. In equilibrium the torques of the two fields cancel: mB1sin⁡θ1=mB2sin⁡θ2mB_1\sin\theta_1 = mB_2\sin\theta_2.
  2. Angle with B1B_1 is 30∘30^\circ, so the angle with B2B_2 is 75∘−30∘=45∘75^\circ - 30^\circ = 45^\circ.
  3. B2=15×sin⁡30∘sin⁡45∘=7.50.707≈10.6B_2 = \frac{15 \times \sin30^\circ}{\sin45^\circ} = \frac{7.5}{0.707} \approx 10.6 mT
  4. So the answer is (a) 11 mT.
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