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JEE Main 2017 (9 Apr, Shift 1) · Current Loop as a Magnetic Dipole

Current Loop as a Magnetic Dipole question from JEE Main 2017 (9 Apr, Shift 1)

Q79JEE Main 2017 · 9 APR · SHIFT 1Medium

Current Loop as a Magnetic Dipole

A uniform magnetic field B of 0.3 T is along the positive Z-direction. A rectangular loop (abcd) of sides 10 cm × 5 cm carries a current I of 12 A. Out of the following different orientations which one corresponds to stable equilibrium?

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Answer: (c)

  1. Stable equilibrium: m⃗\vec m parallel to B⃗\vec B (U=−mBU = -mB is minimum).
  2. B⃗\vec B is along +Z+Z, so the loop must lie in the XY plane with current anticlockwise seen from +Z+Z.
  3. In (c) the current goes a→b→c→da \to b \to c \to d, i.e. from +X+X towards +Y+Y: anticlockwise from above, so m⃗\vec m is along +Z+Z.
  4. In (a), (b) m⃗⊥B⃗\vec m \perp \vec B and in (d) m⃗\vec m is along −Z-Z (unstable).
  5. So the answer is (c).
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