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JEE Main 2021 (26 Aug, Shift 2) · Current Loop as a Magnetic Dipole

Current Loop as a Magnetic Dipole question from JEE Main 2021 (26 Aug, Shift 2)

Q58JEE Main 2021 · 26 AUG · SHIFT 2Medium

Current Loop as a Magnetic Dipole

A coil in the shape of an equilateral triangle of side 10 cm lies in a vertical plane between the pole pieces of permanent magnet producing a horizontal magnetic field 20 mT. The torque acting on the coil when a current of 0.2 A is passed through it and its plane becomes parallel to the magnetic field will be x×\sqrt{x} \times 10−-5 Nm. The value of x is .................

Numerical answer type. Work it out, then open the answer.

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Answer: 3

  1. Plane parallel to B⃗\vec B means m⃗⊥B⃗\vec m \perp \vec B, so τ=IAB\tau = IAB.
  2. A=34(0.1)2=34×10−2 m2A = \frac{\sqrt3}{4}(0.1)^2 = \frac{\sqrt3}{4}\times10^{-2}\text{ m}^2
  3. τ=0.2×34×10−2×0.02=3×10−5 N m\tau = 0.2 \times \frac{\sqrt3}{4}\times10^{-2} \times 0.02 = \sqrt3\times10^{-5}\text{ N m}
  4. So x=3x = 3.
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