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NEET PHYSICSMOVING CHARGES AND MAGNETISMEasy

Question

A 250 turn rectangular coil of length 2.1 cm2.1 \text{ cm} and width 1.25 cm1.25 \text{ cm} carries a current of 85 μA85 \, \mu\text{A} and subjected to the magnetic field of strength 0.85 T0.85 \text{ T}. Work done for rotating the coil by 180∘180^{\circ} against the torque is:

A

4.55 μJ4.55 \, \mu\text{J}

B

2.3 μJ2.3 \, \mu\text{J}

C

1.15 μJ1.15 \, \mu\text{J}

D

9.4 μJ9.4 \, \mu\text{J}

Step-by-Step Solution

  1. Magnetic Moment (mm): The rectangular coil acts as a magnetic dipole. Its magnetic moment is given by m=NIAm = NIA, where NN is the number of turns, II is the current, and AA is the area .
  • N=250N = 250
  • I=85 μA=85×10−6 AI = 85 \, \mu\text{A} = 85 \times 10^{-6} \text{ A}
  • A=length×width=(2.1×10−2 m)×(1.25×10−2 m)≈2.625×10−4 m2A = \text{length} \times \text{width} = (2.1 \times 10^{-2} \text{ m}) \times (1.25 \times 10^{-2} \text{ m}) \approx 2.625 \times 10^{-4} \text{ m}^2
  • m=250×(85×10−6)×(2.625×10−4)≈5.58×10−6 A m2m = 250 \times (85 \times 10^{-6}) \times (2.625 \times 10^{-4}) \approx 5.58 \times 10^{-6} \text{ A m}^2
  1. Work Done (WW): The work done in rotating a magnetic dipole from an initial angle θ1\theta_1 to a final angle θ2\theta_2 in a uniform magnetic field BB is given by the change in potential energy: W=ΔU=mB(cos⁡θ1−cos⁡θ2)W = \Delta U = mB(\cos\theta_1 - \cos\theta_2) .
  • "Rotating by 180∘180^{\circ} against the torque" typically implies rotating from the stable equilibrium position (θ1=0∘\theta_1 = 0^{\circ}) to the unstable equilibrium position (θ2=180∘\theta_2 = 180^{\circ}).
  • W=mB(cos⁡0∘−cos⁡180∘)=mB(1−(−1))=2mBW = mB(\cos 0^{\circ} - \cos 180^{\circ}) = mB(1 - (-1)) = 2mB
  1. Calculation:
  • W=2×(5.58×10−6)×0.85W = 2 \times (5.58 \times 10^{-6}) \times 0.85
  • W≈9.48×10−6 J=9.48 μJW \approx 9.48 \times 10^{-6} \text{ J} = 9.48 \, \mu\text{J}
  1. Conclusion: The value closest to the calculated work is 9.4 μJ9.4 \, \mu\text{J}.

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from MOVING CHARGES AND MAGNETISM. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

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