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NEET PHYSICSMOVING CHARGES AND MAGNETISMMedium

Question

A rectangular coil of length 0.12 m0.12 \text{ m} and width 0.1 m0.1 \text{ m} having 5050 turns of wire is suspended vertically in a uniform magnetic field of strength 0.2 Wb/m20.2 \text{ Wb/m}^2. The coil carries a current of 2 A2 \text{ A}. If the plane of the coil is inclined at an angle of 30∘30^\circ with the direction of the field, the torque required to keep the coil in stable equilibrium will be:

A

0.15 N-m

B

0.20 N-m

C

0.24 N-m

D

0.12 N-m

Step-by-Step Solution

  1. Formula: The torque (τ\tau) exerted on a current-carrying coil in a magnetic field is given by τ=NIABsin⁡θ\tau = NIAB \sin \theta, where:
  • NN is the number of turns.
  • II is the current.
  • AA is the area of the coil.
  • BB is the magnetic field strength.
  • θ\theta is the angle between the normal to the coil's area and the magnetic field .
  1. Identify Angle: The problem states the plane of the coil makes an angle of 30∘30^\circ with the field. Therefore, the angle between the normal to the coil and the field is θ=90∘−30∘=60∘\theta = 90^\circ - 30^\circ = 60^\circ .
  2. Calculation:
  • Area A=length×width=0.12×0.1=0.012 m2A = \text{length} \times \text{width} = 0.12 \times 0.1 = 0.012 \text{ m}^2.
  • Substituting values: τ=50×2×0.012×0.2×sin⁡(60∘)\tau = 50 \times 2 \times 0.012 \times 0.2 \times \sin(60^\circ).
  • τ=0.24×32≈0.24×0.866\tau = 0.24 \times \frac{\sqrt{3}}{2} \approx 0.24 \times 0.866.
  • τ≈0.2078 N-m\tau \approx 0.2078 \text{ N-m}.
  1. Conclusion: The value closest to the calculated result is 0.20 N-m0.20 \text{ N-m}.

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.

PHYSICSMOVING CHARGES AND MAGNETISMrectangularlengthhavingsuspendedvertically

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