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Physics · Moving Charges and Magnetic Field

JEE Advanced 2024 — Paper 2 — Question 16

A thin stiff insulated metal wire is bent into a circular loop with its two ends extending tangentially from the same point of the loop. The wire loop has mass mm and radius rr and it is in a uniform vertical magnetic field B0B_{0}, as shown in the figure. Initially, it hangs vertically downwards, because of acceleration due to gravity gg, on two conducting supports at PP and QQ. When a current II is passed through the loop, the loop turns about the

line PQ by an angle θ\theta given by

Question figure
  1. Option A:

    tan⁡θ=πrlBo/(mg)\tan \theta=\pi \mathrm{rlBo} /(\mathrm{mg})

    Correct
  2. Option B:

    tan⁡θ=2πrlBo/(mg)\tan \theta=2 \pi \mathrm{rlBo} /(\mathrm{mg})

  3. Option C:

    tan⁡θ=πrlBo/(2mg)\tan \theta=\pi \mathrm{rlBo} /(2 \mathrm{mg})

  4. Option D:

    tan⁡θ=mg/(πrlBB0)\tan \theta=\mathrm{mg} /\left(\pi \mathrm{rlB} \mathrm{B}_{0}\right)

Answer: A

Step-by-step solution

At equilibrium

(mgsin⁡θ)r=μB0cos⁡θ(mgsin⁡θ)r=(1πr2)B0cos⁡θtan⁡θ=πr∣B0mg\begin{aligned} & (m g \sin \theta) r=\mu B_{0} \cos \theta \\& (m g \sin \theta) r=\left(1 \pi r^{2}\right) B_{0} \cos \theta \\& \tan \theta=\frac{\pi r \mid B_{0}}{m g} \end{aligned}

Answer key and solution verified before publishing.

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Exam
JEE Advanced 2024
Paper
Paper 2
Subject
Physics
Chapter
Moving Charges and Magnetic Field
Topic
Force and Torque on Wires and Loops, Magnetic Dipole Moment

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