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JEE Advanced 2020Paper 1
Exam
JEE Advanced
Year
2020
Paper
Paper 1
Subject
Physics
Chapter
Magnetic Effects of Current

JEE Advanced 2020 · Paper 1 · Physics · Magnetic Effects of Current

A circular coil of radius R and N turns has negligible resistance....

A circular coil of radius RR and NN turns has negligible resistance. As shown in the schematic figure, its two ends are connected to two wires and it is hanging by those wires with its plane being vertical. The wires are connected to a capacitor with charge QQ through a switch. The coil is in a horizontal uniform magnetic field Bo{B}_{o} parallel to the plane of the coil. When the switch is closed, the capacitor gets discharged through the coil in a very short time. By the time the capacitor is discharged fully, magnitude of the angular momentum gained by the coil will be (assume that the discharge time is so short that the coil has hardly rotated during this time)

A circular coil of radius R and N turns has negligible resistance. As shown in the schematic figure, its two ends are

Options

  1. Aπ2NQBoR2\dfrac{\pi}{2}NQ{B}_{o}{R}^{2}
  2. B\piNQBoR2\piNQ{B}_{o}{R}^{2}
  3. C2\piNQBoR22\piNQ{B}_{o}{R}^{2}
  4. D4\piNQBoR24\piNQ{B}_{o}{R}^{2}

Correct answer

B. \piNQBoR2\piNQ{B}_{o}{R}^{2}

Step-by-step solution

τ=M⋅B⋅sin⁡90°τ = M \cdot B \cdot \sin 90 °

τ=NIπR2B0τ = NI\pi{R}^{2}{B}_{0}

\DeltaL=∫0tτ⋅dt=N⋅πR2⋅B∫0tIdt\DeltaL = {∫}_{0}^{t}τ \cdot dt = N \cdot \pi{R}^{2} \cdot B{∫}_{0}^{t}Idt;

\DeltaL=N⋅πR2⋅BQ\DeltaL = N \cdot \pi{R}^{2} \cdot BQ.

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