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Question: Answered & Verified by Expert
A copper disc of radius \( 0.1 \mathrm{~m} \) is rotated about its centre with \( 10 \) revolutions per second in a uniform magnetic field of \( 0.1 \) tesla with its plane perpendicular to the field. The emf induced across the radius of disc is
PhysicsElectromagnetic InductionJEE Main
Options:
  • A \( \frac{\pi}{10} \mathrm{~V} \)
  • B \( \frac{2 \pi}{10} \mathrm{~V} \)
  • C \( \pi \times 10^{-2} \mathrm{~V} \)
  • D \( 2 \pi \times 10^{-2} \mathrm{~V} \)
Solution:
2771 Upvotes Verified Answer
The correct answer is: \( \pi \times 10^{-2} \mathrm{~V} \)

Given,

The magnitude of the magnetic field, B=0.1 T

The radius of disk, R=0.1 m

Rotational speed, ω=2π×revolution per second=20π rad s-1

Consider a small radial segment dr at distance r from the center.

The emf generated in this small elemental rod will be,

dE=vBdr, here v is the velocity of rod.

We know at any radial distance r, linear velocity will be,

v=rω

dE=ωBrdr

Since all these differential rods are connected in series, so net emf will be,

dE=0RωBrdrE=ωBR22E=20π×0.1×0.122=π×10-2 V

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