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Electromagnetic Induction question

2009 · Q142
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Electromagnetic Induction question

2009 · Q142

NEETPhysicsElectromagnetic InductionMCQ+4 / −1
A conducting circular loop is placed in a uniform magnetic field 0.04 T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at 2 mm/s. The induced emf in the loop when the radius is 2 cm is
  1. A
    4.8π\piπμ\muμV
  2. B
    0.8π\piπμ\muμV
  3. C
    1.6π\piπμ\muμV
  4. D
    3.2π\piπμ\muμV
View written solutionFree

Correct answer: D

Constant rate at which radius of the loop shrinks

drdt=2×10−3{{dr} \over {dt}} = 2 \times {10^{-3}}dtdr​=2×10−3 m s-1

Magnetic flux linked with the loop is

ϕ\phi ϕ = BAcosϕ\phi ϕ = B(π\pi πr2)cos0o = Bπ\pi πr2

The magnitude of the induced emf is

|e| = dϕdt=ddt(Bπr2)=Bπ2rdrdt{{d\phi } \over {dt}} = {d \over {dt}}\left( {B\pi {r^2}} \right) = B\pi 2r{{dr} \over {dt}}dtdϕ​=dtd​(Bπr2)=Bπ2rdtdr​

= 0.04 ×\times× π\pi π ×\times× 2 ×\times× 2 ×\times× 10-2 ×\times× 2 ×\times× 10-3

= 3.2π\pi π ×\times× 10-6 V

= 3.2πμV\pi \mu VπμV

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