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NEET 2009
Exam
NEET
Year
2009
Subject
Physics
Chapter
Electromagnetic Induction

NEET 2009 · Physics · Electromagnetic Induction

A conducting circular loop is placed in a uniform magnetic field...

A conducting circular loop is placed in a uniform magnetic field 0.04 T0.04 \mathrm{~T} with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at 2 mm/s2 \mathrm{~mm} / \mathrm{s}. The induced emf in the loop when the redius is 2 cm2 \mathrm{~cm} is :

Options

  1. A1.6πμv1.6 \pi \mu v
  2. B3.2πμv3.2 \pi \mu v
  3. C4.8πμv4.8 \pi \mu v
  4. D0.8πμv0.8 \pi \mu v

Correct answer

B. 3.2πμv3.2 \pi \mu v

Step-by-step solution

e=dϕdt=ddt(Bπr2)=2πrBdrdt=2×π×2×10−2×4×10−2×2×10−3=3.2×10−6πVol=3.2πμV\begin{aligned}\mathrm{e}& =\frac{\mathrm{d} \phi}{\mathrm{dt}}=\frac{\mathrm{d}}{\mathrm{dt}}\left(\mathrm{B} \pi \mathrm{r}^2\right) \\ & =2 \pi \mathrm{rB} \frac{\mathrm{dr}}{\mathrm{dt}}\\ & =2 \times \pi \times2 \times10^{-2} \times4 \times10^{-2} \times2 \times10^{-3} \\ & =3.2 \times10^{-6} \pi \mathrm{Vol}=3.2 \pi \mu \mathrm{V} \end{aligned}
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