Electromagnetic Induction - Result Question 12

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12. A conducting circular loop is placed in a uniform magnetic field of $0.04 T$ 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

======= ####12. A conducting circular loop is placed in a uniform magnetic field of $0.04 T$ 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

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed:content/english/neet-pyq-chapterwise/physics/electromagnetic-induction/electromagnetic-induction—result-question-12.md (a) $4.8 \pi \mu V$

(b) $0.8 \pi \mu V$

(c) $1.6 \pi \mu V$

(d) $3.2 \pi \mu V$

[2009]

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Answer:

Correct Answer: 12. (d)

Solution:

  1. (d) Induced emf in the loop is given by $e=-B \cdot \frac{dA}{dt}$ where $A$ is the area of the loop.

$e=-B \cdot \frac{d}{dt}(\pi r^{2})=-B \pi 2 r \frac{dr}{dt}$

$r=2 cm=2 \times 10^{-2} m$

$dr=2 mm=2 \times 10^{-3} m$

$dt=1 s$

$e=-0.04 \times 3.14 \times 2 \times 2 \times 10^{-2} \times \frac{2 \times 10^{-3}}{1} V$

$=0.32 \pi \times 10^{-5} V$

$=3.2 \pi \times 10^{-6} V$

$=3.2 \pi \mu V$