Q152 / 160 · AP EAMCET 2022 (05 Jul Shift 1) · Physics

A circular loop of wire of radius $14 \mathrm{~cm}$ is placed in magnetic field directed perpendicular to the plane of the loop. If the field decreases at a steady rate of $0.05 \mathrm{Ts}^{-1}$ in some interval, then the magnitude of the emf induced in the loop is

  • A
    $2.08 \mathrm{mV}$
  • Correct answer
    B
    $3.08 \mathrm{mV}$
  • C
    $2.16 \mathrm{mV}$
  • D
    $3.24 \mathrm{mV}$

Solution

Given, Radius of circular loop of wire, $r=14 \mathrm{~cm}=0.14 \mathrm{~m}$ Rate of change of magnetic field with respect to time, $\frac{d B}{d t}=0.05 \mathrm{Ts}^{-1}$ According to Faraday law of electromagnetic induction, induced emf, $|e|=\frac{d \phi}{d t}$ $=\frac{d}{d t}(B A)$ $(\therefore \phi=B A)$ $\begin{aligned} & =\frac{A d B}{d t}=\pi r^2 \frac{d B}{d t} \\ & =\frac{22}{7} \times 0.14 \times 0.14 \times 0.05=0.00308 \\ & =3.08 \times 10^{-3} \mathrm{~V}=3.08 \mathrm{mV}\end{aligned}$

Hence, the correct answer is option: 'B'.

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