A circular loop of wire of radius $14 \mathrm{~cm}$ is placed in magnetic field directed perpendicular to…
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
$2.08 \mathrm{mV}$
$3.08 \mathrm{mV}$
$2.16 \mathrm{mV}$
$3.24 \mathrm{mV}$
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, $|e|=\frac{d \phi}{d t}$
$=\frac{d}{d t}(B A)$ $(\therefore \phi=B A)$
$\begin{aligned} & =\frac{A d B}{d t}=\pi r^2 \frac{d B}{d t} \\ & =\frac{22}{7} \times 0.14 \times 0.14 \times 0.05=0.00308 \\ & =3.08 \times 10^{-3} \mathrm{~V}=3.08 \mathrm{mV}\end{aligned}$