Q129 / 197 · NEET 2009 (Mains) · Physics
A conducting circular loop is placed in a uniform magnetic field $0.04 \mathrm{~T}$ with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at $2 \mathrm{~mm} / \mathrm{s}$. The induced emf in the loop when the redius is $2 \mathrm{~cm}$ is :
- A$1.6 \pi \mu v$
- Correct answerB$3.2 \pi \mu v$
- C$4.8 \pi \mu v$
- D$0.8 \pi \mu v$
Solution
$$
\begin{aligned}
\mathrm{e} & =\frac{\mathrm{d} \phi}{\mathrm{dt}}=\frac{\mathrm{d}}{\mathrm{dt}}\left(\mathrm{B} \pi \mathrm{r}^2\right) \\
& =2 \pi \mathrm{rB} \frac{\mathrm{dr}}{\mathrm{dt}} \\
& =2 \times \pi \times 2 \times 10^{-2} \times 4 \times 10^{-2} \times 2 \times 10^{-3} \\
& =3.2 \times 10^{-6} \pi \mathrm{Vol}=3.2 \pi \mu \mathrm{V}
\end{aligned}
$$
Hence, the correct answer is option: 'B'.