Q169 / 170 · Manipal (MET) 2019 · Physics
A physicist works in a laboratory where the magnetic field is 2 T . She wears a necklace enclosing area $0.01 \mathrm{~m}^2$ in such a way that the plane of the necklace is normal to the field and is having a resistance, $R=0.01 \Omega$. Because of power failure, the field decays to 1 T in time $10^{-3} \mathrm{~s}$. Then what is the total heat produced in her necklace?
- Correct answerA10 J
- B20 J
- C30 J
- D40 J
Solution
Induced emf
$\begin{aligned}
E & =-\frac{\Delta \phi}{\Delta t}=-A \frac{\Delta B}{\Delta t} \\
& =-0.01 \times \frac{1-2}{10^{-3}}=\frac{0.01}{10^{-3}} \\
& =10 \mathrm{~V}
\end{aligned}$
$\therefore$ Heat produced, $H=\frac{E^2}{R} t$
$\begin{aligned}
& =\frac{(10)^2}{0.01} \times 10^{-3} \\
& =\frac{100 \times 10^{-3}}{0.01} \\
& =10 \mathrm{~J}
\end{aligned}$
Hence, the correct answer is option: 'A'.