JEE MAIN - Physics (2023 - 11th April Morning Shift - No. 22)
The magnetic field B crossing normally a square metallic plate of area $$4 \mathrm{~m}^{2}$$ is changing with time as shown in figure. The magnitude of induced emf in the plate during $$\mathrm{t}=2 s$$ to $$\mathrm{t}=4 s$$, is __________ $$\mathrm{mV}$$.
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Answer
8
Explanation
$$
\begin{aligned}
& \mathrm{m}=\tan \theta=\frac{10}{5}=2 \\\\
& \mathrm{~B}=\mathrm{mt} \\\\
& \mathrm{B}=2 \mathrm{t}
\end{aligned}
$$
$$ \begin{aligned} & \varepsilon=\left|\frac{\mathrm{d} \phi}{\mathrm{dt}}\right|=\frac{\mathrm{d}(\mathrm{BA})}{\mathrm{dt}}=\frac{\mathrm{AdB}}{\mathrm{dt}} \\\\ & \varepsilon=\frac{4 \mathrm{~d}(2 \mathrm{t})}{\mathrm{dt}}=4 \times 2=8 \mathrm{mV} \end{aligned} $$
$$ \begin{aligned} & \varepsilon=\left|\frac{\mathrm{d} \phi}{\mathrm{dt}}\right|=\frac{\mathrm{d}(\mathrm{BA})}{\mathrm{dt}}=\frac{\mathrm{AdB}}{\mathrm{dt}} \\\\ & \varepsilon=\frac{4 \mathrm{~d}(2 \mathrm{t})}{\mathrm{dt}}=4 \times 2=8 \mathrm{mV} \end{aligned} $$
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