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Two coils have a mutual inductance of $0.004 \mathrm{H}$. The current changes in the first coil according to equation $\mathrm{I}=\mathrm{I}_0 \sin \omega \mathrm{t}$, where $\mathrm{I}_0=10 \mathrm{~A}$ and $\omega=50 \pi \mathrm{rad} \mathrm{s}^{-1}$. The maximum value of e.m.f. in the second coil in volt is
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$2 \pi$
$\begin{aligned} & \left|e_s\right|=M \frac{d_p}{d t} \\ & \left|e_s\right|=M \frac{d}{d t} I_0 \sin \omega t \\ & \left|e_s\right|=M I_0 \omega \cos \omega t \\ \therefore \quad & \left|e_s\right|_{\max }=M I_0 \omega=0.004 \times 10 \times 50 \pi \\ \therefore \quad & \left|e_s\right|_{\max }=(2 \pi) \text { volt }\end{aligned}$
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