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The magnetic flux in a closed circuit of resistance $10 \Omega$ varies with time as $\phi=\left(2 \mathrm{t}-4 \mathrm{t}^{2}+1\right)$. The current in the loop will change its direction after a time of
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$0.25 \mathrm{sec}$
$\begin{aligned} \mathrm{e} &=-\frac{\mathrm{d} \phi}{\mathrm{dt}}=[-2+8 \mathrm{t}+0] \\ & \Rightarrow 8 \mathrm{t}=2 \Rightarrow \mathrm{t}=\frac{1}{4} \mathrm{sec}=0.25 \mathrm{sec} \end{aligned}$
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