The magnetic flux linked to a circular coil of radius $R$ is: $\phi=2 t^3+4 t^2+2 t+5 \mathrm{~Wb}$ The magnitude of induced emf in the coil at $t=5 \mathrm{~s}$ is:

Question

Aicharya · Accepted Answer

Given:
$\phi=2 t^3+4 t^2+2 t+5,$
& $t=5 \mathrm{~s}$
By Faraday's law of EMI, we have,
$\mathrm{emf}=-\frac{d \phi}{d t}$
(where, the symbols have their usual meanings)
$\begin{aligned}
E=\left|\frac{d \phi}{d t}\right| & =\left|\frac{d}{d t}\left(2 t^3+4 t^2+2 t+5\right)\right| \\
& =6 t^2+8 t+2
\end{aligned}$
$\begin{aligned}
\text{At } t & =5 s \\
E & =6(5)^2+8(5)+2 \\
& =192 \mathrm{~V}
\end{aligned}$

The magnetic flux linked to a circular coil of radius $R$ is: $\phi=2 t^3+4 t^2+2 t+5 \mathrm{~Wb}$ The…

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