The magnetic flux linked with the coil with time as $\Phi=3 \mathrm{t}^2+4 \mathrm{t}+7$. The magnitude of…
The magnetic flux linked with the coil with time as $\Phi=3 \mathrm{t}^2+4 \mathrm{t}+7$. The magnitude of the induced e.m.f at $t=2 \mathrm{~s}$ is
$16 \mathrm{~V}$
$29 \mathrm{~V}$
$11 \mathrm{~V}$
$19 \mathrm{~V}$
Solution
Given that
Total magnetic flux $\phi=3 t^2+4 t+7$
We know that,
The induced e.m.f
$\mathrm{e}=\left|\frac{-\mathrm{d} \phi}{\mathrm{dt}}\right|=\frac{\mathrm{d}\left(3 \mathrm{t}^2+4 \mathrm{t}+7\right.}{\mathrm{dt}}=6 \mathrm{t}+4$
Now, the induced e.m.f at $\mathrm{t}=2 \mathrm{sec}$
$e=6 \times 2+4=16$ volt
Hence, the magnitude of induced e.m.f is 16 volt