A conducting circular loop is placed in X - Y plane in presence of magnetic field B → = 3 t 3 j ^ + 3…

By the faraday's law in electromagnetic induction

${\epsilon }_{ind}=-\frac{d\varphi }{dt}=-\frac{d\left(\overrightarrow{B}·\overrightarrow{A}\right)}{dt}$

Magnetic flux is $\varphi =\overrightarrow{\mathrm{B}}·\overrightarrow{\mathrm{A}}$$=\left(3t^3\hat{j}+3t^2\hat{k}\right)·\left(\pi {\left(1\right)}^2\hat{k}\right)$

So, $\varphi =3t^2\pi$

Now, induced emf is ${\epsilon }_{ind}=\left|\frac{d\varphi }{dt}\right|=6t\pi$

At $t=2, {\epsilon }_{ind}=6\left(2\right)\pi =12\pi \mathrm{V}$.

Thus, the value of $n=12$.