Thank you for reporting, we will resolve it shortly
Q.
The magnetic flux through a loop of resistance $10 \,\Omega$ is given by $\phi = 5t^2 - 4t + 1$ Weber. How much current is induced in the loop after $0.2$ sec ?
The flux is given by $\phi=5 t^{2}-4\, t+1$.
The emf induced in the resistance would be equal to
$e=-\frac{d \phi}{d t}=10\, t-4$
Thus, the current induced in the loop is equal to
$i=\frac{e}{R}=-\left(\frac{10\, t-4}{10}\right)$
at $t=0.2\, s$, we have
$i=-\left(\frac{10 \times 0.2-4}{10}\right)$
$=\frac{2}{10}=0.2 \,A$