Figure shows a conducting rectangular loop of electrical resistance R with its plane in xy plane. There exists a uniform magnetic field given by  $\overrightarrow{B}=B_0(10t^2-5t)\widehat{k}$ (where ‘$t$’ is the time in seconds) in the region. The current in the loop at

The flux through the loop is  $\varphi =\left[B_0(10t^2-5t)\right]\times 2=2B_0[10t^2-5t]$

The emf induced in the loop is   $e=\left|\frac{d\varphi }{dt}\right|$

                        $$\begin{gathered} =\left|2B_0[20t-5]\right| \\ \mathrm{At}t=0,e=10B_0 \\ \mathrm{And}i=\frac{10B_0}{R}\mathrm{from} A \mathrm{to} B \\ \mathrm{At}t=\frac{1}{4}\mathrm{s},i=\frac{2B_0}{R}[5-5]=0 \\ \mathrm{At}t=1\mathrm{s},i=\frac{2B_0}{R}[20-5]=\frac{30B_0}{R}\mathrm{from}B\mathrm{to}A \end{gathered}$$