In below figure, the square loop of wire has sides of length $2.0 cm$ . A magnetic field is directed out of the page; its magnitude is given by $B = 4.0t^{2}y$ , where $B$ is in tesla, $t$ in second, and $y$ in metre. Determine the emf around the square at $t = 2.5 s$ and give its direction.

The magnetic flux through the strip of area $\left(ldy\right)$ ,
                             $d\varphi = \left(4t^{2}y\right)ldy$

The total flux through the square

                             $\phi = {\int }_0^l\left(4t^{2}y\right)ldy$

                                $= 4t^{2}l{{\left|\frac{y^2}{2}\right|}^l}_0 = 2t^2{l}^3$

The Induced emf,   $\left|e\right| = \frac{d\varphi }{dt}=4t{l}^3$

At $t=2.5 s$             $$\begin{gathered} \left|e\right| = 4\times 2.5\times {\left(0.02\right)}^3 \\ = 8\times {10}^{-5} V \end{gathered}$$