Two concentric circular coils, C 1 and C 2 , are placed in the X Y plane. C 1 has 500 turns, and a radius of…

$I=\left(5t^2+2t+C\right)$

$\frac{di}{dt}=(10t+2)$

${\varphi }_{\text{small }}=BA=\left(\frac{{\mu }_{0}I{N}_2}{2R}\right)\left(\pi r^2\right)$

induced emf in small coil

$\mathrm{e}=\frac{\mathrm{d}\varphi }{\mathrm{dt}}=\left(\frac{{\mu }_0{\mathrm{N}}_2}{2\mathrm{r}}\right)\pi {\mathrm{r}}^2{\mathrm{N}}_1\frac{\mathrm{di}}{\mathrm{dt}}=\left(\frac{{\mu }_0{\mathrm{N}}_1{\mathrm{N}}_2\pi {\mathrm{r}}^2}{2\mathrm{R}}\right)(10\mathrm{t}-2)$

at $t=1$

$\mathrm{e}=\left(\frac{{\mu }_0{\mathrm{N}}_1{\mathrm{N}}_2\pi {\mathrm{r}}^2}{2\mathrm{R}}\right)8=4\frac{{\mu }_0{\mathrm{N}}_1{\mathrm{N}}_2\pi {\mathrm{r}}^2}{\mathrm{R}}=\frac{4\left(4\pi \right){10}^{-7}\times 200}{20}\times 500\times \frac{{10}^{-4}}{{10}^{-2}}\pi$

$=80\times {\pi }^2\times {10}^{-7}\times 10\times {10}^2\times {10}^{-2}=8\times {10}^{-4} \mathrm{volt}=0.8 \mathrm{mV}=\frac{4}{x}$

$x=5$