Two concentric circular coils, C_1 and C_2, are placed in the XY plane. C_1 has 500 turns, and a radius of 1 cm. C_2 has 200 turns and radius of 20…

Two concentric circular coils, $\displaystyle \mathrm{C}_1$ and $\displaystyle \mathrm{C}_2$, are placed in the XY plane. $\displaystyle \mathrm{C}_1$ has $\displaystyle 500$ turns, and a radius of $\displaystyle 1$ cm. $\displaystyle \mathrm{C}_2$ has $\displaystyle 200$ turns and radius of $\displaystyle 20 \mathrm{~cm} . \mathrm{C}_2$ carries a time dependent current $\displaystyle \mathrm{I}(\mathrm{t})=\left(5 \mathrm{t}^2-2 \mathrm{t}+3\right) \mathrm{A}$ where $\displaystyle t$ is in $\displaystyle s$. The emf induced in $\displaystyle C_1$ $\displaystyle ($ in mV$\displaystyle )$, at the instant $\displaystyle \mathrm{t}=1 \mathrm{~s}$ is $\displaystyle \frac{4}{x}$. The value of $\displaystyle x$ is \_\_\_\_.