Two concentric circular coils with radii 1 cm and 1000 cm , and number of turns 10 and 200 respectively are placed coaxially with centers coinciding . The mutual inductance of this arrangement will be _______x 10^-8 H. (Take, $\mathrm{\pi }$² = 10 )

Magnetic field at the centre of length
Coil ${\mathrm{B}}_1=\frac{{\mathrm{\mu }}_0{n}_1\mathrm{i}}{2{\mathrm{r}}_1} ......\left(1\right)$
Magnetic field through smaller coil
$$\begin{gathered} \begin{array}{l}\mathrm{\varphi }={\mathrm{B}}_1{\mathrm{Av}}_2\\ \mathrm{\varphi }={\mathrm{B}}_1\times {\mathrm{\pi r}}_2^2{\mathrm{N}}_2^2\\ \mathrm{Mi}={\mathrm{B}}_1{\mathrm{\pi r}}_2^2{\mathrm{N}}_2\end{array} \\ \begin{array}{l}\mathrm{Mi}=\frac{{\mathrm{\mu }}_0{\mathrm{N}}_1\mathrm{i}}{2{\mathrm{r}}_1}\times {\mathrm{\pi r}}_2^2{\mathrm{N}}_2\\ \mathrm{M}=\frac{{\mathrm{\mu }}_0{\mathrm{N}}_1{\mathrm{N}}_2{\mathrm{\pi r}}_2^2}{2{\mathrm{r}}_1}\\ \mathrm{M}=4\mathrm{\pi }\times {10}^{-7}\times {\mathrm{N}}_1{\mathrm{N}}_2\mathrm{\pi }\frac{{\mathrm{r}}_2^2}{2{\mathrm{r}}_1}=4{\mathrm{\pi }}^2\frac{{\mathrm{N}}_1{\mathrm{N}}_2{\mathrm{r}}_2^2}{2{\mathrm{r}}_1}\times {10}^{-2}\\ \mathrm{M}=\frac{4\times 10\times 200\times 10\times {\left({10}^{-2}\right)}^2\times {10}^{-7}}{2\times 1000\times {10}^{-2}}=4\times {10}^{-8}\end{array} \end{gathered}$$