Two concentric circular coils with radii 1cm and 1000cm and number...

Let the magnetic field of the $200$ turns be ${B}_{1}$. The formula of magnetic field is given by $B = \dfrac{{\mu}_{0}i}{2r}$

Let $r = 1000cm$. Thus,

${B}_{1} = \dfrac{n{\mu}_{0} \times I}{2 \times 10} = \dfrac{200{\mu}_{0}I}{2 \times 10}$

The flux through the coil of radius ${r}_{1} = 1cm$ is $ϕ = 10 \times \left(\overset{\to}{B} \cdot \overset{\to}{A}\right)$= 10 \times {B}_{1}\pi{r}^{2}1$</p><p>$⇒ ϕ = 10 \times \dfrac{200{\mu}_{0}I}{2 \times 10} \times \pi{\left(0 . 01\right)}^{2}$</p><p>$L = 10 \times \dfrac{200{\mu}_{0}}{2 \times 10} \times \pi{\left(0 . 01\right)}^{2} = 10 \times \dfrac{200\left(4\pi \times {10}^{- 7}\right)}{2 \times 10} \times \pi{\left(0 . 01\right)}^{2} = 4 \times {10}^{- 8}H