A circular loop of radius $0.3cm$ lies parallel to a much bigger circular loop of radius $20cm.$ The centre of the small loop is on the axis of the bigger loop. The distance between their centres is $15cm.$ If a current of 2.0 A flows through the smaller loop, then the flux linked with bigger loop is

As field due to current loop 1 at an axial point $\therefore B_1=\frac{{\mu }_0{I}_1{R}^2}{2{(d^2+R^2)}^{3/2}}$

Flux linked with smaller loop 2 due to $B_1$ is ${\varphi }_2=B_1{A}_2=\frac{{\mu }_0{I}_1{R}^2}{2{(d^2+R^2)}^{3/2}}\pi r^2$

The coefficient of mutual inductance between the loops is $M=\frac{{\varphi }_{21}}{i_1}=\frac{{\mu }_0{R}^2\pi r^2}{2{(d^2+R^2)}^{3/2}}$

Flux linked with bigger loop 1 is ${\varphi }_1=M{I}_2=\frac{{\mu }_0{R}^2\pi r^2{I}_2}{2{(d^2+R^2)}^{3/2}}$

Substituting the given values, we get 

${\varphi }_1=\frac{4\pi \times {10}^{-7}\times {(20\times {10}^{-2})}^2\times \pi \times {(0.3\times {10}^{-2})}^2\times 2}{2{[{(15\times {10}^{-2})}^2+{(20\times {10}^{-2})}^2]}^{3/2}}$

${\varphi }_1=9.1\times {10}^{-11}weber$