A circle loop of radius 0.3 cm 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
$\therefore {\mathrm{B}}_1=\frac{{\mathrm{\mu }}_0{\mathrm{I}}_1{\mathrm{R}}^2}{2{\left({\mathrm{d}}^2+{\mathrm{R}}^2\right)}^{3/2}}$
Flux linked with smaller loop 2 due to B₁ is 
${\mathrm{\varphi }}_{21}={\mathrm{B}}_1{\mathrm{A}}_2=\frac{{\mathrm{\mu }}_0{\mathrm{I}}_1{\mathrm{R}}^2}{2{\left({\mathrm{d}}^2+{\mathrm{R}}^2\right)}^{3/2}}{\mathrm{\pi r}}^2$
The coefficient of mutual inductance between the loops is 
$\mathrm{M}=\frac{{\mathrm{\varphi }}_{21}}{{\mathrm{I}}_1}=\frac{{\mathrm{\mu }}_0{\mathrm{R}}^2}{2{\left({\mathrm{d}}^2+{\mathrm{R}}^2\right)}^{3/2}}{\mathrm{\pi r}}^2$
Flux linked with bigger loop 1 is 
${\mathrm{\varphi }}_{12}={\mathrm{MI}}_2=\frac{{\mathrm{\mu }}_0{\mathrm{R}}^2{\mathrm{\pi r}}^2{\mathrm{I}}_2}{2{\left({\mathrm{d}}^2+{\mathrm{R}}^2\right)}^{3/2}}$
Substituting the given values, we get
$\begin{array}{l}{\mathrm{\varphi }}_1=\frac{4\mathrm{\pi }\times {10}^{-7}\times {\left(20\times {10}^{-2}\right)}^2\times \mathrm{\pi }\times {\left(0.3\times {10}^{-2}\right)}^2\times 2}{2{\left[{\left(15\times {10}^{-2}\right)}^2+{\left(20\times {10}^{-2}\right)}^2\right]}^{3/2}}\\ {\mathrm{\varphi }}_1=9.1\times {10}^{-11}\text{ Weber }\end{array}$