$=\left(\frac{\pi \eta^{2}}{\pi a^{2}}\right) \times I,$ where $I$ is total current

$\therefore$ Magnetic field at $P_{1}$ is

$B_{1}=\frac{\mu_{0} \times \text { current enclosed }}{\text { Path }}$

$ \Rightarrow {B_1} = \frac{{{\mu _0} \times \left( {\frac{{\pi r_1^2}}{{\pi {a^2}}}} \right) \times I}}{{2\pi {r_1}}} = \frac{{{\mu _0} \times I\eta }}{{2\pi {a^2}}}{\text{ }}$

${\text{Now, magnetic field at point }}{P_2},$

${B_2} = \frac{{{\mu _0}}}{{2\pi }} \cdot \frac{I}{{(2a)}} = \frac{{{\mu _0}I}}{{4\pi a}}$

Required ratio $=\frac{B_{1}}{B_{2}}=\frac{\mu_{0} I r_{1}}{2 \pi a^{2}} \times \frac{4 \pi a}{\mu_{0} I}$

$=\frac{2 r_{1}}{a}=\frac{2 \times \frac{a}{2}}{a}=1$