The magnetic field at the centre of circular loop in the circuit shown below is

The magnetic field due to the circular coil is $B=\frac{{\mu }_{0}i}{2r}\odot$

The magnetic field due to the straight conducting wire is $\mathrm{B}\text{'}=\frac{{\mathrm{\mu }}_0\mathrm{i}}{2\mathrm{\pi r}}\otimes$

As both of the magnetic fields are in opposite directions, the resultant field will be ${\mathrm{B}}_{\mathrm{r}}=\frac{{\mathrm{\mu }}_0}{2\mathrm{\pi }}\frac{\mathrm{i}}{\mathrm{r}}(\mathrm{\pi }-1)\odot$