Two wire loops PQRSP formed by joining two semicircular wires of radii -R₁, and R₂, carries a current as shown in fig. The magnitude of the magnetic 

induction at the centre C is

Magnetic inductions at C due to straight portions PQ and RS will be equal to zero because they are on the same line of centre. Magnetic fields due to semi-circular portions will be just in opposite direction as current through them are opposite.
$\begin{array}{l}\therefore {\mathrm{B}}_2=\frac{{\mathrm{\mu }}_0\mathrm{i}(1/2)}{2{\mathrm{R}}_2}\text{ and }{\mathrm{B}}_1=\frac{{\mathrm{\mu }}_0\mathrm{i}(1/2)}{2{\mathrm{R}}_1}\\ \therefore \mathrm{B}={\mathrm{B}}_1-{\mathrm{B}}_2=\frac{{\mathrm{\mu }}_0\mathrm{i}}{4}\left[\frac{1}{{\mathrm{R}}_1}-\frac{1}{{\mathrm{R}}_2}\right]\end{array}$