A wire carrying current I has the shape as shown in adjoining figure. Linear parts of the wire are very long and parallel to X -axis while semicircular portion of radius R is lying in Y-Z plane. Magnetic field at point O is

 

Given situation is shown in the figure. 

Parallel wires 1 and 3 are semi-infinite, so magnetic field at O due to them

${\overrightarrow{B}}_1={\overrightarrow{B}}_3=-\frac{{\mu }_{0}I}{4\pi R}\hat{k}$

Magnetic field at O due to semi-circular arc in Y Z -plane is given by

${\overrightarrow{B}}_2=-\frac{{\mu }_{0}I}{4R}\hat{i}$

$\text{ Net magnetic field at point }O\text{ is given by }$

$\overrightarrow{B}={\overrightarrow{B}}_1+{\overrightarrow{B}}_2+{\overrightarrow{B}}_3$

$\begin{array}{l}=-\frac{{\mu }_{0}I}{4\pi R}\hat{k}-\frac{{\mu }_{0}I}{4R}\hat{i}-\frac{{\mu }_{0}I}{4\pi R}\hat{k}\\ =-\frac{{\mu }_{0}I}{4\pi R}(\pi \hat{i}+2\hat{k})\end{array}$