In the given arrangement find the electric field at C in the figure. Here the $U-$ shaped infinite wire uniformly charged with linear charge density $\lambda .$ 

 

Here we shall divide the arrangement into three parts as shown and then apply the principle of superposition. 

${\left(E_1\right)}_x=\frac{\lambda }{4\pi {\epsilon }_{0}a}(along+xaxis)$

Similarly ${\left(E_3\right)}_x=\frac{\lambda }{4\pi {\epsilon }_{0}a}$ (along $-x$ axis)

and ${\left(E_2\right)}_x=0$

 ${\left(E_2\right)}_y=\frac{\lambda }{2\pi {\epsilon }_{0}a}$ (along $+y$ axis)

So, ${\overrightarrow{E}}_C={\overrightarrow{E}}_1+{\overrightarrow{E}}_2+{\overrightarrow{E}}_3\Rightarrow {\overrightarrow{E}}_C=\overrightarrow{0}$