Two very long line charges of uniform charge densities $+\lambda$ and $-\lambda$ are placed along same line with the separation between the nearest ends being 2a , as shown in figure. The electric field intensity at point O is

The field at O due to small element dx is

$\begin{array}{l}dE=\frac{1}{4\pi {\epsilon }_0}\frac{\lambda dx}{x^2}\\ \text{ Hence, due to one wire, }\\ E_1={\int }_a^{\mathrm{\infty }} \frac{1}{4\pi {\epsilon }_0}\cdot \frac{\lambda dx}{x^2}\\ E_1=\frac{1}{4\pi {\epsilon }_0}\cdot \frac{\lambda }{a}\text{ towards left }\end{array}$

Similarly, Electric field at O due to other wire,

$\begin{array}{l}{E}_2=\frac{1}{4\pi {\epsilon }_0}\cdot \frac{\lambda }{a}\text{ toward left }\\ \therefore \text{ Net field at }\mathrm{O}\text{ is }E=2\times \frac{1}{4\pi {\epsilon }_0}\frac{\lambda }{a}=\frac{\lambda }{2\pi {\epsilon }_{0}a}\end{array}$