Two infinitely long thin straight wires having uniform linear charge densities $2\lambda$ and $3\lambda$ are arranged parallel to each other at a distance $R$ apart. The intensity at a point midway between them is

Given for first infinitely long straight wire, linear charge density $=2\lambda$.
For second infinitely long straight wire, linear charge density $3\mathrm{\lambda }$
The distance between to infinite parallel straight wires =$R$
Distance of point $p$ from first and second wire =$\frac{R}{2}$

Electric field due to a long wire having charge density $2\lambda$=$\frac{2\lambda }{2\pi {\epsilon }_{0}R}$
Electric field intensity at $P$ due to the first wire,$E_1=\frac{2\mathrm{\lambda }}{2{\mathrm{\pi \epsilon }}_0{\displaystyle \frac{R}{2}}}=\frac{2\mathrm{\lambda }}{{\mathrm{\pi \epsilon }}_{0}R} ...\left(1\right)$
Electric field intensity at $P$ due to the second wire, $E_2=\frac{\mathrm{\lambda }\text{'}}{2{\mathrm{\pi \epsilon }}_0{\displaystyle \frac{R}{2}}}=\frac{3\mathrm{\lambda }}{{\mathrm{\pi \epsilon }}_{0}R}$
∴ Electric field intensity at a middle point due to Both wires $E=E_2-E_1 +=\frac{3\mathrm{\lambda }}{{\mathrm{\pi \epsilon }}_{0}R}-\frac{2\mathrm{\lambda }}{{\mathrm{\pi \epsilon }}_{0}R}=\frac{\mathrm{\lambda }}{{\mathrm{\pi \epsilon }}_{0}R}$