Two infinite linear charges are placed parallel to each other at a distance $0.1m$ from each other. If the linear charge density on each is $5\mu C/m$ then the force (in $N/m$) acting on a unit length of each linear charge will be

Electric field due to an infinite line of charge at a distance $r$ is:
$E=\frac{\lambda }{2\pi {ϵ}_{0}r}$
Given $\lambda =5\times {10}^{-6}C/m,r=0.1m$
Electric field due to $1$,

$E=5\times \frac{{10}^{-6}}{2\pi {ϵ}_0\left(0.1\right)}$
Force per unit length on wire $2$
$F=E\times \text{charge on unit length of wire}$
$F=E\times 5\times {10}^{-6}$
$=\frac{5\times {10}^{-6}\times 5\times {10}^{-6}}{2\pi {ϵ}_0\left(0.1\right)}$
$=4.5N/m$
Hence, force per unit length of wire is
$4.5N/m$.