Electric field due to rod \((1)\) at distance \(d=\frac{\lambda}{2 \pi \varepsilon_0 d}\)

So, force per unit length \(\frac{F}{l}=\frac{q E}{l}=\lambda\left[\frac{\lambda}{2 \pi \varepsilon_0 d}\right]\)

\(=\frac{k 2 \lambda^2}{d}\)