Question

Two long thin charged rods with charge density $\lambda$ each are placed parallel to each other at a distance d apart. The force per unit length exerted on one rod by the other will be $(wherek=\frac{1}{4\pi {\epsilon }_0})$

Answer 1

Electric field due to rod 1 at a distance 'd' is given by -

due to electric field from rod 1, rod 2 experiences an electric force.

So, force per unit length is given by $\left(f\right)$

$f=\frac{F}{L}=E\lambda$ ($\lambda$ : charge/ length)

From (1),

$f=\frac{2k{\lambda }^2}{d}$.