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 (where $k=\frac{1}{4\pi {ϵ}_0}$)

• A. $\frac{k2\lambda }{d}$
• B. $\frac{k2{\lambda }^2}{d}$
• C. $\frac{k2\lambda }{d^2}$
• D. $\frac{k2{\lambda }^2}{d^2}$

Answer 1

The correct option is B $\frac{k2{\lambda }^2}{d}$

Electric field due to wire (2) $=\frac{1}{4\pi {ϵ}_0}\frac{2{\lambda }_2}{R}$
Charge per unit length on wire (1) $={\lambda }_2$
Force per unit length on wire (1) $={\lambda }_1\times E$
$=\lambda \times \frac{1}{4\pi {ϵ}_0}\frac{2{\lambda }_2}{R}$
$=\frac{K\left(2{\lambda }_1{\lambda }_2\right)}{R}$
Here ${\lambda }_1={\lambda }_2=\lambda$ and R = d
$\therefore F=\frac{K.2{\lambda }^2}{d}$
Option (2) is correct.