Question

Two infinitely long parallel wires having linear charge densities ${\lambda }_1$ and ${\lambda }_2$ respectively are placed at a distance R. The force per unit length on either wire will be :-

• A. $\frac{2k{\lambda }_1{\lambda }_2}{R^2}$
• B. $\frac{2k{\lambda }_1{\lambda }_2}{R}$
• C. $\frac{k{\lambda }_1{\lambda }_2}{R^2}$
• D. $\frac{k{\lambda }_1{\lambda }_2}{R}$

Answer 1

The correct option is B $\frac{2k{\lambda }_1{\lambda }_2}{R}$

$\text{Force on}l\text{length of the wire}2\text{is}$

$F_2=Q{E}_1=\left({\lambda }_{2}l\right)\frac{2k{\lambda }_1}{R}$

$\Rightarrow \frac{F_2}{l}=\frac{2k{\lambda }_1{\lambda }_2}{R}$

$\text{Also}\frac{F_1}{l}=\frac{F_2}{l}=\frac{F}{l}=\frac{2k{\lambda }_1{\lambda }_2}{R}$

Therefore, option b is correct.