Question

Two infinitely long parallel wires having linear charge densities $\lambda_{1}$, and $\lambda_{2}$ respectively, are placed at a distance of $R$ metres. The force per unit length on either wire will be $\left(k=\frac{1}{4 \pi \varepsilon_{0}}\right)$

• A. $k \frac{2 \lambda_{1} \lambda_{2}}{R^{2}}$
• B. $k \frac{2 \lambda_{1} \lambda_{2}}{R}$
• C. $k \frac{\lambda_{1} \lambda_{2}}{R^{2}}$
• D. $k \frac{\lambda_{1} \lambda_{2}}{R}$

Answer 1

Answer: (B)

Force on $l$ length of the wire 2 is
$F_{2}=Q E_{1}=\left(\lambda_{2} l\right) \frac{2 k \lambda_{1}}{R}$
$\Rightarrow \frac{F_{2}}{l}=\frac{2 k \lambda_{1} \lambda_{2}}{R}$
Also, $\frac{F_{1}}{l}=\frac{F_{2}}{l}=\frac{F}{l}=\frac{2 k \lambda_{1} \lambda_{2}}{R}$