# Two infinite 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 wire (1) will be:

$(A)\;\frac{K 2 \lambda_1 \lambda_2}{R} \\ (B)\;K \frac{2 \lambda_1^2}{R} \\ (C)\; Zero \\ (D)\;none$

Electric field due to wire (2)$= \large\frac{1}{4 \pi \in _0} \frac{2 \lambda_2}{R}$
Charge per unit length on wire $(1)=\lambda _2$
Force per unit length on wire $(1) =\lambda_1 \times E$
$\qquad= \lambda \times \large\frac{1}{4 \pi \in _0}\frac{2 \lambda_2}{R}$
$\qquad= \large\frac{K(2 \lambda _1 \lambda_2)}{R}$
Hence A is the correct answer.