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

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$K \frac{2 λ_{1} λ_{2}}{R^{2}}$

$k \frac{2 λ_{1} λ_{2}}{R}$

$k \frac{λ_{1} λ_{2}}{R^{2}}$

$k \frac{λ_{1} λ_{2}}{R}$

answer is B.

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Detailed Solution

Force on 'l' length of the wire 2 is

$F_{2} = {QE}_{1} = (λ_{2} l) \frac{2 {kλ}_{1}}{R} \Rightarrow \frac{F_{2}}{l} = \frac{2 {kλ}_{1} λ_{2}}{R} Also, \frac{F_{1}}{l} = \frac{F_{2}}{l} = \frac{F}{l} = \frac{2 {kλ}_{1} λ_{2}}{R}$

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