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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 $(k = \frac{1}{4 π ε_{0}})$

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$K \frac{{2λ}_{1} λ_{2}}{R^{2}}$

$K \frac{{2λ}_{1} λ_{2}}{R}$

$K \frac{λ_{1} λ_{2}}{R}$

$K \frac{λ_{1} λ_{2}}{R^{2}}$

answer is B.

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Detailed Solution

Force on l length of the wire 2 is $F_{2} {=QE}_{1} = (λ_{2} l) \frac{{2kλ}_{1}}{R}$
$\Rightarrow \frac{F_{2}}{l} = \frac{{2kλ}_{1} λ_{2}}{R}$
Also $\frac{F_{1}}{l} = \frac{F_{2}}{l} = \frac{F}{l} = \frac{{2kλ}_{1} λ_{2}}{R}$
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