First slide

Electric field

Question

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

Moderate

A

$k \frac{2 λ_{1} λ_{2}}{R^{2}}$
B

$k \frac{2 λ_{1} λ_{2}}{R}$
C

$k \frac{λ_{1} λ_{2}}{R^{2}}$
D

$k \frac{λ_{1} λ_{2}}{R}$

Solution

Force on l length of the wire 2 due to 1 is
$\begin{array}{l} F_{21} = Q_{2} E_{1} = (λ_{2} l) \frac{2 k λ_{1}}{R} \\ \Rightarrow \frac{F_{21}}{l} = \frac{2 k λ_{1} λ_{2}}{R} \\ Also \frac{F_{12}}{l} = \frac{F_{21}}{l} = \frac{F}{l} = \frac{2 k λ_{1} λ_{2}}{R} \end{array}$

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