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Two positively charged infinitely long wires $(λ_{1} > λ_{2})$ are placed parallel to each other at $x = - a and x = + a$ and as in figure. Find the x- coordinate of a point at which electric field is zero.

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$\frac{λ_{2}}{λ_{1}} a$

$\frac{λ_{1}}{λ_{2}} a$

$(\frac{λ_{1} + λ_{2}}{λ_{1} - λ_{2}})$

$\frac{(λ_{1} - λ_{2})}{λ_{1} + λ_{2}} a$

answer is C.

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Detailed Solution

$Let coordinates of P are (x, 0)$

the distance of P from wire 1 = (a + x) and from wire 2 = (a - x)

$∵ E_{1} = E_{2} ∴ \frac{2 k λ_{1}}{(a + x)} = \frac{2 k λ_{2}}{(a - x)}$

$\Rightarrow λ_{1} (a - x) = λ_{2} (a + x) \Rightarrow λ_{1} a$

$- λ_{1} x = λ_{2} a + λ_{2} x$

$\Rightarrow (λ_{1} - λ_{2}) a = (λ_{1} + λ_{2}) x \Rightarrow x$

$= \frac{(λ_{1} - λ_{2}) a}{(λ_{1} + λ_{2})}$

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