An infinite line of charge with uniform line charge density of 1 C/m is placed along the y-axis. A charge of 1C is placed on the X-axis at a distance of d=3m from the origin. At what distance r from the origin on the x-axis, the total electric field is zero (Assume 0 < r < d)

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1.75m

2 m

2.5 m

answer is B.

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Detailed Solution

For electric field zero at X

$E_{l i n e c h \arg e} = E_{p o int c h \arg e}$

$\frac{2 k λ}{x} = \frac{k q}{{(3 - x)}^{2}}$

$\Rightarrow 2 x^{2} - 13 x + 18 = 0$

$x_{1} = 4.5 (o r) x = 2 m$

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