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A rod of length l with uniform charge per unit length $λ$ is placed at a distance d from origin along the x-axis. A similar rod is placed at the same distance along Y-axis. Determine the magnitude of net electric field intensity at the origin.

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2 $- \frac{\sqrt{2} λ l}{4 π ϵ_{0} d (d + l)}$

$\frac{\sqrt{2} λ l}{4 π ϵ_{0} d (d + l)}$

$- \frac{\sqrt{2} λ l}{4 π ϵ_{0} d (d + l)}$

answer is C.

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Detailed Solution

$\begin{array}{l} d E_{x} = \frac{K d Q}{x^{2}} = \frac{K λ d x}{x^{2}} \\ \Rightarrow E_{x} = \int_{d}^{d + l} \frac{K λ d x}{x^{2}} = \frac{K λ l}{d (d + l)} \end{array}$

Similarly, $E_{y} = \frac{Kλl}{d (d + I)}$

$∴ E = \sqrt{E_{x}^{2} + E_{y}^{2}} = \frac{\sqrt{2} λ l}{4 π ε_{0} d (d + l)}$

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