Two parallel infinite line charges with linear charge densities + λ… | NEET 2019

Q101NEET 2019Medium

Electric Flux & Gauss's Law

Two parallel infinite line charges with linear charge densities + $\lambda$ C/m and - $\lambda$ C/m are placed at a distance of 2R in free space. What is the electric field mid-way between the two line charges?

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Answer: (c)

Field of an infinite line charge: $E = \frac{\lambda}{2\pi\varepsilon_0 r}$ ; here $r = R$ from each line.
At the midpoint the field of $+\lambda$ points away from it and the field of $-\lambda$ points towards it, so both point the same way (towards $-\lambda$ ) and add.
$E = 2 \times \frac{\lambda}{2\pi\varepsilon_0 R} = \frac{\lambda}{\pi\varepsilon_0 R}$
So the answer is (c) $\frac{\lambda}{\pi\varepsilon_0 R}$ N/C.

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