Two parallel infinite line charges with linear charge densities $+ 10 C / m and - 10 C / m$ are placed at a distance of 20 m in free space. What is the electric field mid-way between the two line charges?

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$36 \times 10^{10} N / C$

$zero$

$3.6 \times 10^{9} N / C$

$3.6 \times 10^{10} N / C$

answer is D.

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Detailed Solution

$Electric field due to an infinite line charge, E = \frac{λ}{2 {πε}_{0} r} Net electric field at mid-point O,$

${\vec{E}}_{0} = {\vec{E}}_{1} + {\vec{E}}_{2} As, E_{1} = E_{2} = \frac{λ}{2 {πε}_{0} R} ∴ E_{0} = 2 E_{1} = \frac{λ}{{πε}_{0} R} = \frac{9 \times 10^{9} \times 4 \times 10}{10} = 3.6 \times 10^{10} {NC}^{- 1}$

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