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Q.

Two parallel infinite line charges with linear charge densities $+ λC / m and - λC / m$ 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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a

$\frac{λ}{2 π ε_{0} R} N / C$

b

$zero$

c

$\frac{2 λ}{π ε_{0} R} N / C$

d

$\frac{λ}{π ε_{0} R} N / C$

answer is D.

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Detailed Solution

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

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

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