Two parallel infinite line charges with linear charge densities + m ^ - 1 and - m ^ - 1 are placed at a distance of 2R in free space. What is the electric field mid-way between the two-line charges?

Correct answer: C. λ π ϵ _ 0 R N C ^ - 1 E _ 1 = λ 2π ε _ 0 R E _ 2 = λ 2π ε _ 0 R E _ net = E _ 1 + E _ 2 = λ π ε _ 0 R N C ^ - 1

NEET 2019

Exam: NEET
Year: 2019
Subject: Physics
Chapter: Electrostatics

NEET 2019 · Physics · Electrostatics

Two parallel infinite line charges with linear charge densities + m...

Two parallel infinite line charges with linear charge densities

+ \lambdaC{m}^{- 1}

and

- \lambdaC{m}^{- 1}

are placed at a distance of

2R

in free space. What is the electric field mid-way between the two-line charges? Two parallel infinite line charges with linear charge densities + m ^ - 1 and - m ^ - 1 are placed at a distance of 2R

Two parallel infinite line charges with linear charge densities + m ^ - 1 and - m ^ - 1 are placed at a distance of 2R

Options

Azero
B $\dfrac{2\lambda}{\pi{ϵ}_{0}R}N{C}^{- 1}$
C $\dfrac{\lambda}{\pi{ϵ}_{0}R}N{C}^{- 1}$
D $\dfrac{\lambda}{2\pi{ϵ}_{0}R}N{C}^{- 1}$

Correct answer

C. $\dfrac{\lambda}{\pi{ϵ}_{0}R}N{C}^{- 1}$

Step-by-step solution

{E}_{1} = \dfrac{\lambda}{2\pi{ε}_{0}R}

{E}_{2} = \dfrac{\lambda}{2\pi{ε}_{0}R}

{E}_{net} = {E}_{1} + {E}_{2}

= \dfrac{\lambda}{\pi{ε}_{0}R}N{C}^{- 1}

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