1. zero 2. 2λ/πε₀ R N/C 3. λ/πε₀ R N/C 4. λ/2πε₀ R N/C

Answer: 3. λ/πε₀ R N/C The field of an infinite line charge at distance r is E=λ/2πε₀r . Midway, r=R for each line. The + λ line pushes away from itself, and the -λ line pulls towards itself. Both fields point the same way, so they add. E=2×λ/2πε₀R=λ/πε₀R .

Topic: Electric field, field lines, field of point charge· Electrostatics

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

1. zero

2. \(\frac{2\lambda}{\pi\epsilon_0 R}\) N/C

3. \(\frac{\lambda}{\pi\epsilon_0 R}\) N/C

4. \(\frac{\lambda}{2\pi\epsilon_0 R}\) N/C

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Answer: 3. \(\frac{\lambda}{\pi\epsilon_0 R}\) N/C

The field of an infinite line charge at distance \(r\) is \(E=\dfrac{\lambda}{2\pi\epsilon_0r}\).

Midway, \(r=R\) for each line. The +\(\lambda\) line pushes away from itself, and the \(-\lambda\) line pulls towards itself. Both fields point the same way, so they add.

\(E=2\times\dfrac{\lambda}{2\pi\epsilon_0R}=\dfrac{\lambda}{\pi\epsilon_0R}\).

Doubtly AI · 30 Oct 2026 AI-generated · not yet verified Report

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Two parallel infinite line charges with linear charge densities +λ C/m and -λ 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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