Question

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 ?

• A. $\frac{\lambda}{\pi\epsilon_oR}$N/C
• B. $\frac{\lambda}{2\pi\epsilon_oR}$N/C
• C. zero
• D. $\frac{2\lambda}{\pi\epsilon_oR}$N/C

Answer 1

The Correct Option is A

The correct answer is A:\(\frac{\lambda}{\pi \varepsilon_0 R}\hat{i}N/C\)
The electric field produced by two line charges, denoted as \(E_1\) and \(E_2\), can be calculated individually using the formula:
\(\vec{E_1} = \frac{\lambda}{2\pi \varepsilon_0R}\hat{i}N/C\) 
\(\vec{E_2} = \frac{\lambda}{2\pi \varepsilon_0R}\hat{i}N/C\)
The net electric field, \(E_{net}\), due to both line charges is determined by adding \(E_1\) and \(E_2\):
\(\vec{E_{net}} = E_1 + E_2\)
This simplifies to:
\(\vec{E_{net}} = \frac{\lambda}{\pi \varepsilon_0 R}\hat{i}N/C\)