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

Answer: (A)

$\frac{\lambda}{\pi\epsilon_oR}$N/C

Answer 2

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:
$\vec{E_{net}} = \frac{\lambda}{\pi \varepsilon_0 R}\hat{i}N/C$