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. $\frac{\lambda }{\pi {ϵ}_{o}R}$N/C
• B. $\frac{\lambda }{2\pi {ϵ}_{o}R}$N/C
• C. zero
• D. $\frac{2\lambda }{\pi {ϵ}_{o}R}$N/C

Answer 1

Answer: (A)

Electric field due to line charge (1)
$\overrightarrow{E_1}=\frac{\lambda }{2\pi {\epsilon }_{0}R}\hat{i}N/C$
Electric field due to line charge (2)
$\overrightarrow{E_2}=\frac{\lambda }{2\pi {\epsilon }_{0}R}\hat{i}N/C$
${\vec{E}}_{net}={\vec{E}}_1+\overrightarrow{E_2}$
$=\frac{\lambda }{2\pi {\epsilon }_{0}R}\hat{i}+\frac{\lambda }{2\pi {\epsilon }_{0}R}\hat{i}$
$=\frac{\lambda }{\pi {\epsilon }_{0}R}\hat{i}N/C$