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. 0 $N/C$
• B. $\frac{2\lambda }{\pi {\epsilon }_{0}R}N/C$
• C. $\frac{\lambda }{\pi {\epsilon }_{0}R}N/C$
• D. $\frac{\lambda }{2\pi {\epsilon }_{0}R}N/C$

Answer 1

The correct option is C $\frac{\lambda }{\pi {\epsilon }_{0}R}N/C$

$\overrightarrow{E}=\overrightarrow{E_1}+\overrightarrow{E_2}=\frac{\lambda }{2\pi {\epsilon }_{0}R}+\frac{\lambda }{2\pi {\epsilon }_{0}R}=\frac{\lambda }{\pi {\epsilon }_{0}R}N/C$