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)

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