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 ?

Answer 1

Correct option is C. $$\dfrac{\lambda}{\pi \varepsilon_0 R} N/C$$
Electric field due to line charge (1)
$$\vec{E}_1 = \dfrac{\lambda}{2 \pi \varepsilon_0 R} \hat{i} N/C$$
Electric field due to line charge (2)
$$\vec{E}_2 = \dfrac{\lambda}{2 \pi \varepsilon_0 R} \hat{i} N/C$$
$$\vec{E}_{net} = \vec{E}_1 + \vec{E}_2$$
$$= \dfrac{\lambda}{2 \pi \varepsilon_0 R} \hat{i} + \dfrac{\lambda}{2 \pi \varepsilon_0 R} \hat{i}$$
$$= \dfrac{\lambda}{\pi \varepsilon_0 R} \hat{i} N/C$$