Question

167. Two parallel infinite line charges with linear
charge densities + AC/m and -C/m are placed
at a distance of 2R in free space. What is the
electric field mid-way between the two line
charges?

options are in photo
​

Answer 1

electric field due to infinitely long straight wire perpendicular to its axis is given by, $E=\frac{\lambda}{2\pi\epsilon_0r}$

where, r is the separation between point of observation to straight wire.

now come to the question,

electric field due to wire of linear charge density is $+\lambda$ C/m at midway , E = $\frac{\lambda}{2\pi\epsilon_0R}$

similarly, electric field due to wire of linear charge density is $-\lambda$ C/m at midway , E' = $\frac{\lambda}{2\pi\epsilon_0R}$ along E

so, net electric field = E + E'

= $\frac{2\lambda}{2\pi\epsilon_0R}$

= $\frac{\lambda}{\pi\epsilon_0R}$

hence, option (3) should be correct.