Question

Two parallel infinite line charges with linear
charge densities +λ C/m and –λ 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

$\huge{\mathfrak{HEYA\:MATE\:!!}}$

Answer...

please refer to the attachment

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Answer 2

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

2πϵ0 rλ

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+λ C/m at midway , E = \frac{\lambda}{2\pi\epsilon_0R}

2πϵ0 Rλ

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

2πϵ0Rλ

along E

so, net electric field = E + E'

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

2πϵ0R2λ

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

πϵ0Rλ