# Two parallel infinite line charges with linear charges 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 ?  Option 1) zero Option 2) $\frac{2 \lambda }{\pi \epsilon _0 R} N/C$ Option 3) $\frac{ \lambda }{\pi \epsilon _0 R} N/C$ Option 4) $\frac{\lambda }{2\pi \epsilon _0 R} N/C$

$\left | E_1 \right | = \left | E_2 \right | \\\\ E_1 =\frac{ \lambda}{2 \pi R\epsilon _0} \\\\ E_{ net} = E_ 1 + E_2 \\\\ E _{ net } =\frac{ \lambda}{ \pi R\epsilon _0}$

Option 1)

zero

Option 2)

$\frac{2 \lambda }{\pi \epsilon _0 R} N/C$

Option 3)

$\frac{ \lambda }{\pi \epsilon _0 R} N/C$

Option 4)

$\frac{\lambda }{2\pi \epsilon _0 R} N/C$

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