A thin infinite line charge has linear charge density of $2.0×10^{-9}C/m$. The electric field intensity at a distance of 3 m from the line charge is: $\left(\frac{1}{4πε_0}=9×10^9\right)$

$12 NC^{-1}$

The correct answer is Option (1) → $12 NC^{-1}$

Electric field intensity (E) due to an infinite charge is calculated using the formula:

$E=\frac{λ}{2πε_0r}$

where,

$λ$, linear charge density = $2×10^{-9}C/m$ [given]

$ε_0$, Permittivity of free space = $8.85×10^{-12}F/m$

$r$, Perpendicular distance from line charge = 3 m

$E=\frac{2×10^{-9}}{2π×8.85×10^{-12}×3}$

$=\frac{2.0×10^{-9}}{1.667×10^{-10}}≃12.0N/C$