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: $\left(\frac{1}{4πε_0}=9×10^9\right)$
Answer & explanation
Correct answer: option 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
$E=\frac{2×10^{-9}}{2π×8.85×10^{-12}×3}$
$=\frac{2.0×10^{-9}}{1.667×10^{-10}}≃12.0N/C$