Q. An infinite line charge produce a field of $7.182 \times 10^{8}NC^{- 1}$at a distance of 2 cm. The linear charge density is
A) $7.27 \times 10^{- 4}Cm^{- 1}$
B) $7.98 \times 10^{- 4}Cm^{- 1}$
C) $7.11 \times 10^{- 4}Cm^{- 1}$
D) $7.04 \times 10^{- 4}Cm^{- 1}$
Explanation
(b) Electric field intensity due to infinite line charge is
$E = \frac{\lambda}{2\pi\varepsilon_{0}r}$
Given,
$E = 7.182 \times 10^{8}NC^{- 1}$
$r = 2cm = 2 \times 10^{- 2}m$
$\lambda = ?\ $
$\Longrightarrow \ \ \ \ \lambda = 2\pi\varepsilon_{0}rE = \frac{2 \times 2\pi\varepsilon_{0}rE}{2}$
$= \frac{1 \times 2 \times 10^{- 2} \times 7.182 \times 10^{8}}{2 \times 9 \times 10^{9}}$
$= 7.98 \times 10^{- 4}Cm^{- 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.