Question

An infinite line charge produces a field of $9\times {10}^4$N/C at a distance of 2 cm. Calculate the linear charge density.

Answer 1

$\text{Step 1: Electric field due to infinite line charge}$

Electric field due to infinite line charge is given by:

$E=\frac{\lambda }{2\pi {\in }_{0}d}$

$\Rightarrow \lambda =2\pi {\in }_{0}Ed$ $....\left(1\right)$

Where $\lambda$ is the linear charge density and $d$ is the perpendicular distance of point from the infinite line charge.

$\text{Step 2: Substituting the values}$

$\because \frac{1}{4\pi {\in }_0}=9\times {10}^{9}N{m}^2{C}^{-2}$

$\Rightarrow 2\pi {\in }_0=\frac{1}{18\times {10}^{9}N{m}^2{C}^{-2}}$

From Eq $\left(1\right):$ $\lambda =\frac{1\times 9\times {10}^{4}N{C}^{-1}\times 0.02m}{18\times {10}^{9}N{m}^2{C}^{-2}}={10}^{-7}C{m}^{-1}$