Question

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

Answer 1

Let $\lambda$ be the linear charge density.
Given, distance r=2 cm=$2\times {10}^{-2}m$
Electric field E=$9\times {10}^{4}N/C$
Using the formula of electric field due to an infinite line charge.
Electric field due to infinite line charge, $E=\frac{\lambda }{2\pi {\epsilon }_{0}r}$
Dividing and multiplying by 2 to get $\frac{1}{4\pi {\epsilon }_0}$ because, we have the value of $\frac{1}{4\pi {\epsilon }_0}$,
$E=\frac{2}{2}\times \frac{\lambda }{2\pi {\epsilon }_{0}r}=\frac{2\lambda }{4\pi {\epsilon }_{0}r}$
Putting the values, we get
the linear charge density is ${10}^{-7}C/m$