Question

An infinite line charge produce a field of $7.182\times {10}^{8}N/C$ at a distance of 2 cm. The linear charge density is:

• A. $7.27\times {10}^{-4}C/m$
• B. $7.98\times {10}^{-4}C/m$
• C. $7.11\times {10}^{-4}C/m$
• D. $7.04\times {10}^{-4}C/m$

Answer 1

The correct option is B $7.98\times {10}^{-4}C/m$

Electric field intensity due to infinite line charge is:
$E=\frac{\lambda }{2\pi {\epsilon }_{0}r}$
Given, $E=7.182\times {10}^{8}N/C$
$r=2cm=2\times {10}^{-2}m$
$\lambda =?$
$\Rightarrow \lambda =2\pi {\epsilon }_{0}rE=\frac{2\times 2\pi {\epsilon }_{0}rE}{2}$
$=\frac{1\times 2\times {10}^{-2}\times 7.182\times {10}^8}{2\times 9\times {10}^9}$
$=7.98\times {10}^{-4}C/m$