Question

Electric field produced due to an infinitely long straight uniformly charged wire at a perpendicular distance of $2$cm is $3\times {10}^8$ NC${}^{-1}$. Then, linear charge density on the wire is (K = $9\times {10}^9$ SI unit)

• A. $3.33\frac{\mu C}{m}$
• B. $333\frac{\mu C}{m}$
• C. $666\frac{\mu C}{m}$
• D. $6.66\frac{\mu C}{m}$

Answer 1

The correct option is B $333\frac{\mu C}{m}$

$\begin{array}{c}E=\frac{2K\lambda }{r}\\ \Rightarrow \lambda =\frac{E.r}{2K}\\ =\frac{3\times {10}^8\times 2\times {10}^{-2}}{2\times 9\times {10}^9}\\ =\frac{1}{3}\times {10}^{-3}\\ =\frac{1000}{3}\frac{\mu c}{m}\\ =333\frac{\mu c}{m}\\ Hence,\\ optionBiscorrectanswer.\end{array}$