Physics - Electrostatics Question with Solution | TestHub

Charge density or charge per unit length of long wire
According to Gauss theorem $$\begin{array}{l}\oint \vec{E}\cdot d\vec{S}=\frac{q}{{\epsilon }_0}\\ \begin{array}{r}\Rightarrow E\oint dS=\frac{q}{{\epsilon }_0}\text{ or }E\times 2\pi rl=\frac{q}{{\epsilon }_0}\\ \Rightarrow E=\frac{q}{2\pi {\epsilon }_{0}rl}=\frac{q/l}{2\pi {\epsilon }_{0}r}\\ =\frac{\lambda \times 2}{2\pi {\epsilon }_{0}r\times 2}=\frac{\lambda \times 2}{4\pi {\epsilon }_{0}r}\\ =9\times 10^9\times \frac{1}{3}\times 2\times \frac{1}{18\times 10^{-2}}\\ =0.33\times 10^{11}{\mathrm{NC}}^{-1}\end{array}\end{array}$$