An externally long wire is uniformly charged an electron is resolving about the wire and making  ${10}^8$

revolutions per second in an orbit of radius 2cm .  Linear charge density of wire in $nC/m$

is

$$\begin{gathered} The electric force "eE" will provide necessary centripetal force \\ \therefore eE=mr{w}^2 \\ \Rightarrow e\left(\frac{\lambda }{2\pi {\epsilon }_{0}r}\right)=mr\left(4{\pi }^2{n}^2\right) \\ \Rightarrow \lambda =\frac{\left(4\pi {\epsilon }_o\right)2m{r}^2{n}^2{\pi }^2}{e} \\ =\frac{2\times 9\times {10}^{-31}\times (4\times {10}^{-4})\times {10}^{16}\times 10}{9\times {10}^9\times 1.6\times {10}^{-19}}\left({\pi }^2\approx 10\right) \\ =50\times {10}^{-9}C/m \\ =50nC/m \end{gathered}$$