Q.The electric field at a point 2 cm from an infinite line charge of linear charge density $10^{-7}$ cm$^{-1}$ is :

The electric field at 2 cm from the infinite line charge works out to $9\times10^4\ N\,C^{-1}$.

The electric field at perpendicular distance $r$ from an infinite line charge of linear charge density $\lambda$ is

$E = \frac{\lambda}{2\pi\varepsilon_0 r} = \frac{2k\lambda}{r}, \qquad k = \frac{1}{4\pi\varepsilon_0} = 9\times10^9\ N\,m^2\,C^{-2}$

Note on units: the printed linear charge density "$10^{-7}\ cm^{-1}$" is dimensionally incomplete (a charge density needs charge/length); taking it as intended to read $\lambda = 10^{-7}\ C\,m^{-1}$ (a very standard textbook value) reproduces one of the given options exactly, confirming this reading. …