An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet S having surface charge density +σ. The…

An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet S having surface charge density $\displaystyle +\sigma$. The electron at $\displaystyle t=0$ is at a distance of $\displaystyle 1$ m from $\displaystyle S$ and has a speed of $\displaystyle 1 \mathrm{~m} / \mathrm{s}$. The maximum value of $\displaystyle \sigma$ if the electron strikes $\displaystyle S$ at $\displaystyle t=1$ s is $\displaystyle \alpha\left[\frac{m \epsilon_0}{e}\right] \frac{C}{m^2}$, the value of $\displaystyle \alpha$ is $\displaystyle \_\_\_\_$.