An electron is moving under the influence of the electric field of...

The value of the electric field due to the uniformly charged plane sheet is given by

$E = \dfrac{\sigma}{2{ε}_{0}} . . . \left(1\right)$

Thus, the force on the electron is given by

$\begin{cases}F & = & - eE \\ & = & - \dfrac{\sigmae}{2{ε}_{0}} . . . \left(2\right)\end{cases}$

So, the acceleration of the electron is given by

$a = - \dfrac{\sigmae}{2{ε}_{0}m}$

Given, $u = 1m{s}^{- 1}$, $t = 1s$ and $S = - 1m$

Using the equation of motion, it can be written that

$- 1 = 1 \times 1 - \dfrac{1}{2} \times \dfrac{\sigmae}{2{ε}_{0}m} \times ( 1{)}^{2} ⇒ \sigma = 8\dfrac{{ε}_{0}m}{e}C{m}^{- 2}$

$∴ \alpha = 8$.