Electrostatics Question 11
Question 11 - 2024 (29 Jan Shift 1)
An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet $S$ having surface charge density $+\sigma$. The electron at $t=0$ is at a distance of $1 m$ from $S$ and has a speed of $1 m / s$. The maximum value of $\sigma$ if the electron strikes $S$ at $t=1 s$ is $\alpha\left[\frac{m \epsilon _0}{e}\right] \frac{C}{m^{2}}$ the value of $\alpha$ is
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Answer: (8)
$u=1 m / s ; a=-\frac{\sigma e}{2 \varepsilon _0 m}$
$t=1 s$
$S=-1 m$
Using $S=ut+\frac{1}{2} at^{2}$
$-1=1 \times 1-\frac{1}{2} \times \frac{\sigma e}{2 \varepsilon _0 m} \times(1)^{2}$
$\therefore \sigma=8 \frac{\varepsilon _0 m}{e}$
$\therefore \alpha=8$
