An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet $\mathrm{S}$ having surface charge density $+\sigma$. The electron at $t=0$ is at a distance of $1 \mathrm{~m}$ from $S$ and has a speed of $1 \mathrm{~m} / \mathrm{s}$. The maximum value of $\sigma$ if the electron strikes $S$ at $t=1 \mathrm{~s}$ is $\alpha\left[\frac{m \epsilon_0}{e}\right] \frac{C}{m^2}$, the value of $\alpha$ is ___________.
Answer (integer)
8
Solution
<p>$$\begin{aligned}
& \mathrm{u}=1 \mathrm{~m} / \mathrm{s} ; \mathrm{a}=-\frac{\sigma \mathrm{e}}{2 \varepsilon_0 \mathrm{~m}} \\
& \mathrm{t}=1 \mathrm{~s} \\
& \mathrm{~S}=-1 \mathrm{~m} \\
& \text { Using } \mathrm{S}=\mathrm{ut}+\frac{1}{2} \mathrm{at}^2 \\
& -1=1 \times 1-\frac{1}{2} \times \frac{\sigma \mathrm{e}}{2 \varepsilon_0 \mathrm{~m}} \times(1)^2 \\
& \therefore \sigma=8 \frac{\varepsilon_0 \mathrm{~m}}{\mathrm{e}} \\
& \therefore \alpha=8
\end{aligned}$$</p>
About this question
Subject: Physics · Chapter: Electrostatics · Topic: Coulomb's Law
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