Question 720: Electrostats & Capacitance

Question

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 ___________.

Accepted Answer

$$\begin{aligned}
& \mathrm{u}=1 \mathrm{~m} / \mathrm{s} ; \mathrm{a}=-\frac{\sigma \mathrm{e}}{2 \varepsilon_0 \mathrm{~m}} \
& \mathrm{t}=1 \mathrm{~s} \
& \mathrm{~S}=-1 \mathrm{~m} \
& 	ext { Using } \mathrm{S}=\mathrm{ut}+\frac{1}{2} \mathrm{at}^2 \
& -1=1 	imes 1-\frac{1}{2} 	imes \frac{\sigma \mathrm{e}}{2 \varepsilon_0 \mathrm{~m}} 	imes(1)^2 \
& 	herefore \sigma=8 \frac{\varepsilon_0 \mathrm{~m}}{\mathrm{e}} \
& 	herefore \alpha=8
\end{aligned}$$

Electrostats & Capacitance

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