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 $1 \mathrm{~m}$ from $\mathrm{S}$ and has a speed of $1 \mathrm{~m} / \mathrm{s}$. The maximum value of $\sigma$ if the electron strikes $\mathrm{S}$ at $\mathrm{t}=1 \mathrm{~s}$ is $\alpha\left[\frac{\mathrm{m} \epsilon_{0}}{\mathrm{e}}\right] \frac{\mathrm{C}}{\mathrm{m}^{2}}$ the value of $\alpha$ is
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Answer: (8)
$\mathrm{u}=1 \mathrm{~m} / \mathrm{s} ; \mathrm{a}=-\frac{\sigma \mathrm{e}}{2 \varepsilon_{0} \mathrm{~m}}$
$\mathrm{t}=1 \mathrm{~s}$
$\mathrm{S}=-1 \mathrm{~m}$
Using $\mathrm{S}=\mathrm{ut}+\frac{1}{2} \mathrm{at}^{2}$
$-1=1 \times 1-\frac{1}{2} \times \frac{\sigma \mathrm{e}}{2 \varepsilon_{0} \mathrm{~m}} \times(1)^{2}$
$\therefore \sigma=8 \frac{\varepsilon_{0} \mathrm{~m}}{\mathrm{e}}$
$\therefore \alpha=8$
