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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$$^{-1}$$. The maximum value of $$\sigma$$, if the electron strikes $$S$$ at $$t = 1$$ s is $$\alpha \left[\frac{m\varepsilon_0}{e}\right] \frac{C}{m^2}$$. The value of $$\alpha$$ is _______.
Correct Answer: 8
Take away from sheet as positive.
Then electron starts moving away:
u=1
Displacement to reach sheet:
s=−1
Acceleration is toward sheet, hence negative:
$$a=-\frac{e\sigma}{2m\epsilon_0}$$
Using
$$s=ut+\frac{1}{2}at^2$$
with t=1,
$$-1=1+\frac{1}{2}a$$
$$\frac{a}{2}=-2$$
a=−4
Now
$$-\frac{e\sigma}{2m\epsilon_0}=-4$$
$$\frac{e\sigma}{2m\epsilon_0}=4$$
$$\sigma=8\frac{m\epsilon_0}{e}$$
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