An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet S having surface charge density . 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 if the elect

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Solution

Q.
An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet S having surface charge density $+ σ$ . 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 $σ$ if the electron strikes S at t = 1s is $α [\frac{m ε_{0}}{e}] \frac{C}{m^{2}},$ the value of $α$ is _________ . [2024]

Ans.
(8)

Initially the electron must move away from sheet

Electric field due to infinite plane sheet of charge,

$E = \frac{σ}{2 ε_{0}}$

Force experienced by the electron towards the sheet, $F = e E$

Hence, acceleration of the electron, $a = \frac{F}{m}$

$a = \frac{e E}{m} = \frac{e σ}{2 ε_{0} m}$

Using $s = u t + \frac{1}{2} a t^{2}$

$- 1 = 1 \times 1 + \frac{1}{2} (- \frac{e σ}{2 ε_{0} m}) 1^{2}$

$\frac{e σ}{4 ε_{0} m} = 2 \Rightarrow σ = 8 \frac{ε_{0} m}{e}$

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