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A large flat metal surface has uniform charge density $+ σ$ . An electron of mass m and charge e leaves the surface at an angle at point A with speed v , and return to it at point B. The maximum value of AB is ____

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$\frac{{vmϵ}_{0}}{σe}$

$\frac{v^{2} m \in_{0}}{eσ}$

$\frac{v^{2} e}{ϵ_{0} σm}$

$\frac{v^{2} σe}{ϵ_{0} m}$

answer is B.

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Detailed Solution

$Field near metal surface E = \frac{σ}{ϵ_{0}}$

$Force on electron = eE = \frac{eσ}{ϵ_{0}}$

$Acceleration of electron a = \frac{eσ}{m \in_{0}}$

It will act as projectile with max range $= \frac{u^{2}}{a} = \frac{u^{2}}{eσ} \times m \in_{0}$

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