Question

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

• A. $\frac{vm{ϵ}_0}{\sigma e}$
• B. $\frac{v^{2}m{ϵ}_0}{\sigma e}$
• C. $\frac{v^{2}e}{{ϵ}_0\sigma m}$
• D. $\frac{v^2\sigma e}{{ϵ}_{0}m}$

Answer 1

Answer: (B)

$\frac{v^{2}m{ϵ}_0}{\sigma e}$

Field near metal surface $E=\frac{\sigma }{{ϵ}_o}$

Force on electron $=eE=\frac{e\sigma }{{ϵ}_o}$

Acceleration of electron $=a=\frac{e\sigma }{m{ϵ}_o}$

Max Range $=\frac{v^2}{a}=\frac{v^{2}m{ϵ}_o}{e\sigma }$