Question

A $100$ eV electron is projected directly toward a large metal plate that has surface charge density of $-2.0\times {10}^{-6}C{m}^{-2}$. From what distance must the electron be projected, if it is to just fail to strike that plate?

• A. $0.44mm$
• B. $0.2mm$
• C. $1mm$
• D. $0.30mm$

Answer 1

The correct option is A $0.44mm$

Electric field due to large metal plate is $\sigma /{\epsilon }_0$
Since the electron has energy of $100$ eV, so it can just cross a potential difference of $100$ V only
$100=\frac{\sigma }{{\epsilon }_0}d$
$d=\frac{100\times {ϵ}_0}{\sigma }$
$d=\frac{100\times 8.85\times {10}^{-12}}{2\times {10}^{-6}}=0.44mm$