Question

An electron of 100eV is fired directly towards a metal plate having surface charge density $-2\times {10}^{-6}c{m}^{-2}$. Find distance from where the electron be projected so that it just fails to strike the plate.

• A. $0.22mm$
• B. $0.44mm$
• C. $0.66mm$
• D. $0.33mm$

Answer 1

Answer: (B)

$0.44mm$

Total energy of system will always remain constant
$K.E{.}_1+P.E{.}_1=K.E{.}_2+P.E{.}_2$ $P.E{.}_1=0$ $K.E{.}_2=0$
$K.E{.}_1=P.E{.}_2$ ; $K.E{.}_1=100eV$ ; $P.E{.}_2=\frac{ed\sigma }{{ϵ}_0}$
Distance of electron projection from the metal plate $\left(d\right)=\frac{K.E{.}_1{ϵ}_0}{\sigma }$
$d=\frac{100\times 8.85\times {10}^{-12}}{2\times {10}^{-6}}$
$d=0.44mm$