Q. A 100 eV electron is fired directly towards a large metal plate having surface charge density $- 2 \times 10^{- 6\ }cm^{- 2}.$ The distance from where the electrons be projected so that it just fails to strike the plate is
A) 0.22mm
B) 0.44mm
C) 0.66mm
D) 0.88mm
Explanation
(b) Here, KE $= 100\ eV = 100 \times 1.6 \times 10^{- 19}J$
This is lost when electron moves through a distance (d) towards the negative plate.
$KE = work\ done = F \times s \Rightarrow qE \times s = e\left( \frac{\sigma}{\varepsilon_{0}} \right)d = \left( \frac{(KE)\varepsilon_{0}}{e\sigma} \right)$
$d = \frac{100 \times 1.6 \times 10^{- 19} \times 8.86 \times 10^{- 12}J}{1.6 \times 10^{- 19} \times 2 \times 10^{- 6}} = 4.43 \times 10^{- 4}m$
= 0.443 mm
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.