Question

Some of the electrons which are emitted at low velocities from a hot wire (cathode) go through a small hole in a plate that is at a potential of 1000volts with respect to the cathode. What is the velocity of the electrons when they are passing through the hole? A second plate is parallel to the first and 20cm beyond it and is at a potential of -2000volts with respect to the cathode. Describe the motion of electrons in the region between the two plates.

Answer 1

$qV=mv^2/2\to v=\sqrt{2qV/m}=$

$=\sqrt{2\cdot1.6\cdot10^{-19}\cdot1000/(9.1\cdot 10^{-34})}=1.9\cdot10^7\ (m/s)$

In the region between the two plates: $F=ma\to qE=ma\to qV/d=ma\to$

$a=qV/(dm)=1.6\cdot10^{-19}\cdot(-3000)/(0.2\cdot9.1\cdot10^{-31})=-2.6\cdot10^{15}\ (m/s^2)$

In the region between the two plates the electron will move with acceleration

$a=-2.6\cdot10^{15}\ (m/s^2)$ .