Question

An electron gun with its collector at a potential of 100 V fires out electrons in a spherical bulb containing hydrogen gas at low pressure ( 10⁻² mm of Hg). A magnetic field of 2.83 × 10⁻⁴ T curves the path of the electrons in a circular orbit of radius 12.0 cm. (The path can be viewed because the gas ions in the path focus the beam by attracting electrons, and emitting light by electron capture; this method is known as the ‘fine beam tube’ method. Determine e/m from the data.

Answer 1

Potential of an anode, V = 100 V
Magnetic field experienced by the electrons, B = 2.83 × 10⁻⁴ T
Radius of the circular orbit r = 12.0 cm = 12.0 × 10⁻² m
Mass of each electron = m
Charge on each electron = e
Velocity of each electron = v
The energy of each electron is equal to its kinetic energy, i.e.,

It is the magnetic field, due to its bending nature, that provides the centripetal force