Question

Electrons emitted with negligible speed from an electron gun are accelerated through a potential difference V

along the X-axis. These electrons emerge from a narrow-hole into a uniform magnetic field B directed along this axis. However, some of the electrons emerging from the hole make slightly divergent angles as shown in figure (34-E18). Show that these paraxial electrons are refocused on the X-axis at a distance

Answer 1

Given magnetic field = B, Pd = V, mass of electron = m, Charge =q,

Let electric field be ‘E’ ∴ E = V/R,

Force Experienced = eE

Time taken by particle to cover the arc = 2πm/qB = 2πm/eB

Since the acceleration is along ‘Y’ axis.

Hence it travels along x axis in uniform velocity