# Motion of Electron Beam in Electric and Magnetic Field

Published date: 25 Jun 2021 ## The motion of Electron Beam in Electric and Magnetic Field

The conceptual notes on Motion of Electron Beam in Electric and Magnetic Field are explained below: Let us consider a beam of an electron is projected in between two ‘p’ and ‘Q’ as shown in the figure. Let ‘V’ and ‘d’ be potential differences and distances between two plates.

Now, Considering horizontal motion at the x-axis of an electron when electrons are parallel to the plates.

Then,  ### The motion of Electron Beam in a magnetic field Fig: Circular motion in the uniform magnetic field

Let us consider an electron beam moving horizontally with speed ‘v’ which enters a uniform magnetic field of magnitude B acting perpendicular to the direction of motion shown in the figure.

from the figure,

a force acting on it,

F=BeV …………………………………..(I)

If the magnetic field is uniform the force is constant in magnitude and beam travels in a circle of radius ‘r’ provides a centripetal force.

If the magnetic field is uniform the force is constant in magnitude and beam travels in a circle of radius ‘r’ provides a centripetal force.  In other words, it is the radius of the circular motion of a charged particle in the presence of a uniform magnetic field. If the velocity is not perpendicular to the magnetic field, then v is the component of the velocity perpendicular to the field. The component of the velocity parallel to the field is unaffected since the magnetic force is zero for motion parallel to the field. We’ll explore the consequences of this case in a later section on the spiral motion.