Determine the charge to mass ratio (e/m) of an electron.

Consider a narrow beam of electrons moving with a constant velocity V is projected at right  angle to a known uniform magnetic field B directed into plane of paper then magnetic force on an electron will be

F = -e (V x B) —-> 1 

The direction of force will be perpendicular to both V and B. This force is used to change the direction of velocity. But magnitude of velocity remains the same. The magnitude of magnetic force is given by

F = eVB Sin theta —–> 2

As V is perpendicular to B. Then , theta = 90 as Sin 90 = 1 Then

F = eVB —-> 3

As V and B both do not change due to which magnitude of F remains constant. This magnetic force F = BeV provides a centripetal force = mv^2/r to the electron to move along a circle of radius “r”. Then

BeV = mv^2/r

e/m = V/Br —–>4

If V and r are known, e/m of the electron is determined.