Crossed fields

The velocity of cathode-ray electrons (etc.) can be determined by passing the beam through crossed (orthogonal) electric and magnetic fields, adjusted so that the beam is undeflected. When no deflection takes place....

Bev = Ee

Canceling e and rearranging gives the speed v as the ratio....

v = E/B

= V/Bd

... V is the plate voltage, and d is the separation.

In a real case; in a cathode ray tube where the anode voltage is 3000iV and the field is 2x10-3 T, with a plate separation of 5 cm, (5x10-2 m), the electron velocity is given by....

v = 3x103 / (2x10-3 x (5x10-2)

= 3x10(3 + 3 +2 - 1)

= 3x107 m/s ...10% of the speed of light!