What is the frequency for a beam of electrons orbiting in a field of 4.62 x 10^-3 T? Let the mass of an electrons m = 9.31 x 10^-31 kg, and the charge on an electron q = -1.60 x 10^-19 C.

Frequency:

Explanation:

The force experienced by an electron in a magnetic field is

where

is the electron charge

v is the speed of the electron

B is the strength of the magnetic field

Since the force is perpendicular to the direction of motion of the electron, the force acts as centripetal force, so we can write:

where

r is the radius of the orbit

is the mass of the electron

Re-arranging the equation,

(1)

We also know that in a circular motion, the speed is equal to the ratio between circumference of the orbit and orbital period (T):

Substituting into (1),

We also know that 1/T is equal to the frequency f, so

In this problem,

Therefore, the frequency of the electrons is

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