Show that the frequency of revolution, of a charged particle (in the X-Y plane), in a uniform magnetic field `vecB(=Bhatk)` is independent of its speed.
Which pratical machine makes use of this fact?
What is the frequency of the alternating electric field used in this machine?

Explanation

The radius of the cirucular path traced by charged particle in a perpendicular uniform magnetic field is `r=(mv)/(qB)`
Frequency of revolution,
`v_c=1/T=(v)/(2pir)=(vxxqB)/(2pixxmv)=(qB)/(2pim)`
which is independent of speed v.
A cyclotron makes use of this fact in which alternating electric field of frequency `v_c` is applied.