CBSE Class 12-science Answered

Since time taken by the ion to describe a semi—circular path                

Now, if T is the time period of oscillating electric field then

T = 2 t 

Therefore frequency of oscillating field is given by,  

 therefore,  

This frequency of oscillating electric field is commonly referred as the cyclotron frequency. It is also known as magnetic resonance frequency. From the expression, it is clear that the cyclotron frequency depends on magnetic field B as well as the charge and mass of ion beam to be accelerated. However, the cyclotron frequency is independent of the speed of the charged particle or radius of semi—circular path described by them