Question

Question 4.12: In Exercise 4.11 obtain the frequency of revolution of the electron in its circular orbit. Does the answer depend on the speed of the electron? Explain.

Class 12 - Physics - Moving Charges And Magnetism Moving Charges And Magnetism Page-169

Answer 1

$\text{time period can be calculated by,}\\T=\frac{2\pi r}{v}\\\\\text{but we know,}\\r=\frac{mv}{qB}\\\\so,T=\frac{2\pi\frac{mv}{qB}}{v}=\frac{2\pi m}{qB}\\\\\because, frequency=\frac{1}{Time\: period}=\frac{qB}{2\pi m}\\\\so,\text{frequency},\nu=\frac{6.5\times10^{-4}\times1.6\times10^{-19}}{2\pi\times9.1\times10^{-31}}\\\\=18.2\times10^6Hz=18.2MHz$

here you can see that frequency of revolution of electron, f = qB/2πm , it is independent of speed of electron