Question

An electron with a rest mass of 9.11×10^-31kg moves in a circular orbit of radius 1.4×10^-7m in a uniform magnetic field of 3.5×10^-1 Tesla, perpendicular to the speed of light with which electrons moves. Find the cyclotron frequency of the moving electron

Answer 1

According to the special theory of relativity, the angular cyclotron frequency is:

$$\omega = \dfrac{eB}{\gamma m_e}$$

where $e$ and $m_e$ are charge and mass of electron respectively, $B$ is the magnetic field and $\gamma = \dfrac{1}{\sqrt{1-\left ( \frac{v}{c} \right )^2}}$

If electon moves with the speed of light ( $v = c$ ), then, according to the previous expression, $\gamma \to \infty$.

Then $\omega =0$.

Answer. The cyclotron frequency is 0.