Question

An electron is moving with a speed of 0.9c in a magnetic field of strength (10)6 G. Calculate the peak frequency at which the electron will radiate.

Answer 1

Answer on Question #45914, Physics, Astronomy

An electron is moving with a speed of 0.9c in a magnetic field of strength (10)6 G. Calculate the peak frequency at which the electron will radiate

Solution

We will use formula for maximum:

$\omega=\omega_{H}\left(\frac{E}{mc^{2}}\right)^{3}$

where

$\omega_{H}=\frac{|q|B}{mc}$

is cyclotron resonance frequency and $E=\frac{mc^{2}}{\sqrt{1-v^{2}/c^{2}}}$ is full energy of electron. Hence we have

$\omega=\frac{|q|B}{mc}\frac{1}{(1-v^{2}/c^{2})^{3/2}}=\frac{0.9\cdot 10^{6}}{9.1\cdot 10^{-31}}\frac{1}{0.19^{3/2}}\approx 1.2\cdot 10^{37}\,Hz$