Answer to Question #104750 in Astronomy | Astrophysics for rupal

Question #104750
An electron is moving with a speed of 0.97c in a magnetic field of strength 10^8 G. Calculate the peak frequency at which the electron will radiate.
1
Expert's answer
2020-03-09T10:53:53-0400

Interestingly, the peak frequency of radiation of an electron that makes circles in a magnetic field that is at 90-degree angle to the velocity vector does not depend on the speed and is sometimes called gyrofrequency or cyclotron frequency. For a non-relativistic particle that frequency is


"f=\\frac{qB}{2\\pi m}."

For a relativistic particle that value decreases:


"f_\\text{rel}=f\\sqrt{1-\\frac{v^2}{c^2}}=\\frac{qB}{2\\pi m}\\sqrt{1-\\frac{v^2}{c^2}}."

Calculations give us the values of


"f=2.8\\cdot10^{14}\\text{ Hz}"

if we omit the fact that the particle moves at such a high speed and


"f_\\text{rel}=6.8\\cdot10^{13}\\text{ Hz}"

if we calculate it according to the second equation.

Don't forget that G (Gauss) is not a SI unit! 10 000 Gauss is 1 T (Tesla), which is a SI unit.


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