i had a basis question i read a rule in electromagnetic when a charge is moving and it has accelerator it will emit electromagnetic wave. now i want to find a explicit equation that describe this rule ? for example when a charge single electron has accelerator $$\frac{1m}{s^{2}}$$ it will emit wavelength .7 um and.......

where i can find this formula ? is there such formula in electromagnetic?

thanks for reply


1 Answer 1


There are two types of radiation that are emitted from an accelerating charged particle: synchrotron radiation (if the acceleration causes circular motion) and bremsstrahlung radiation (if the acceleration is from speeding up or slowing down).

The total power emitted from synchrotron radiation is given by: $$P = \frac{q^2\gamma^4a^2}{6\pi\epsilon_0c^3}.$$ where $q$ is the electric charge of the particle, $c$ is the speed of light, $\gamma$ is the Lorentz factor, $\epsilon_0$ is the permittivity of the vacuum, and $a$ is the particle's centripetal acceleration. This equation describes the total power emitted from the particle since the radiation has a very broad spectrum. Photon count as a function of photon energy

Bremsstrahlung radiation gives of power $$P = \frac{q^2\gamma^6a^2}{6\pi\epsilon_0c^3}.$$ Note that the only difference from synchrotron radiation is a factor of $\gamma^2$. Below is a plot (the blue line) of photon energy versus the total power of those photons. Bremsstrahlung photon power versus photon energy


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