# is there explicit eqution between radiation electromagnetic wave and accelerator a charge that has curve moving path?

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?

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.
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.