Larmor radiation is produced by an accelerating particle. The power of the radiation depends only on the magnitude of the charge and the acceleration of the particle. both of these increasing leads to a quadratic increase in the radiation.
When an electric charge accelerates, the change in the direction of its electric field can only travel at the speed of light, so an oscillation of the electric field travels outward from the original position of the charge. This oscillation releases radiation.
Since the disturbance will move radially outward a distance in the same time than the field will oscillate tangentially a distance So the ratio of the respective components of the electric field is
The intensity is given by the Poynting vector.
In order to calculate the power, integrate over all possible angles for Since
In the relativistic doppler effect, the radiation does not move out at a constant rate, but instead is subject to the Doppler effect. This is summarized by Liénard's generalization.
Show that Liénard's generalization reduces to the Larmor formula when
Two things happen as a result of