Larmor formula

The Larmor formula is used to calculate the total power radiated by a non relativistic point charge as it accelerates. This is used in the branch of physics known as electrodynamics and is not to be confused with the Larmor precession from classical nuclear magnetic resonance. It was first derived by J. J. Larmor in 1897, in the context of the wave theory of light. P = − 2 3 q 2 m 2 c 3 d p μ d τ d p μ d τ . {displaystyle P=-{frac {2}{3}}{frac {q^{2}}{m^{2}c^{3}}}{frac {dp_{mu }}{d au }}{frac {dp^{mu }}{d au }}.} P = 2 q 2 γ 6 3 c [ ( β ˙ ) 2 − ( β × β ˙ ) 2 ] . {displaystyle P={frac {2q^{2}gamma ^{6}}{3c}}left.} The Larmor formula is used to calculate the total power radiated by a non relativistic point charge as it accelerates. This is used in the branch of physics known as electrodynamics and is not to be confused with the Larmor precession from classical nuclear magnetic resonance. It was first derived by J. J. Larmor in 1897, in the context of the wave theory of light. When any charged particle (such as an electron, a proton, or an ion) accelerates, it radiates away energy in the form of electromagnetic waves. For velocities that are small relative to the speed of light, the total power radiated is given by the Larmor formula: where a {displaystyle a} is the proper acceleration, q {displaystyle q} is the charge, and c {displaystyle c} is the speed of light. A relativistic generalization is given by the Liénard–Wiechert potentials. In either unit system, the power radiated by a single electron can be expressed in terms of the classical electron radius and electron mass as: We first need to find the form of the electric and magnetic fields. The fields can be written (for a fuller derivation see Liénard–Wiechert potential)