# Abraham-Lorentz-Dirac force

﻿
Abraham-Lorentz-Dirac force

In electrodynamics, the Abraham-Lorentz-Dirac force is the force experienced by a relativistic charged particle due to an electromagnetic field. It is a modification of the Abraham-Lorentz force, which describes the same effect, but does not account for the effects of special relativity.

Definition

The expression for the Abraham-Lorentz-Dirac force was derived by Paul Dirac in 1938 [Dirac, P.A.M. (1938) Classical theory of radiating electrons. Proc. Roy. Soc. of London. A929:0148-0169. [http://www.jstor.org/view/00804630/ap000639/00a00000/0 JSTOR] ] and is given by :$F^\left\{mbox\left\{rad_mu = frac\left\{mu_o q^2\right\}\left\{6 pi m c\right\}left\left(frac\left\{d^2 p_mu\right\}\left\{d au^2\right\}+frac\left\{p_mu\right\}\left\{m^2 c^2\right\} ,left\left(frac\left\{d p_ u\right\}\left\{d au\right\}frac\left\{d p^ u\right\}\left\{d au\right\} ight\right) ight\right)$

One can show this to be a valid force by manipulating the time average equation for power.

:$frac\left\{1\right\}\left\{Delta t\right\}int_0^t P dt = frac\left\{1\right\}\left\{Delta t\right\}int_0^t extbf\left\{F\right\} cdot extbf\left\{v\right\} dt$

Larmor's Formula describes the power of a system in a non-relativistic interpretation.

There are pathological solutions using the Abraham–Lorentz-Dirac equation that anticipate a change in the external force and according to which the particle accelerates "in advance" of the application of a force, so-called "preacceleration" solutions! One resolution of this problem was discussed by Yaghjiancite book
author=Arthur D. Yaghjian
title=Relativistic dynamics of a charged sphere: Updating the Lorentz-Abraham model
publisher= Springer
location=Berlin
year=1992
page=Chapter 8
isbn=3540978879
] , and a fuller discussion of its resolution is made by Rohrlich [http://wwwphy.princeton.edu/~kirkmcd/examples/EM/rohrlich_ajp_65_1051_97.pdf F. Rohrlich: "The dynamics of a charged sphere and the electron" Am J Phys 65 (11) p. 1051 (1997)] ] , and Medina. [ [http://arxiv.org/abs/physics/0508031v3 Rodrigo Medina "Radiation reaction of a classical quasi-rigid extended particle" J. Phys. A: Math. Gen. A39 (2006) 3801-3816] ]

Non-Relativistic form

:$P = frac\left\{mu_o q^2 a^2\right\}\left\{6 pi c\right\}$

Relativistic form

Liénard generalized Larmor's formula into a relativistic formulation in the co-moving frame.

:$P = frac\left\{mu_o q^2 a^2 gamma^6\right\}\left\{6 pi c\right\}$

References

ee also

*Abraham-Lorentz force

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• Abraham-Lorentz force — In the physics of electromagnetism, the Abraham Lorentz force is the recoil force on an accelerating charged particle caused by the particle emitting electromagnetic radiation. It is also called the radiation reaction force. The formula for the… …   Wikipedia

• Paul Dirac — Paul Adrien Maurice Dirac Born Paul Adrien Maurice Dirac 8 August 1902(1902 08 08) Bristol, England …   Wikipedia

• Electron — For other uses, see Electron (disambiguation). Electron Experiments with a Crookes tube first demonstrated the particle nature of electrons. In this illustration, the profile of the cross shaped target is projected against the tube face at right… …   Wikipedia

• Larmor formula — In physics, in the area of electrodynamics, the Larmor formula is used to calculate the total power radiated by a nonrelativistic point charge as it accelerates. It was first derived by J. J. Larmor in 1897, in the context of the wave theory of… …   Wikipedia

• Synchrotron radiation — This article concerns the physical phenomenon of synchrotron radiation. For details on the production of this radiation and applications in laboratories, see Synchrotron light source. The electromagnetic radiation emitted when charged particles… …   Wikipedia

• Électron — Traduction à relire Electron → …   Wikipédia en Français

• Renormalization — Quantum field theory (Feynman diagram) …   Wikipedia

• Quantum field theory — In quantum field theory (QFT) the forces between particles are mediated by other particles. For instance, the electromagnetic force between two electrons is caused by an exchange of photons. But quantum field theory applies to all fundamental… …   Wikipedia

• Inhomogeneous electromagnetic wave equation — Localized time varying charge and current densities can act as sources of electromagnetic waves in a vacuum. Maxwell s equations can be written in the form of a inhomogeneous electromagnetic wave equation (or often nonhomogeneous electromagnetic… …   Wikipedia

• Electrón — Saltar a navegación, búsqueda Electrón e− Representación en corte transversal de los orbitales s, p y d del átomo de hidrógeno para los tres primeros números cuánticos. La intensidad del color indica la densidad de …   Wikipedia Español