Abraham-lorentz-dirac Force

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Abraham-lorentz-dirac Force

DEFINITION

The expression for the Abraham-Lorentz-Dirac force was derived by Paul Dirac in 1938 and is given by
:

F^{\mbox{rad}}_\mu = rac{\mu_o q^2}{6 \pi m c}
\left(rac{d^2 p_\mu}{d 	au^2}+rac{p_\mu}{m^2 c^2} \,
\left(rac{d p_
u}{d 	au}rac{d p^
u}{d 	au}
ight)

ight)

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

:

rac{1}{\Delta t}\int_0^t P dt = rac{1}{\Delta t}\int_0^t 	extbf{F} \cdot 	extbf{v} dt

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

Non-Relativistic form

:

P = rac{\mu_o q^2 a^2}{6 \pi c}

Relativistic form

Liénard generalized Larmor's formula into a relativistic formulation in the Co-moving Frame .

:

P = rac{\mu_o q^2 a^2 \gamma^6}{6 \pi c}