The simplest model for calculating electric susceptibility of dielectrics,is a driven oscillation of an electric dipole with a resistive force proportional to its velocity.Its equation is like below:
[itex] m\ddot{x}+\gamma \dot{x}+kx=-eE [/itex]
We know that the restoring force is the same force binding the electron to its nucleus and the driving force is due to an external field.Now,for a bound charge,the only interpretation of the resistive force can be the radiation reaction due to the electron's radiation because of its acceleration.My question is this:
The radiation reaction is given(classically) by the Abraham–Lorentz formula which says its proportional to the time derivative of the acceleration.How can such a force be approximated by a term proportional to velocity???
Thanks
[itex] m\ddot{x}+\gamma \dot{x}+kx=-eE [/itex]
We know that the restoring force is the same force binding the electron to its nucleus and the driving force is due to an external field.Now,for a bound charge,the only interpretation of the resistive force can be the radiation reaction due to the electron's radiation because of its acceleration.My question is this:
The radiation reaction is given(classically) by the Abraham–Lorentz formula which says its proportional to the time derivative of the acceleration.How can such a force be approximated by a term proportional to velocity???
Thanks
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