What are the equations of motion for two charges where the two charges are the only sources for the EM field? (No background field)(adsbygoogle = window.adsbygoogle || []).push({});

What I'm looking for is given two particles of mass m_1 and m_2 with respective position vectors x_1 and x_2, what are f_1 and f_2 such that

[tex]m_1\frac{d^2x_1}{dt^2}=f_1(x_1,\dot{x}_1,x_2,\dot{x}_2)[/tex]

[tex]m_2\frac{d^2x_2}{dt^2}=f_2(x_1,\dot{x}_1,x_2,\dot{x}_2)[/tex]

?

Anyone know of a text which covers this? A Lagrangian or Hamiltonian for the same situation would do as well.

I'm looking for the relativistic case in which the propagation time is taken into effect. That is, [tex]x_2,\dot{x}_2[/tex] in the expression for [tex]f_1[/tex] should be taken at the "retarded time", and similarly for [tex]x_1,\dot{x}_1[/tex] in [tex]f_2[/tex].

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# Eqs of motion for 2-body problem in EM?

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