- #1
pellman
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What are the equations of motion for two charges where the two charges are the only sources for the EM field? (No background field)
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].
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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