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Radar uses the principle of retarded time to calculate distances Since $x=ct$, $dx =c dt$! Define $dx=x_1-x_2$. If $x_1$ - radar location and $x_2$ -target location, $dt=dx/c=(x1-x2)/dt$ where $dt$ is the time required to travel to target! So round trip time $=2 dt$ which is recorded by electronic clocks. This is an example of retarded time not special ...


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Both equations (for the instantaneous field of a charge moving with constant velocity $v$) are correct. (Well, maybe the primes should be swapped in the second equation, so that the unprimed frame is that in which the charge is moving.) The first figure is not an accurate representation of the first equation: as Jan Lalinsky stated, the field lines should ...


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I won't try to defend Feynman's derivation, which seems strangely non-relativistic. (A similar argument is used by Schwartz in his "Principles of Electro-Dynamics".) However, I will defend the result (the Lienard-Wiechert potentials), and specifically claim that they are not in conflict with your discrete charge example, at least for the case of uniform ...


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I don't think the increase in potential due to the moving charge leading to an "overcounting" IS in disagreement with Feynman's result. In fact, the "overcounting" is what leads to the 1/(1-v/c) enhancement factor in the potential equation precisely accounts for the fact that the slow moving charge has some of it's charge contributions "overcounted" because ...



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