If there is a charge $Q$ kept firmly at rest and another charge $q$ is brought in the vicinity of $q$,it's obvious that $q$ will accelerate towards $Q$. Now,when we say that coulombs law is not accurate for moving charges and only accurate for static charges,do we mean that at position $r$ from $Q$,the force on $q$ won't be $\frac{CQq}{r^2}$? So does it mean at each instant as $r$ varies,the force $F(r)$ won't be instantaneously $\frac{CQq}{r^2}$. If not what else do we mean by when we say coulombs law is not valid for charges in motion?
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"Coulombs law is not accurate for moving charges", means that is not accurate if the force exerting the charge is accelerating. Q is at rest, so Coulomb's law does apply to the force on q. The force on Q is more complicated because q is accelerating. The electric field acting on Q is given by the Lienard-Wiechert electric field for an accelerating particle. The two forces are not equal and opposite, because there is electromagnetic momentum that has to be included for conservation of momentum.
Jerrold Franklin
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