Of course not. The Coulomb law+Lorentz transformations only works if the particle moves with constant velocity. Of course, this is quite a lot easier to calculate for this special case, but otherwise you need the Lienard Wiechert potentials.

Leonard Wiechert Potential: Coulomb Law & Lorentz Transforms

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Leonard Wiechert Potential: Coulomb Law & Lorentz Transforms

Discussion

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