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Say you have a charged particle moving along some prescribed path. The electric field propagates outward at speed c, leading to a "retarded" time that you need to calculate in order to get the true electric field at any point.

My question: Of course, in this scenario, the curl of E will not be zero due to the changing magnetic field produced. But will there be an additional "curliness" due to including the time-delay of the field?

Thanks in advance(d time)! (har har)