[math-fun] Lienard–Wiechert potentials
The wikipedia article I cited also gives the equations for the fields. Take beta=0 in those equations (stationary observer) and you will find the fields arise from retarded not instantaneous positions of source charges, and this also happens if the source charges move at constant velocities.. Perhaps the source of ES's confusion is he is thinking of situation where all charges (source and observer) move at equal velocity, i.e. all are stationary in my ref frame.
On 7/19/15, Warren D Smith <warren.wds@gmail.com> wrote:
The wikipedia article I cited also gives the equations for the fields. Take beta=0 in those equations (stationary observer) and you will find the fields arise from retarded not instantaneous positions of source charges, and this also happens if the source charges move at constant velocities..
--no; I apologize. Wikipedia suddenly switched notation so the beta_s they had before, became plain beta. I thought plain beta was obviously about the observer while beta_s was about the source, so beta=0 was appropriate for stationary observer. But apparently not. So wikipedia claims the potential arises from retarded source location, but the field includes 2 terms, one based on retarded and one based on instantaneous (if constant source velocities) location; and the second term is 0 if the sources never accelerate... so E.Salamin was right. Interesting... my old E&M textbook did not discuss these subtleties at all, just doing potentials only.
I'm at rest in my rest frame. A charge is moving at constant velocity. Its position at my time t is (vt,0,0) in my frame. At my time t at my location (x,y,z) the electric field points along (x-vt,y,z), i.e. towards the instantaneous location of the charge, not its retarded location. This is stated in Landau & Lifschitz, "Classical Theory of Fields", 4th ed., eq. (38.6). -- Gene From: Warren D Smith <warren.wds@gmail.com> To: math-fun@mailman.xmission.com Sent: Sunday, July 19, 2015 11:35 AM Subject: [math-fun] Lienard–Wiechert potentials The wikipedia article I cited also gives the equations for the fields. Take beta=0 in those equations (stationary observer) and you will find the fields arise from retarded not instantaneous positions of source charges, and this also happens if the source charges move at constant velocities.. Perhaps the source of ES's confusion is he is thinking of situation where all charges (source and observer) move at equal velocity, i.e. all are stationary in my ref frame.
participants (2)
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Eugene Salamin -
Warren D Smith