According to special relativity the information can transmit only at the speed of light. However,the electric field at a point due to a charge moving at constant velocity changes its direction the moment charge moves and is always radial from the instantaneous position of charge.How?
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$\begingroup$ Where did you get your information from in the first place? That is what expression are you saying indicates this conclusion. $\endgroup$– TriatticusCommented Mar 19 at 21:49
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2 Answers
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The electric field isn't "always radial from the instantaneous position of [the] charge". That's only true if the charge isn't accelerating. For accelerating charges, the "updates" in the field direction do indeed travel away at the speed of light. See this applet for a visualization of this.
answered Mar 19 at 18:56
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$\begingroup$ That's why i wrote 'constant velocity' in the question $\endgroup$ Commented Mar 20 at 4:22
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$\begingroup$ @Mr.Wayne: I think I got confused by your assertion that the field "changes its direction the moment [the] charge moves", which implies a non-constant velocity (i.e., first it's at rest and then at some moment it's moving at constant velocity.) That's what my answer was trying to refute. Can you edit your question to clarify your concerns? I will then try to edit my answer appropriately. $\endgroup$ Commented Mar 20 at 11:54
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(1). In the general case of a charge in an arbitrary motion the electric field at a point changes at present time $\:t\:$ by a "signal" emitted from the retarded position of the charge at the retarded time $\:t_{ret}$. This "signal" propagates with velocity $\:c\:$ from the retarded position to the field point for a time period $\:\Delta t = t-t_{ret}$. In general the electric field is not directed radially with respect to the retarded position. See equations (01.1),(01.2) in my answer here
: Electric field associated with moving charge. In these equations the electromagnetic field is expressed as function of the retarded position and time.
(2). In the special case of a charge moving with constant velocity the electric field is accidentally expressed as function of the present position and time and is directed radially with respect to the present position. See equation (04) and Figure-01 also in my answer here : Electric field associated with moving charge. This fact seemingly gives us the impression that the field changes instantaneously and simultaneously with the instantaneous motion of the charge, i.e. an infinite speed interaction.
Related : How can direction of electric field due to a moving charge be from the present position of charge?.
