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Does the electric field of a moving charge (constant velocity) change with time? Or it remains the same?

I know that changing electric fields produce a magnetic field, but in a straight, current-carrying wire also the magnetic field is produced. So the electric field of the charge in the wire is constant, that's the question I have asked in the first paragraph.

Please don't use high level mathematics like Maxwell's equations.

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  • $\begingroup$ Hint. Perform a Lorentz transformation on the electric and magnetic fields of a still charge. $\endgroup$ Commented Jan 3, 2022 at 15:55
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    $\begingroup$ Maxwell's equations are the equations that govern electrodynamics. Why would you expect an explanation to avoid them? $\endgroup$
    – ACuriousMind
    Commented Jan 3, 2022 at 16:13
  • $\begingroup$ Coz I don't understand them $\endgroup$
    – user324098
    Commented Jan 3, 2022 at 16:22

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The electric field of a single moving charge does depend on time, and curiously we don't really have to think about Maxwell's equations to understand it.

The electric field certainly is smaller the further away you are from the charge. If the charge is moving, it means that if you stay in the same place, its distance to you will change with time. Since the electric field is smaller the further away the charge is and the distance changes with time, the electric field necessarily changes with time as well.

However, thing change in a wire. We usually assume the charge density in the wire to not depend on time, the idea being that as one electron leaves some spot in the wire by moving forward, some other electron comes behind and takes its place. Hence, even though each individual electron is moving, there is always some electron in every place. As a consequence, the fields won't change with time.

It is worth mentioning also that changing electric fields aren't the only source of magnetic fields. Magnetic fields are also produced by currents. In fact, it is more fair to say that magnetic fields are always produced by currents and the presence of a changing electric field indicates the presence of a current, but I don't know how to reach this level of detail without diving deep into Maxwell's equations and Jefimenko's equations (which are derived from Maxwell's).

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    $\begingroup$ "presence of a changing electric field indicates the presence of a current," but previously you said that in a wire E field is constant, so how can changing E field incidates presence of current $\endgroup$
    – user324098
    Commented Jan 4, 2022 at 6:03
  • $\begingroup$ @VaibhavTiwari If there is a changing electric field, there is a current, but it is possible for a current to exist without there being a changing electric field. This is similar to "Socrates is a man indicates he is mortal". If Socrates is a man, then he is mortal, but the statement allows for the possibility of Socrates being mortal without being a man (for example, he could be a chicken) $\endgroup$ Commented Jan 4, 2022 at 7:11
  • $\begingroup$ In the case of a straight wire, there is a current, but there is not a changing electric field. $\endgroup$ Commented Jan 4, 2022 at 7:11

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