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In the search for understanding electromagnetism on deeper level, one of the earliest observations was that magnetic field is created around a current carrying wire. Then it was noticed that changing magnetic field can cause electric field to rise.

So, from symmetry it was demanded that magnetic field should also get induced due to changing electric field; and it was true.

My question is, then how could steady current through a wire create magnetic field around it as steady current should mean steady electric field near the region of the wire?

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  • $\begingroup$ A current is constituted by moving charges, which is a source of magnetic fields. $\endgroup$
    – Cross
    Jul 8, 2022 at 8:44
  • $\begingroup$ @Cross Is it because moving charged particles implies changing electric field near it? If this is the case, in a wire with steady current, E should remain the same. And if the sole reason for induced magnetic field is moving charged particles with the notion of changing E being unnecessary, then why does changing electric field induce magnetic field where there might be no moving charges? $\endgroup$ Jul 8, 2022 at 8:56
  • $\begingroup$ (4) Why don't stationary charge feel force from a current carrying wire?. $\endgroup$
    – Frobenius
    Jul 8, 2022 at 10:41
  • $\begingroup$ It is my private opinion that electrons moving together align their intrinsic magnetic dipoles. Exactly the way this happens in permanent magnets in a static way. Electrons are not only electric charges, they also have magnetic dipoles. Charge separation to generate macroscopic electric fields can be achieved by an electric potential difference. An alignment of the magnetic dipoles can be in self-induction. The movement of the charges is probably part of this, along with the alignment in an external magnetic field. $\endgroup$ Jul 9, 2022 at 4:08

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A changing electric field is a source for a magnetic field, but it's not the only source. The other source for magnetic fields is current. So even without a changing electric field we can have a magnetic field induced by the current in the wire.

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The idea that a changing magnetic field creates and electric field is both frame dependent and a-causal. Maybe it's the curl in the electric field that is changing the magnetic field?

An equivalent formulation of Maxwell's equations by Jefimenko (https://en.wikipedia.org/wiki/Jefimenko%27s_equations) in terms of charges and currents on the past light cone shows that the sources of the electric field are charge, changing charge, and changing current. The sources of magnetic field are current and changing current.

The resulting electric and magnetic fields conform to Maxwell's equations, so that the time derivative of a magnetic field is proportional to the curl of the electric field, but neither field is that cause of the other. They are both created by charge, current, and their time derivates on the past light cone of the point (and time) in question.

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  • $\begingroup$ Jefimenkos equations are not equivelant. They are only equivelant with specific boundary conditions. Maxwells equations allow for far more solutions that jefimenkos equations, for example non zero homogenous wave solution $\endgroup$ Jul 8, 2022 at 14:09

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