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I work as a physics teacher at a high school and I have to explain these days the magnetic field of a curreny carrying wire. Of course I may just give the formulae and describe how the field $\vec{B}$ looks like. However, I would like to give a bit of insight to them on the physics behind this.

Before that I explained what is a dipole, and then, from that, I explained ferromagnetism. I was wondering if I can explain the $\vec{B}$ created by a moving particle without going into Special Relativity. Thus, I was wondering if a moving charge could be considered as a dipole, since by passing through some material, the negative charge goes forward, and the holes go inwards, so that somehow we have got there a dipole. Could this be somehow a correct intuitive explanation?

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    $\begingroup$ The magnetic field from a moving charge is nothing like a dipole field. For starters, a dipole field drops off proportionally to $1/r^{3}$ while the field (both magnetic and electric) due to moving charge (at constant velocity) drops off proportionally to $1/r^{2}$. I do, however, agree that it would be a bit much to talk about special relativity. $\endgroup$ Mar 3 '20 at 19:52
  • $\begingroup$ Related : Magnetic field due to a single moving charge. $\endgroup$
    – Frobenius
    Jul 10 at 11:06
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No, this is an incorrect explanation. Even a moving charge in vacuum produces a magnetic field.

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A magnetic field really is a consequence of relativity. I don't think you can explain the origin of magnetic field without at least knowing something about length contraction in a moving frame of reference.

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