Would a magnetic current cause a looping electric field?

Question

An electric current, composed of electrons moving in a wire, creates a magnetic field looping around the wire. Would a current of magnetic monopoles moving through a wire create an electric field looping around the wire?

I'm aware of this question, but it seems to be asking about how Maxwell's equations, which describe the behavior of the electric and magnetic fields themselves, would change if magnetic monopoles were a thing and could move in a current. I'm asking what our current best models predict would happen.

Answer 1

The magnetic field around a long straight wire carrying a current comes from the Maxwell equation:

$$ \nabla \times \mathbf B = \frac{1}{c}\left(4\pi \mathbf J + \frac{\partial \mathbf E}{\partial t} \right) $$

which since in this case $\partial \mathbf E/\partial t = 0$ simplifies to Ampère's circuital law. The problem is that you specifically say you don't want to consider the changes to the equations that would be needed if magnetic monopoles existed, as described in What would Maxwell's Equations be if we had magnetic charges and magnetic currents? But without these changes the corresponding Maxwell equation for the electric field is:

$$ \nabla \times \mathbf E = -\frac{1}{c} \frac{\partial \mathbf B}{\partial t} $$

and since in your example $\partial \mathbf E/\partial t = 0$ the electric field would be zero. You cannot describe the effects of a magnetic current unless you modify the equation to include it. If you make this change then you will find that yes you do get circular electric field lines centred on the magnetic current, just like the magnetic field lines from a long straight wire.

Answer 2

I'm asking what our current Maxwell's equations predict would happen.

The "current" Maxwell's equations predict magnetic monopoles cannot exist, c.f. Maxwell II: $$\nabla \cdot \mathbf{B}=0,$$ so the question is nonsense.