A Relationship between magnetic potential and current density in Maxwell

[JH_1870]

I am currently studying to solve Maxwell's equations using FEM.

I have a question about Maxwell's equations while studying.

I understood that the magnetic potential becomes ▽^2 Az = -mu_0 Jz when the current flows only in the z-axis.

I also understood the effect of the current flowing in a conductor on the magnetic potential of the surrounding iron core by the Biot-Savar law. However, in the referenced FEM example, the current density (Jz) in the iron core is set to zero.

If the current flows only in the z-axis direction in the wire, it is considered correct that the z-axis current of the iron core is 0.

However, if this is applied as it is, it is understood that only Jz in the wire exists and Jz in the iron core is 0. Therefore, even if the current density of the wire is changed, it is understood that the magnetic potential of the iron core is not affected.

Obviously, the current density flowing in the conductor affects the magnetic potential of the surrounding iron core, but setting Jz of the iron core to 0 creates a contradiction.

Regarding this, I wonder if I have misunderstood the relationship between current density and magnetic potential, or if the method of setting Jz in the iron core to 0 is wrong.

I'm also wondering how to set the current density if the iron core's current density is not set to zero. The url below is my reference.

https://jorgensd.github.io/dolfinx-tutorial/chapter3/em.html

 

[Charles Link]

I don't know whether I have a completely definitive answer, but if the iron core develops a magnetization $\vec{M}$, you will get a $J_m=\nabla \times \vec{M}$ that needs to be taken into account, and what goes hand-in-hand with this is the magnetic surface current density per unit length $\vec{K}_m=\vec{M} \times \hat{n}$ that contributes to the vector potential.

 

[JH_1870]

I don't know whether I have a completely definitive answer, but if the iron core develops a magnetization $\vec{M}$, you will get a $J_m=\nabla \times \vec{M}$ that needs to be taken into account, and what goes hand-in-hand with this is the magnetic surface current density per unit length $\vec{K}_m=\vec{M} \times \hat{n}$ that contributes to the vector potential.

Thanks, the question has been solved.