What is the magnetic boundary conditions between air and copper?

[yungman]

I understand $\vec J_{free}$ only exist on boundary surface of perfect conductors. Copper is close enough and have surface current. Also copper is paramagnetic material which implies $\mu_{cu} = \mu_0$ or very very close.

In order to find the exact angle of the of the magnetic field inside the perfect conductor like copper, we need to know the magnitude of the current density. My question is how do I find the quantity of the surface current density?

I read somewhere that I cannot find again...that static magnetic field cannot penetrade perfect conductor. Is this true?

Thanks

 

[dgOnPhys]

If by $J_{free}$ you mean current density of free (as opposed to bound) electric charge, that can exist inside an ideal conductor, the only things constrained at the surface of ideal conductors are static charge and time-varying currents.

The boundary conditions for magnetic fields across an interface can be found http://en.wikipedia.org/wiki/Interface_conditions_for_electromagnetic_fields"

A static magnetic field can exist inside an ideal conductor, time varying fields cannot.

 

[yungman]

If by $J_{free}$ you mean current density of free (as opposed to bound) electric charge No, it is the free $\vec {J_s}$ , that can exist inside an ideal conductor, the only things constrained at the surface of ideal conductors are static charge and time-varying currents.

The boundary conditions for magnetic fields across an interface can be found http://en.wikipedia.org/wiki/Interface_conditions_for_electromagnetic_fields"

A static magnetic field can exist inside an ideal conductor, time varying fields cannot.

Thanks for your reply. I figure that the static mag field can penetrate an ideal conductor. I forgot the formula

$$\hat {n_2} X ( \vec {H_2} - \vec {H_1}) = \vec {J_s}$$

But that also bring back to the point that by definition of tangential boundary condition that the current is limited on the surface as the formula indicated. But I can see your point that current don't have to stay on the surface of the ideal conductor as oppose to the charge.