A magnetostatics problem of interest 2

[Charles Link]

@aclaret See also https://www.overleaf.com/read/kdhnbkpypxfk

 

[Charles Link]

nice! my em knowledge is from course in applied linear analysis, so i don't understand so much about physical principles of the problem. if i may, let me ask, does there exist physical significance of quantity $j_{M}$ ("magnetic current"...)? i think, look like just mathematical trick ;)

The magnetization $M$ gives the number of microscopic/atomic current loops circulating per unit volume. When $M$ is uniform, there is zero magnetic current density $j_m$. The $j_m$ arises in a way that you can picture in two dimensions with a chess or checkerboard, where each square has a current loop circulating counterclockwise on its outer perimeter. The currents in adjacent squares precisely cancel, and the net effect is a current circulating on the outside of the board. That is basically what the magnetic current density $j_m$ or magnetic surface current per unit length $K_m$ is all about. $j_m=\nabla \times M/\mu_o$, and $K_m=M \times \hat{n}/\mu_o$, basically a $j_m$ with Stokes theorem applied at the surface boundary.

 

[Charles Link]

@aclaret See https://www.physicsforums.com/threa...perature-relationship-in-ferromagnets.923380/ for an interesting experiment with the temperature effects of permanent magnets that a couple of students did. See also post 21 where I measured the magnetic field from a permanent magnet using a boy scout compass.