# Small question about maxwell's equation curl of H

• Tom 4 billion tom

#### Tom 4 billion tom

The first page of this short pdf from MIT sums the starting point to formulate my question:
https://ocw.mit.edu/courses/physics/8-022-physics-ii-electricity-and-magnetism-fall-2006/lecture-notes/lecture29.pdf

We can see that
∇xH = Jfree
and
∇xB o (Jfree +∇xM)
∇xB o (Jfree +JB)

And now my question is, if KB ≠ 0 , how I can't see its contribution to B in the last equation?
I have been solving problems in class and in them it appears a contribution to B , after using the curl theorem, like this
∫KB·dl

I assume that by ##\vec K_B## you mean the bound surface currents on a magnetized material. These are a subset of the bound current density ##\vec J_B##, namely the bound currents that lie on the surface of the material (idealized as an infinitesimally thin sheet) rather than being distributed through the volume of its interior.

Mathematically I think you might incorporate ##\vec K_B## into the last equation by multiplying it by a Dirac delta function that represents the surface, thereby converting it to a volume current density.

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