Auxiliary Magnetic Field, <b>H</b>

Auxiliary Magnetic Field, H

A long solenoid (turns/length=n, current=I) has its core filled from radius=a to r=2a with a linear magnetic material. Demonstrate that you understand the differing concepts of the fields B, M, and H, by finding each inside the filled portion of the solenoid and the surface current on the inner surface of the magnetic filler.

QUESTIONS
(Score is number right minus number wrong.)

In magnetostatics, the magnetic field B and the fields M and H are fundamentally different because the divergence of B always vanishes but the divergences of M and H do not necessarily vanish.

: True; False

In Equation (6) we define a new fictitious field B(vac), but the change is purely cosmetic to create a curl equation that looks just like the one Maxwell says a magnetic field should satisfy. Still, the divergence of H and hence of the fictitious field do not necessarily vanish.

Refer to the diagram. Where in the solenoid is it likely that the divergences of M and hence of H do not vanish. (See Equation (7)).

: At the center of the solenoid.; Between the magnetic material and the windings.; At the z-boundary (end) of the solenoid.; At the inner radial boundary of the magnetic filler material.

Assuming that the length of the solenoid is large compared to the radius, where is it likely that the divergence of H vanishes?

: Where the z-component of M vanishes but the other components do not.; Where the z-component of M is constant as a function of z and the other (orthogonal to z) components vanish.; Where the z-component of M varies with respect to z.

If we stay away from the places in the solenoid where div H does not vanish, then Equation (6b) describes a regular magnetostatics field with vanishing divergence. We should know the answer for the field inside a solenoid that satisfies this equation.

For the solenoid shown in the figure with a free surface current, the field B (vac) inside (but away from the edges) is