Question

Apologies in advance for the basic question - I haven't taken physics in a while.

In trying to understand an electromagnet from first principles, I'm left wondering why magnetic field lines should warp due to a high permeability material. So for example, if I have an electromagnet with a high permeability core, my understanding is that the magnetic field lines would be stronger through the core and weaker outside the core (as compared to the case without the core). But why would the magnetic field outside the core be any different if I remove the core?

Specifically, Ampere's law as I understand it states (assuming steady state)

∇×H=J
and
B=μH.

Regardless of what μ is anywhere, shouldn't the H field be identical because the differential equation fully defines H? And in that case, why would either B or H change outside the material (where μ=μ_0) if I remove the core?

Answer 1

The magnetic field outside an electromagnet with a high permeability core is affected by the core's ability to guide magnetic field lines. Ampere's law indicates that a change in permeability influences the B-field but not the H-field, thus the external B-field weakens when a high permeability material channels the H-field lines.

Step-by-step explanation:

The presence of a high permeability core in an electromagnet affects the magnetic field lines due to the material's ability to channel magnetic field lines more effectively than air (which has lower permeability). Ampere's law, expressed as ∇×H = J, where H is the magnetic field strength and J is the current density, along with the relation B = μH, where B is the magnetic flux density and μ is the permeability of the material, tells us that a change in permeability changes the B-field but not necessarily the H-field.

When a high permeability core is present, the H-field may be 'guided' by the core, thus the H-field lines are denser within the core. Outside the core, where μ equals the permeability of free space μ0, the external B-field is influenced by the presence of the core because the H-field lines that were previously concentrated due to the core are now 'released' and spread out, causing the external B-field to weaken.

However, if the core is removed, the H-field is no longer concentrated, and the external B-field might appear stronger instead, as the H-field is not 'bound' by the high permeability material.

This bending and warping of magnetic field lines, therefore, is not due to a change in the H-field, but rather as a consequence of the change in permeability between the core and the surrounding air, affecting the B-field.