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2.7: Magnetic Field Intensity

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Magnetic field intensity H is an alternative description of the magnetic field in which the effect of material is factored out. For example, the magnetic flux density B (reminder: Section 2.5) due to a point charge q moving at velocity v can be written in terms of the Biot-Savart Law:

B=μ qv4πR2׈R

where ˆR is the unit vector pointing from the charged particle to the field point r, R is this distance, “×” is the cross product, and μ is the permeability of the material. We can rewrite Equation ??? as:

BμH

with:

H=qv4πR2׈R

so H in homogeneous media does not depend on μ.

Dimensional analysis of Equation ??? reveals that the units for H are amperes per meter (A/m). However, H does not represent surface current density, as the units might suggest. While it is certainly true that a distribution of current (A) over some linear cross-section (m) can be described as a current density having units of A/m, H is associated with the magnetic field and not a particular current distribution (the concept of current density is not essential to understand this section; however, a primer can be found in Section 6.2). Said differently, H can be viewed as a description of the magnetic field in terms of an equivalent (but not actual) current.

The magnetic field intensity H (A/m), defined using Equation ???, is a description of the magnetic field independent from material properties.

It may appear that H is redundant information given B and μ, but this is true only in homogeneous media. The concept of magnetic field intensity becomes important – and decidedly not redundant – when we encounter boundaries between media having different permeabilities. As we shall see in Section 7.11, boundary conditions on H constrain the component of the magnetic field which is tangent to the boundary separating two otherwise-homogeneous regions. If one ignores the characteristics of the magnetic field represented by H and instead considers only B, then only the perpendicular component of the magnetic field is constrained.

The concept of magnetic field intensity also turns out to be useful in a certain problems in which μ is not a constant, but rather is a function of magnetic field strength. In this case, the magnetic behavior of the material is said to be nonlinear. For more on this, see Section 7.16.


This page titled 2.7: Magnetic Field Intensity is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Steven W. Ellingson (Virginia Tech Libraries' Open Education Initiative) .

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