# Magnetic Field Intensity

Magnetic field intensity

is an alternative description of the magnetic field in which the effect of material is factored out. For example, the magnetic flux density

(reminder: Section 2.5) due to a point charge

moving at velocity

can be written in terms of the *Biot-Savart Law*:

where

is the unit vector pointing from the charged particle to the field point

,

is this distance, “

” is the cross product, and

is the permeability of the material. We can rewrite Equation 2.7.1 as:

with:

so

in homogeneous media does not depend on

.

Dimensional analysis of Equation 2.7.3 reveals that the units for

are amperes per meter (A/m). However,

does not represent surface current density,^{1} 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,

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,

can be viewed as a description of the magnetic field in terms of an equivalent (but not actual) current.

The magnetic field intensity

(A/m), defined using Equation 2.7.2, is a description of the magnetic field independent from material properties.

It may appear that

is redundant information given

and

, 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

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

and instead considers only

, 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

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.

## Footnotes

## Additional Reading

- “Magnetic field” on Wikipedia.
- “Biot-Savart law” on Wikipedia.

Ellingson, Steven W. (2018) Electromagnetics, Vol. 1. Blacksburg, VA: VT Publishing. https://doi.org/10.21061/electromagnetics-vol-1 CC BY-SA 4.0

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