2

MAGNETIC FIELDS OF DC CURRENTS (STEADY FLOW OF CHARGE)

As discussed in Chapter 1, inductance is intimately related to a closed loop of dc current which produces magnetic flux through the surface surrounded by the current loop. So our first priority is to understand the computation of the magnetic fields of steady (dc) currents that do not vary with time for various configurations of those currents.

2.1 MAGNETIC FIELD VECTORS AND PROPERTIES OF MATERIALS

The fundamental magnetic field vectors are the *magnetic field intensity* **H,** whose units are A/m, and *magnetic flux density* **B,** whose units are Wb/m^{2} = T. In a simple (but very common) linear, homogeneous, and isotropic medium, **B** and **H** are related as [3–6]

where *μ* is the *permeability* of the medium. The permeability can be written as the product of the *relative permeability μ _{r}* and the permeability of free space (essentially, air),

*μ*

_{0}

*=*4

*π*× 10

^{–7}H/m:

The units of permeability are named for Joseph Henry of Albany, New York, who essentially discovered Faraday’s law at about the time Faraday did but did not publish his results until much later. Hence, for linear, homogeneous, and isotropic media, **B** and **H** can be freely interchanged according to (2.1). Dielectrics and metals that are not magnetizeable, such as copper, aluminum, ...