In Chapters 2 and 3, we derived the distributions of the magnetic field, electric field, and vector potential ‘‘inside’’ the conductor as a function of the tangential magnetic field at ‘‘the conductor’s surface.’’ This information is sufficient for calculation of such important practical quantities as current density, energy stored in the electromagnetic field, inductance, and power losses. In the case of constant material properties of the conductor, calculation of the quantities mentioned is possible without numerical consideration of the conducting domain. In other words, the surface impedance concept should provide not only local boundary relations between fields or potentials, but also analytical formulae for calculation of ‘‘integral’’ or ‘‘volume’’ quantities using only the distributions of the EM field at the surface of the conductor. Once the distribution of the electric and magnetic fields inside a domain V is

obtained, energy-related quantities such as ohmic power loss (Joule loss)Pw and the magnetic field energyWm associated with V can be calculated as follows:

PW ¼ ð V

s1J2 dv (4:1)

Wm ¼ 12 ð V

~H ~B dv (4:2)

where~J and ~B are the current density and the magnetic flux density, respectively. In circuit theory, these quantities are defined as

PW ¼ I2R (4:3)

Wm ¼ 12 LI 2 (4:4)

where R and L are the resistance and inductance of the conductors, respectively.