## ABSTRACT

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.