induction(although he described B as a density of lines of magnetic force). Maxwell also included a quantity designated electromagnetic momentum as an integral part of his theory. We now know this as the vector potential a which is not generally included as a part of the electromagnetics postulate. Many authors follow the original terminology of Maxwell, with some slight modifica- tions. For instance, Stratton [187 calls e the electric field intensity, H the magneti field intensity, D the electric displacement, and B the magnetic induction. Jackson 91 calls e the electric field, H the magnetic field, D the displacement, and B the magnetic induction Other authors choose freely among combinations of these terms. For instance, Kong L01] calls E the electric field strength, H the magnetic field strength, B the magnetic fur density, and d the electric displacement. We do not wish to inject further confusion into the issue of nomenclature; still, we find it helpful to use as simple a naming system as possible. We shall refer to E as the electric field, H as the magnetic field, D as the electric flur density and b as the magnetic fur density. When we use the term electromagnetic field we imply the entire set of field vectors(E, D, B, H) used in Maxwell's theory Invariance of Maxwells equations. Maxwells differential equations are valid for any system in uniform relative motion with respect to the laboratory frame of reference in which we normally do our measurements. The field equations describe the relationships between the source and mediating fields within that frame of reference. This property was first proposed for moving material media by Minkowski in 1908(using the term covariance)[130. For this reason, Maxwell's equations expressed in the form(2. 1)-(2.2) are referred to as the Minkowski form. 2.1.2 Connection to mechanics Our postulate must include a connection between the abstract quantities of charge and field and a measurable physical quantity. A convenient means of linking electromagnetics to other classical theories is through mechanics. We postulate that charges experience mechanical forces given by the Lorentz force equation. If a small volume element dV contains a total charge p dv, then the force experienced by that charge when moving at velocity v in an electromagnetic field is dF=pdVE+pvdV×B. As with any postulate, we verify this equation through experiment. Note that we write the lorentz force in terms of charge pdV, rather than charge density p, since charge n invariant quantity under a Lorentz transformation The important links between the electromagnetic fields and energy and momentum must also be postulated. We postulate that the quantity Sm=E×H represents the transport density of electromagnetic power, and that the quantity gm=D×B represents the transport density of electromagnetic momentum. @2001 by CRC Press LLCinduction (although he described B as a density of lines of magnetic force). Maxwell also included a quantity designated electromagnetic momentum as an integral part of his theory. We now know this as the vector potential A which is not generally included as a part of the electromagnetics postulate. Many authors follow the original terminology of Maxwell, with some slight modifica￾tions. For instance, Stratton [187] calls E the electric field intensity, H the magnetic field intensity, D the electric displacement, and B the magnetic induction. Jackson [91] calls E the electric field, H the magnetic field, D the displacement, and B the magnetic induction. Other authors choose freely among combinations of these terms. For instance, Kong [101] calls E the electric field strength, H the magnetic field strength, B the magnetic flux density, and D the electric displacement. We do not wish to inject further confusion into the issue of nomenclature; still, we find it helpful to use as simple a naming system as possible. We shall refer to E as the electric field, H as the magnetic field, D as the electric flux density and B as the magnetic flux density. When we use the term electromagnetic field we imply the entire set of field vectors (E, D,B, H) used in Maxwell’s theory. Invariance of Maxwell’s equations. Maxwell’s differential equations are valid for any system in uniform relative motion with respect to the laboratory frame of reference in which we normally do our measurements. The field equations describe the relationships between the source and mediating fields within that frame of reference. This property was first proposed for moving material media by Minkowski in 1908 (using the term covariance) [130]. For this reason, Maxwell’s equations expressed in the form (2.1)–(2.2) are referred to as the Minkowski form. 2.1.2 Connection to mechanics Our postulate must include a connection between the abstract quantities of charge and field and a measurable physical quantity. A convenient means of linking electromagnetics to other classical theories is through mechanics. We postulate that charges experience mechanical forces given by the Lorentz force equation. If a small volume element dV contains a total charge ρ dV, then the force experienced by that charge when moving at velocity v in an electromagnetic field is dF = ρ dV E + ρv dV × B. (2.6) As with any postulate, we verify this equation through experiment. Note that we write the Lorentz force in terms of charge ρ dV, rather than charge density ρ, since charge is an invariant quantity under a Lorentz transformation. The important links between the electromagnetic fields and energy and momentum must also be postulated. We postulate that the quantity Sem = E × H (2.7) represents the transport density of electromagnetic power, and that the quantity gem = D × B (2.8) represents the transport density of electromagnetic momentum