Formulation in Terms of Microscopic Fields
In some cases, it may be more appropriate to define the Poynting vector S as
where μ0 is the magnetic constant. It can be derived directly from Maxwell's equations in terms of total charge and current and the Lorentz force law only.
The corresponding form of Poynting's theorem is
where J is the total current density and the energy density u is
where ε0 is the electric constant.
The two alternative definitions of the Poynting vector are equivalent in vacuum or in non-magnetic materials, where B = μ0 H. In all other cases, they differ in that
and the corresponding u are purely radiative, since the dissipation term, (−J • E) covers the total current, while the definition in terms of H has contributions from bound currents which then lack in the dissipation term.
Since only the microscopic fields E and B are needed in the derivation of
assumptions about any material possibly present can be completely avoided, and Poynting's vector as well as the theorem in this definition are universally valid, in vacuum as in all kinds of material. This is especially true for the electromagnetic energy density, in contrast to the case above.
Read more about this topic: Poynting Vector
Famous quotes containing the words formulation, terms, microscopic and/or fields:
“In necessary things, unity; in disputed things, liberty; in all things, charity.”
—Variously Ascribed.
The formulation was used as a motto by the English Nonconformist clergyman Richard Baxter (1615-1691)
“It must be a peace without victory.... Victory would mean peace forced upon the losers, a victor’s terms imposed upon the vanquished. It would be accepted in humiliation, under duress, at an intolerable sacrifice, and would leave a sting, a resentment, a bitter memory upon which the terms of peace would rest, not permanently, but only as upon quicksand.”
—Woodrow Wilson (1856–1924)
“The television screen, so unlike the movie screen, sharply reduced human beings, revealed them as small, trivial, flat, in two banal dimensions, drained of color. Wasn’t there something reassuring about it!—that human beings were in fact merely images of a kind registered in one another’s eyes and brains, phenomena composed of microscopic flickering dots like atoms. They were atoms—nothing more. A quick switch of the dial and they disappeared and who could lament the loss?”
—Joyce Carol Oates (b. 1938)
“Is America a land of God where saints abide for ever? Where golden fields spread fair and broad, where flows the crystal river? Certainly not flush with saints, and a good thing, too, for the saints sent buzzing into man’s ken now are but poor- mouthed ecclesiastical film stars and cliché-shouting publicity agents.
Their little knowledge bringing them nearer to their ignorance,
Ignorance bringing them nearer to death,
But nearness to death no nearer to God.”
—Sean O’Casey (1884–1964)