Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nature of Electric and Magnetic Dipoles Gleaned from the Poynting
  Theorem and the Lorentz Force Law of Classical Electrodynamics   Starting with the most general form of Maxwell's macroscopic equations in
which the free charge and free current densities, rho_free and J_free, as well
as the densities of polarization and magnetization, P and M, are arbitrary
functions of space and time, we compare and contrast two versions of the
Poynting vector, namely, S=ExB/mu_0 and S=ExH. Here E is the electric field, H
the magnetic field, B the magnetic induction, and mu_0 the permeability of free
space. We argue that the identification of one or the other of these Poynting
vectors with the rate of flow of electromagnetic energy is intimately tied to
the nature of magnetic dipoles and the way in which these dipoles exchange
energy with the electromagnetic field. In addition, the manifest nature of both
electric and magnetic dipoles in their interactions with the electromagnetic
field has consequences for the Lorentz law of force. If the conventional
identification of magnetic dipoles with Amperian current loops is extended
beyond Maxwell's macroscopic equations to the domain where energy, force,
torque, momentum, and angular momentum are active participants, it will be
shown that "hidden energy" and "hidden momentum" become inescapable
consequences of such identification with Amperian current loops. Hidden energy
and hidden momentum can be avoided, however, if we adopt S=ExH as the true
Poynting vector, and also accept a generalized version of the Lorentz force
law. We conclude that the identification of magnetic dipoles with Amperian
current loops, while certainly acceptable within the confines of Maxwell's
macroscopic equations, is inadequate and leads to complications when
considering energy, force, torque, momentum, and angular momentum in
electromagnetic systems that involve the interaction of fields and matter.

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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: math
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con