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Traceless multipole moment densities and transformations in macroscopic electromagnetism
1School of Chemical and Physical Sciences, University of KwaZulu-Natal, Scottsville, Pietermaritzburg, South Africa.
Summary
Using traceless multipole moment densities in electromagnetism leads to unphysical results for material constants and response fields. These issues persist even after transformations, unlike primitive moment densities.
Area of Science:
- Macroscopic Electromagnetism
- Condensed Matter Physics
- Theoretical Physics
Background:
- Macroscopic electromagnetism relies on multipole expansions.
- The physical acceptability of using traceless multipole moment densities is debated.
Purpose of the Study:
- To evaluate the physical acceptability of traceless multipole moment densities in macroscopic electromagnetism.
- To compare the results with those obtained using primitive (traced) moment densities.
Main Methods:
- Analysis of harmonic plane wave fields.
- Investigation of constitutive relations derived from multipole theory.
- Examination of transformed response fields and dynamical material constants.
Main Results:
- Traceless electric quadrupole densities yield unphysical constitutive relations and material constants.
- Transformed response fields remain unphysical beyond the electric dipole order.
- Primitive moment densities allow successful transformation of constitutive relations up to electric octopole-magnetic quadrupole order.
Conclusions:
- Use of traceless multipole moment densities in macroscopic electromagnetism does not yield physically acceptable results.
- Primitive moment densities offer a viable alternative for developing physically consistent electromagnetic theories.
- The study highlights limitations in applying traceless multipole expansions for describing electromagnetic phenomena.