About: Toroidal moment

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A toroidal moment is an independent term in the multipole expansion of electromagnetic fields besides magnetic and electric multipoles. In the electrostatic multipole expansion, all charge and current distributions can be expanded into a complete set of electric and magnetic multipole coefficients. However, additional terms arise in an electrodynamic multipole expansion. The coefficients of these terms are given by the toroidal multipole moments as well as time derivatives of the electric and magnetic multipole moments. While electric dipoles can be understood as separated charges and magnetic dipoles as circular currents, axial (or electric) toroidal dipoles describes toroidal charge arrangements whereas polar (or magnetic) toroidal dipole (also called anapole) correspond to the field of

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rdfs:label	トロイダルモーメント (ja) Toroidal moment (en)
rdfs:comment	トロイダルモーメント(英: Toroidal moment)とは、電磁場をした際に、磁気多重極子・電気多重極子とは独立に現われる多重極子項である。静的な電磁場を多重極展開する場合、電荷と電流の分布は、電気多重極子と磁気多重極子のみの線形結合により完全に表現することができる。しかし、動的な電磁場を多重極展開する場合には追加の項が生じ、この項は電気多重極子および磁気多重極子の時間微分だけでなく、トロイダル多重極モーメントも含む。電気双極子は分離された電荷、磁気双極子は循環電流のアナロジーで理解されるが軸性トロイダル双極子（電気トロイダル双極子とも）はトーラス状の電荷分布により、極性トロイダル双極子（磁気トロイダル双極子、アナポール英: anapole とも）はソレノイドをトーラス状に曲げたもののアナロジーで理解される。 (ja) A toroidal moment is an independent term in the multipole expansion of electromagnetic fields besides magnetic and electric multipoles. In the electrostatic multipole expansion, all charge and current distributions can be expanded into a complete set of electric and magnetic multipole coefficients. However, additional terms arise in an electrodynamic multipole expansion. The coefficients of these terms are given by the toroidal multipole moments as well as time derivatives of the electric and magnetic multipole moments. While electric dipoles can be understood as separated charges and magnetic dipoles as circular currents, axial (or electric) toroidal dipoles describes toroidal charge arrangements whereas polar (or magnetic) toroidal dipole (also called anapole) correspond to the field of (en)
dcterms:subject	Moment (physics) Electromagnetism
Wikipage page ID	34727315 (xsd:integer)
Wikipage revision ID	1108111783 (xsd:integer)
Link from a Wikipage to another Wikipage	Electric dipole moment Electromagnetic field Antisymmetric tensor Pauli matrices Condensed matter Multipole expansion Antiferromagnetic Levi-Civita symbol Lorentz force Magnetic dipole Magnetization Magnetoelectric effect Symmetry T-symmetry Cesium Torus Weak interaction Cuprates Current density Feynman diagram Moment (physics) Parity (physics) Electric dipole Magnetic dipole moment Tensor Atomic orbital Electromagnetism Cold dark matter High-temperature superconductivity Phase transition CPT symmetry Spin (physics) Ferroics Majorana fermion Solenoid Multipole Nanomagnet Spheromak Order parameter Electric polarization Yakov Zel'dovich Dirac particle CuO Long-range order Multiferroic
Link from a Wikipage to an external page	https://link.springer.com/book/10.1007/978-3-658-12549-3
sameAs	Toroidal moment Toroidal moment Toroidal moment Toroidal moment Toroidal moment
dbp:wikiPageUsesTemplate	dbt:Frac dbt:ISBN dbt:Math dbt:Reflist dbt:Use_dmy_dates dbt:Or_section
has abstract	A toroidal moment is an independent term in the multipole expansion of electromagnetic fields besides magnetic and electric multipoles. In the electrostatic multipole expansion, all charge and current distributions can be expanded into a complete set of electric and magnetic multipole coefficients. However, additional terms arise in an electrodynamic multipole expansion. The coefficients of these terms are given by the toroidal multipole moments as well as time derivatives of the electric and magnetic multipole moments. While electric dipoles can be understood as separated charges and magnetic dipoles as circular currents, axial (or electric) toroidal dipoles describes toroidal charge arrangements whereas polar (or magnetic) toroidal dipole (also called anapole) correspond to the field of a solenoid bent into a torus. (en) トロイダルモーメント(英: Toroidal moment)とは、電磁場をした際に、磁気多重極子・電気多重極子とは独立に現われる多重極子項である。静的な電磁場を多重極展開する場合、電荷と電流の分布は、電気多重極子と磁気多重極子のみの線形結合により完全に表現することができる。しかし、動的な電磁場を多重極展開する場合には追加の項が生じ、この項は電気多重極子および磁気多重極子の時間微分だけでなく、トロイダル多重極モーメントも含む。電気双極子は分離された電荷、磁気双極子は循環電流のアナロジーで理解されるが軸性トロイダル双極子（電気トロイダル双極子とも）はトーラス状の電荷分布により、極性トロイダル双極子（磁気トロイダル双極子、アナポール英: anapole とも）はソレノイドをトーラス状に曲げたもののアナロジーで理解される。 (ja)
gold:hypernym	Term
prov:wasDerivedFrom	wikipedia-en:Toroidal_moment?oldid=1108111783&ns=0
page length (characters) of wiki page	12506 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Toroidal_moment
is Link from a Wikipage to another Wikipage of	Electric dipole moment Toroid moment Multipole expansion Magnetic moment Magnetic space group Majorana fermion Vortex ring Multiferroics Pickup ion Spheromak Anapole Anapole moment
is Wikipage redirect of	Toroid moment Anapole Anapole moment
is foaf:primaryTopic of	wikipedia-en:Toroidal_moment

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