Dipole approximation

The dipole approximation replaces a spatially extended charge or current distribution with its leading dipole contribution. It neglects higher multipoles or variation in an applied field across the system.

Multipole expansion: A representation of a field or source in terms of contributions ordered by spatial scale and angular structure. The dipole approximation keeps a leading term from this broader expansion and discards later terms.
Electric dipole radiation: Electromagnetic radiation produced by a time-varying electric dipole moment. It is the leading radiation pattern when higher multipole emission is negligible.
Electric charge: A fundamental property of matter that determines its electromagnetic interactions. The spatial distribution of charge is the source from which electric multipole moments are constructed.
Monopole approximation: An approximation that represents a source using only its net charge or total strength. It retains a lower-order term than the dipole approximation and misses dipolar structure.
Electric dipole moment: A vector measure of the separation and magnitude of positive and negative charge in a distribution. This quantity supplies the leading electric contribution retained in the approximation.
Dipole–dipole interaction: An interaction between two dipoles whose strength and sign depend on their orientations and separation. Approximating each extended object by its dipole moment yields this interaction at sufficient distance.
Current density: A vector field describing electric current flowing per unit area at each point in space. Its spatial distribution determines magnetic dipole and higher magnetic multipole contributions.
Quadrupole approximation: An approximation that retains a source's quadrupole contribution as its leading relevant spatial structure. It becomes useful when symmetry suppresses the dipole term or higher accuracy is needed.
Magnetic dipole moment: A vector characterizing the strength and orientation of a localized current loop or magnetic source. For current distributions, this is the dipole quantity retained when higher moments are neglected.
Molecular spectroscopy: The study of how molecules absorb, emit, or scatter electromagnetic radiation at characteristic frequencies. Dipole transition moments determine many spectral intensities under the electric dipole approximation.

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Larmor formulaCompared with: It is a broader source-based approximation, while this formula specifies a point charge's total power.