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In electromagnetism, 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 ...
As a simple example from the physics of magnetically confined plasmas, consider an axisymmetric system with circular, concentric magnetic flux surfaces of radius (a crude approximation to the magnetic field geometry in an early tokamak but topologically equivalent to any toroidal magnetic confinement system with nested flux surfaces) and denote the toroidal angle by and the poloidal angle by .
Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal nĚ‚, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
In physics, the magnetomotive force (abbreviated mmf or MMF, symbol ) is a quantity appearing in the equation for the magnetic flux in a magnetic circuit, Hopkinson's law. [1] It is the property of certain substances or phenomena that give rise to magnetic fields : F = Φ R , {\displaystyle {\mathcal {F}}=\Phi {\mathcal {R}},} where Φ is the ...
This behavior is described by the Landau–Lifshitz–Gilbert equation: [21] [22] = where γ is the gyromagnetic ratio, m is the magnetic moment, λ is the damping coefficient and H eff is the effective magnetic field (the external field plus any self-induced field). The first term describes precession of the moment about the effective field ...
The formula provides a natural generalization of the Coulomb's law for cases where the source charge is moving: = [′ ′ + ′ (′ ′) + ′] = ′ Here, and are the electric and magnetic fields respectively, is the electric charge, is the vacuum permittivity (electric field constant) and is the speed of light.
The magnetic field of permanent magnets can be quite complicated, especially near the magnet. The magnetic field of a small [note 6] straight magnet is proportional to the magnet's strength (called its magnetic dipole moment m). The equations are non-trivial and depend on the distance from the magnet and the orientation of the magnet.
In the electric and magnetic field formulation there are four equations that determine the fields for given charge and current distribution. A separate law of nature, the Lorentz force law, describes how the electric and magnetic fields act on charged particles and currents. By convention, a version of this law in the original equations by ...