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With the appropriate choice of the imaginary current densities, the fields inside the surface or outside the surface can be deduced from the imaginary currents. [4] In a radiation problem with given current density sources, electric current density J 1 {\displaystyle J_{1}} and magnetic current density M 1 {\displaystyle M_{1}} , the tangential ...
Magnetic current density, which has the unit V/m 2 (volt per square meter), is usually represented by the symbols and . [a] The superscripts indicate total and impressed magnetic current density. [1] The impressed currents are the energy sources. In many useful cases, a distribution of electric charge can be mathematically replaced by an ...
Assuming the external magnetic field is uniform and shares a common axis with the paramagnet, the extensive parameter characterizing the magnetic state is , the magnetic dipole moment of the system. The fundamental thermodynamic relation describing the system will then be of the form U = U ( S , V , I , N ) {\displaystyle U=U(S,V,I,N)} .
> is the (volume) magnetic susceptibility, is the magnitude of the resulting magnetization (A/m), is the magnitude of the applied magnetic field (A/m), is absolute temperature , is a material-specific Curie constant (K).
Consequently, processes in ideal MHD that convert magnetic energy into kinetic energy, referred to as ideal processes, cannot generate heat and raise entropy. [ 7 ] : 6 A fundamental concept underlying ideal MHD is the frozen-in flux theorem which states that the bulk fluid and embedded magnetic field are constrained to move together such that ...
When a magnetic field is approximated as force-free, all non-magnetic forces are neglected and the Lorentz force vanishes. For non-magnetic forces to be neglected, it is assumed that the ratio of the plasma pressure to the magnetic pressure —the plasma β —is much less than one, i.e., β ≪ 1 {\displaystyle \beta \ll 1} .
Informally, Alfvén's theorem refers to the fundamental result in ideal magnetohydrodynamic theory that electrically conducting fluids and the magnetic fields within are constrained to move together in the limit of large magnetic Reynolds numbers (R m)—such as when the fluid is a perfect conductor or when velocity and length scales are infinitely large.
MO theory recognizes that some electrons in the graphite atomic sheets are completely delocalized over arbitrary distances, and reside in very large molecular orbitals that cover an entire graphite sheet, and some electrons are thus as free to move and therefore conduct electricity in the sheet plane, as if they resided in a metal.