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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)} .
The current density J is itself the result of the magnetic field according to Ohm's law. Again, due to matter motion and current flow, this is not necessarily the field at the same place and time. However these relations can still be used to deduce orders of magnitude of the quantities in question.
> 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).
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.
For a magnetic crystal, it is tempting to try to define = where the limit is taken as the volume V of the system becomes large. However, because of the factor of r in the integrand, the integral has contributions from surface currents that cannot be neglected, and as a result the above equation does not lead to a bulk definition of orbital magnetization.
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} .