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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 ...
Substitution gives the non-homogeneous Maxwell equations in potential form. Many different choices of A and φ are consistent with given observable electric and magnetic fields E and B, so the potentials seem to contain more, (classically) unobservable information. The non uniqueness of the potentials is well understood, however.
Paramagnetic materials are attracted to magnetic fields, hence have a relative magnetic permeability greater than one (or, equivalently, a positive magnetic susceptibility). The magnetic moment induced by the applied field is linear in the field strength, and it is rather weak. It typically requires a sensitive analytical balance to detect the ...
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 n̂, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
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.
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)} .
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} .