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Two pairs of gauge transformed potentials (φ, A) and (φ′, A′) are called gauge equivalent, and the freedom to select any pair of potentials in its gauge equivalence class is called gauge freedom. Again by the Poincaré lemma (and under its assumptions), gauge freedom is the only source of indeterminacy, so the field formulation is ...
The demagnetizing field, also called the stray field (outside the magnet), is the magnetic field (H-field) [1] generated by the magnetization in a magnet.The total magnetic field in a region containing magnets is the sum of the demagnetizing fields of the magnets and the magnetic field due to any free currents or displacement currents.
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.
Jefimenko says, "...neither Maxwell's equations nor their solutions indicate an existence of causal links between electric and magnetic fields. Therefore, we must conclude that an electromagnetic field is a dual entity always having an electric and a magnetic component simultaneously created by their common sources: time-variable electric ...
Electric field from positive to negative charges. Gauss's law describes the relationship between an electric field and electric charges: an electric field points away from positive charges and towards negative charges, and the net outflow of the electric field through a closed surface is proportional to the enclosed charge, including bound charge due to polarization of material.
This phenomenon is called hysteresis and the remaining magnetic field is called remanent magnetism. The residual magnetization of the core can be removed by degaussing . In alternating current electromagnets, such as those used in motors, the core's magnetization is constantly reversed, and the remanence contributes to the motor's losses.
Magnetic hysteresis can be characterized in various ways. In general, the magnetic material is placed in a varying applied H field, as induced by an electromagnet, and the resulting magnetic flux density (B field) is measured, generally by the inductive electromotive force introduced on a pickup coil nearby the sample.
In Earth science, magnetism is a useful parameter to describe and analyze rocks. Additionally, the anisotropy of magnetic susceptibility (AMS) within a sample determines parameters as directions of paleocurrents , maturity of paleosol , flow direction of magma injection, tectonic strain, etc. [ 2 ] It is a non-destructive tool which quantifies ...