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Saturation puts a practical limit on the maximum magnetic fields achievable in ferromagnetic-core electromagnets and transformers of around 2 T, which puts a limit on the minimum size of their cores. This is one reason why high power motors, generators, and utility transformers are physically large; to conduct the large amounts of magnetic flux ...
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.
The source free equations can be written by the action of the exterior derivative on this 2-form. But for the equations with source terms (Gauss's law and the Ampère-Maxwell equation), the Hodge dual of this 2-form is needed. The Hodge star operator takes a p-form to a (n − p)-form, where n is the number of dimensions.
Some observed electromagnetic phenomena cannot be explained with Maxwell's equations if the source of the electromagnetic fields are the classical distributions of charge and current. These include photon–photon scattering and many other phenomena related to photons or virtual photons , " nonclassical light " and quantum entanglement of ...
Interface conditions describe the behaviour of electromagnetic fields; electric field, electric displacement field, and the magnetic field at the interface of two materials. The differential forms of these equations require that there is always an open neighbourhood around the point to which they are applied, otherwise the vector fields and H ...
The standard way to calculate the T-matrix is the null-field method, which relies on the Stratton–Chu equations. [6] They basically state that the electromagnetic fields outside a given volume can be expressed as integrals over the surface enclosing the volume involving only the tangential components of the fields on the surface.
The electromagnetic wave equation is a second-order partial differential equation that describes the propagation of electromagnetic waves through a medium or in a vacuum. It is a three-dimensional form of the wave equation. The homogeneous form of the equation, written in terms of either the electric field E or the magnetic field B, takes the form:
Galilean electromagnetism is a formal electromagnetic field theory that is consistent with Galilean invariance.Galilean electromagnetism is useful for describing the electric and magnetic fields in the vicinity of charged bodies moving at non-relativistic speeds relative to the frame of reference.