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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 ...
In other cases, Maxwell's equations are solved in a finite region of space, with appropriate conditions on the boundary of that region, for example an artificial absorbing boundary representing the rest of the universe, [24] [25] or periodic boundary conditions, or walls that isolate a small region from the outside world (as with a waveguide or ...
The electromagnetism uniqueness theorem states the uniqueness (but not necessarily the existence) of a solution to Maxwell's equations, if the boundary conditions provided satisfy the following requirements: [1] [2] At =, the initial values of all fields (E, H, B and D) everywhere (in the entire volume considered) is specified;
Curvature of spacetime affects electrodynamics. An electromagnetic field having energy and momentum also generates curvature in spacetime. Maxwell's equations in curved spacetime can be obtained by replacing the derivatives in the equations in flat spacetime with covariant derivatives. (Whether this is the appropriate generalization requires ...
[1] [2] The technique is also known as null field method and extended boundary condition method (EBCM). [3] In the method, matrix elements are obtained by matching boundary conditions for solutions of Maxwell equations. It has been greatly extended to incorporate diverse types of linear media occupying the region enclosing the scatterer. [4]
The solutions of Maxwell's equations in the Lorenz gauge (see Feynman [5] and Jackson [7]) with the boundary condition that both potentials go to zero sufficiently fast as they approach infinity are called the retarded potentials, which are the magnetic vector potential (,) and the electric scalar potential (,) due to a current distribution of ...
Electromagnetic field solvers (or sometimes just field solvers) are specialized programs that solve (a subset of) Maxwell's equations directly. They form a part of the field of electronic design automation, or EDA, and are commonly used in the design of integrated circuits and printed circuit boards. They are used when a solution from first ...
These equations can be viewed as a generalization of the vacuum Maxwell's equations which are normally formulated in the local coordinates of flat spacetime. But because general relativity dictates that the presence of electromagnetic fields (or energy / matter in general) induce curvature in spacetime, [ 1 ] Maxwell's equations in flat ...