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For materials without polarization and magnetization, the constitutive relations are (by definition) [9]: 2 =, =, where ε 0 is the permittivity of free space and μ 0 the permeability of free space. Since there is no bound charge, the total and the free charge and current are equal.
This equation is completely coordinate- and metric-independent and says that the electromagnetic flux through a closed two-dimensional surface in space–time is topological, more precisely, depends only on its homology class (a generalization of the integral form of Gauss law and Maxwell–Faraday equation, as the homology class in Minkowski ...
In free space, where ε = ε 0 and μ = μ 0 are constant everywhere, Maxwell's equations simplify considerably once the language of differential geometry and differential forms is used. The electric and magnetic fields are now jointly described by a 2-form F in a 4-dimensional spacetime manifold.
Electromagnetic waves are predicted by the classical laws of electricity and magnetism, known as Maxwell's equations. There are nontrivial solutions of the homogeneous Maxwell's equations (without charges or currents), describing waves of changing electric and magnetic fields. Beginning with Maxwell's equations in free space:
Its presence in the equations now used to define electromagnetic quantities is the result of the so-called "rationalization" process described below. But the method of allocating a value to it is a consequence of the result that Maxwell's equations predict that, in free space, electromagnetic waves move with the speed of light.
μ 0 ≈ 12.566 × 10 −7 H/m is the magnetic constant, also known as the permeability of free space, ε 0 ≈ 8.854 × 10 −12 F/m is the electric constant, also known as the permittivity of free space, c is the speed of light in free space, [9] [10] The reciprocal of Z 0 is sometimes referred to as the admittance of free space and ...
Another of Heaviside's four equations is an amalgamation of Maxwell's law of total currents (equation "A") with Ampère's circuital law (equation "C"). This amalgamation, which Maxwell himself had actually originally made at equation (112) in "On Physical Lines of Force", is the one that modifies Ampère's Circuital Law to include Maxwell's ...
These equations are sometimes referred to as the curved space Maxwell equations. Again, the second equation implies charge conservation (in curved spacetime): Again, the second equation implies charge conservation (in curved spacetime):