Interface conditions for electromagnetic fields

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Maxwell's equations describe the behavior of electromagnetic fields; electric field, magnetic field, electric flux density and magnetic flux density. The differential forms of these equations require that there's always an open neighbourhood around the point they're applied to, otherwise the vector fields E, D, B and H are not differentiable. In other words the medium must be continuous. On the interface of two different medium with different values for electrical permittivity and magnetic permeability that doesn't apply.

However the interface conditions for the elecromagnetic field vectors can be derived from the integral forms of Maxwell's equations.

1 Interface conditions for electric field vectors
- 1.1 For electric flux density
- 1.2 For electric field
2 Interface conditions for magnetic field vectors
- 2.1 For magnetic flux density
- 2.2 For magnetic field
3 See also
4 References

[edit] Interface conditions for electric field vectors

[edit] For electric flux density

$(\mathbf{D}_2 - \mathbf{D}_1) \cdot \mathbf{n}_{12} = \rho_{s}$

where:
$\mathbf{n}_{12}$ is normal vector from medium 1 to medium 2.
$ρ s$ is the surface charge between the media.

Therefore the normal component of D has a step of surface charge on the interface surface. If there's no surface charge on the interface, the normal component of D is continuous.