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When light is transmitted through a layer of magneto-optic material, the result is called the Faraday effect: the plane of polarization can be rotated, forming a Faraday rotator. The results of reflection from a magneto-optic material are known as the magneto-optic Kerr effect (not to be confused with the nonlinear Kerr effect).
In three dimensions, the derivative has a special structure allowing the introduction of a cross product: = + = + from which it is easily seen that Gauss's law is the scalar part, the Ampère–Maxwell law is the vector part, Faraday's law is the pseudovector part, and Gauss's law for magnetism is the pseudoscalar part of the equation.
The most usual and simple example is a fully reflecting (electric wall) boundary - the outer medium is considered as a perfect conductor. In some cases, it is more complicated: for example, the reflection-less (i.e. open) boundaries are simulated as perfectly matched layer or magnetic wall that do not resume to a single interface.
Michael Faraday holding a piece of glass of the type he used to demonstrate the effect of magnetism on polarization of light, c. 1857.. By 1845, it was known through the work of Augustin-Jean Fresnel, Étienne-Louis Malus, and others that different materials are able to modify the direction of polarization of light when appropriately oriented, [4] making polarized light a very powerful tool to ...
In the following, Hering's paradox is first shown experimentally in a video and -- in a similar way as suggested by Grabinski -- it is shown, that when carefully treated with full mathematical consistency, the experiment does not contradict Faraday's Law of Induction. Finally, the typical pitfalls of applying Faraday's Law are mentioned.
The Maxwell–Faraday version of Faraday's law of induction describes how a time-varying magnetic field corresponds to curl of an electric field. [3] In integral form, it states that the work per unit charge required to move a charge around a closed loop equals the rate of change of the magnetic flux through the enclosed surface.
The source equations (Gauss' law for electricity and the Maxwell-Ampère law) are =. while the other two (Gauss' law for magnetism and Faraday's law) are obtained from the fact that F is the 4-curl of A, or, in other words, from the fact that the Bianchi identity holds for the electromagnetic field tensor.
Reflection of light is either specular (mirror-like) or diffuse (retaining the energy, but losing the image) depending on the nature of the interface.In specular reflection the phase of the reflected waves depends on the choice of the origin of coordinates, but the relative phase between s and p (TE and TM) polarizations is fixed by the properties of the media and of the interface between them.