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Using the differential form of Faraday's law, ∇ × E = − ∂B / ∂t , this gives =. By definition, B = μ 0 (H + M), where M is the magnetization of the material and μ 0 is the vacuum permeability.
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.
Faraday's law of induction (or simply Faraday's law) is a law of electromagnetism predicting how a magnetic field will interact with an electric circuit to produce an electromotive force (emf). This phenomenon, known as electromagnetic induction , is the fundamental operating principle of transformers , inductors , and many types of electric ...
Faraday's law describes two different phenomena: the motional emf generated by a magnetic force on a moving wire (see Lorentz force), and the transformer emf that is generated by an electric force due to a changing magnetic field (due to the differential form of the Maxwell–Faraday equation).
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 are not differentiable. In other words, the medium must be continuous[no need to be continuous][This paragraph need to be revised, the wrong concept of "continuous" need to be ...
Substituting into yields the familiar differential form of the Maxwell-Ampère law. Equation (D) implicitly contains the Lorentz force law and the differential form of Faraday's law of induction . For a static magnetic field, ∂ A / ∂ t {\displaystyle \partial \mathbf {A} /\partial t} vanishes, and the electric field E becomes conservative ...
The electromagnetic tensor, conventionally labelled F, is defined as the exterior derivative of the electromagnetic four-potential, A, a differential 1-form: [1] [2] = . Therefore, F is a differential 2-form— an antisymmetric rank-2 tensor field—on Minkowski space. In component form,
Faraday showed that the magnitude of the electromotive force (EMF) generated in a conductor forming a closed loop is proportional to the rate of change of the total magnetic flux passing through the loop (Faraday's law of induction). Thus, for a typical inductance (a coil of conducting wire), the flux linkage is equivalent to magnetic flux ...