Электромагнетизмнің негізгі заңы: Фарадей заңы

Basic law of electromagnetism

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 motors, generators and solenoids. The Maxwell–Faraday equation (listed as one of Maxwell's equations) describes the fact that a spatially varying (and also possibly time varying, depending on how a magnetic field varies in time) electric field always accompanies a time varying magnetic field, while Faraday's law states that there is emf (electromotive force, defined as electromagnetic work done on a unit charge when it has traveled one round of a conductive loop) on a conductive loop when the magnetic flux through the surface enclosed by the loop varies in time. Faraday's law had been discovered and one aspect of it (transformer emf) was formulated as the Maxwell–Faraday equation later. The equation of Faraday's law can be derived by the Maxwell–Faraday equation (describing transformer emf) and the Lorentz force (describing motional emf). The integral form of the Maxwell–Faraday equation describes only the transformer emf, while the equation of Faraday's law describes both the transformer emf and the motional emf.

Electromagnetic induction was discovered independently by Michael Faraday in 1831 and Joseph Henry in 1832. Faraday was the first to publish the results of his experiments. Faraday's notebook on August 29, 1831 describes an experimental demonstration of electromagnetic induction (see figure) that wraps two wires around opposite sides of an iron ring (like a modern toroidal transformer). His assessment of newly discovered properties of electromagnets suggested that when current started to flow in one wire, a sort of wave would travel through the ring and cause some electrical effect on the opposite side. Indeed, a galvanometer's needle measured a transient current (which he called a "wave of electricity") on the right side's wire when he connected or disconnected the left side's wire to a battery. This induction was due to the change in magnetic flux that occurred when the battery was connected and disconnected. In Maxwell's papers, the time varying aspect of electromagnetic induction is expressed as a differential equation which Oliver Heaviside referred to as Faraday's law even though it is different from the original version of Faraday's law, and does not describe motional emf. Heaviside's version (see Maxwell–Faraday equation below) is the form recognized today in the group of equations known as Maxwell's equations. Lenz's law, formulated by Emil Lenz in 1834, describes "flux through the circuit", and gives the direction of the induced emf and current resulting from electromagnetic induction (elaborated upon in the examples below). According to Albert Einstein, much of the groundwork and discovery of his special relativity theory was presented by this law of induction by Faraday in 1834.

It is tempting to generalize Faraday's law to state: If ∂Σ is any arbitrary closed loop in space whatsoever, then the total time derivative of magnetic flux through Σ equals the emf around ∂Σ. This statement, however, is not always true and the reason is not just from the obvious reason that emf is undefined in empty space when no conductor is present. As noted in the previous section, Faraday's law is not guaranteed to work unless the velocity of the abstract curve ∂Σ matches the actual velocity of the material conducting the electricity. The two examples illustrated below show that one often obtains incorrect results when the motion of ∂Σ is divorced from the motion of the material. where "it is very important to notice that (1) ['v'm] is the velocity of the conductor not the velocity of the path element d'l' and (2) in general, the partial derivative with respect to time cannot be moved outside the integral since the area is a function of time." In the latter half of Part II of that paper, Maxwell gives a separate physical explanation for each of the two phenomena. A reference to these two aspects of electromagnetic induction is made in some modern textbooks. As Richard Feynman states:

In the general case, explanation of the motional emf appearance by action of the magnetic force on the charges in the moving wire or in the circuit changing its area is unsatisfactory. As a matter of fact, the charges in the wire or in the circuit could be completely absent, will then the electromagnetic induction effect disappear in this case? This situation is analyzed in the article, in which, when writing the integral equations of the electromagnetic field in a four dimensional covariant form, in the Faraday’s law the total time derivative of the magnetic flux through the circuit appears instead of the partial time derivative. Thus, electromagnetic induction appears either when the magnetic field changes over time or when the area of the circuit changes. From the physical point of view, it is better to speak not about the induction emf, but about the induced electric field strength , that occurs in the circuit when the magnetic flux changes. In this case, the contribution to from the change in the magnetic field is made through the term , where is the vector potential. If the circuit area is changing in case of the constant magnetic field, then some part of the circuit is inevitably moving, and the electric field emerges in this part of the circuit in the comoving reference frame K’ as a result of the Lorentz transformation of the magnetic field , present in the stationary reference frame K, which passes through the circuit. The presence of the field in K’ is considered as a result of the induction effect in the moving circuit, regardless of whether the charges are present in the circuit or not. In the conducting circuit, the field causes motion of the charges. In the reference frame K, it looks like appearance of emf of the induction , the gradient of which in the form of , taken along the circuit, seems to generate the field .