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Maxwell's equations

Maxwell's equations
Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies. Maxwell's equations describe how electric and magnetic fields are generated and altered by each other and by charges and currents. They are named after the Scottish physicist and mathematician James Clerk Maxwell, who published an early form of those equations between 1861 and 1862. The equations have two major variants. The "microscopic" set of Maxwell's equations uses total charge and total current, including the complicated charges and currents in materials at the atomic scale; it has universal applicability but may be unfeasible to calculate. The term "Maxwell's equations" is often used for other forms of Maxwell's equations. Formulation in terms of electric and magnetic fields[edit] Flux and divergence[edit]

Related:  InductorsCollection

Faraday paradox The Faraday paradox (or Faraday's paradox) is any experiment in which Michael Faraday's law of electromagnetic induction appears to predict an incorrect result. The paradoxes fall into two classes: 1. Faraday's law predicts that there will be zero EMF but there is a non-zero EMF. 2. Kennedy–Thorndike experiment Figure 1. The Kennedy–Thorndike experiment Improved variants of the Kennedy–Thorndike experiment have been conducted using optical cavities or Lunar Laser Ranging. For a general overview of tests of Lorentz invariance, see Tests of special relativity. The experiment[edit]

Weber (unit) The weber is named after the German physicist Wilhelm Eduard Weber (1804–1891). The weber may be defined in terms of Faraday's law, which relates a changing magnetic flux through a loop to the electric field around the loop. A change in flux of one weber per second will induce an electromotive force of one volt (produce an electric potential difference of one volt across two open-circuited terminals). Officially, Time dilation of moving particles Relation between the Lorentz factor γ and the time dilation of moving clocks. Time dilation of moving particles as predicted by special relativity can be measured in particle lifetime experiments. According to special relativity, the rate of clock C traveling between two synchronized laboratory clocks A and B is slowed with respect to the laboratory clock rates. This effect is called time dilation.

Inductance In electromagnetism and electronics, inductance is the property of an electrical conductor by which a change in current flowing through it induces an electromotive force in both the conductor itself[1] and in any nearby conductors by mutual inductance.[1] These effects are derived from two fundamental observations of physics: a steady current creates a steady magnetic field described by Oersted's law,[2] and a time-varying magnetic field induces an electromotive force in nearby conductors, which is described by Faraday's law of induction.[3] According to Lenz's law,[4] a changing electric current through a circuit that contains inductance induces a proportional voltage, which opposes the change in current (self-inductance). The varying field in this circuit may also induce an e.m.f. in neighbouring circuits (mutual inductance). Circuit analysis[edit]

Relativistic Doppler effect Diagram 1. A source of light waves moving to the right, relative to observers, with velocity 0.7c. The frequency is higher for observers on the right, and lower for observers on the left. The relativistic Doppler effect is the change in frequency (and wavelength) of light, caused by the relative motion of the source and the observer (as in the classical Doppler effect), when taking into account effects described by the special theory of relativity. The relativistic Doppler effect is different from the non-relativistic Doppler effect as the equations include the time dilation effect of special relativity and do not involve the medium of propagation as a reference point. They describe the total difference in observed frequencies and possess the required Lorentz symmetry.

Moving magnet and conductor problem Conductor moving in a magnetic field. The moving magnet and conductor problem is a famous thought experiment, originating in the 19th century, concerning the intersection of classical electromagnetism and special relativity. In it, the current in a conductor moving with constant velocity, v, with respect to a magnet is calculated in the frame of reference of the magnet and in the frame of reference of the conductor. The observable quantity in the experiment, the current, is the same in either case, in accordance with the basic principle of relativity, which states: "Only relative motion is observable; there is no absolute standard of rest".[1] However, according to Maxwell's equations, the charges in the conductor experience a magnetic force in the frame of the magnet and an electric force in the frame of the conductor. The same phenomenon would seem to have two different descriptions depending on the frame of reference of the observer. Introduction[edit]

Ives–Stilwell experiment Ives–Stilwell experiment (1938). "Canal rays" (a mixture of mostly H2+ and H3+ ions) were accelerated through perforated plates charged from 6,788 to 18,350 volts. The beam and its reflected image were simultaneously observed with the aid of a concave mirror offset 7° from the beam.[1] (The offset in this illustration is exaggerated.) The Ives–Stilwell experiment tested the contribution of relativistic time dilation to the Doppler shift of light.[1][2] The result was in agreement with the formula for the transverse Doppler effect, and was the first direct, quantitative confirmation of the time dilation factor.