A moving charge in a uniform electric field travels along a catenary (which tends to a parabola if the charge velocity is much less than the speed of light ). The surface of revolution with fixed radii at either end that has minimum surface area is a catenary revolved about the -axis.
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Every time a moving charge changes direction it has to give off radiation of corresponding energy. In X-ray tubes this directional change is the electron hitting the metal target (Anode) in synchrotrons it is the outer magnetic field accelerating the electron into a circular path. There are many different kind of X-ray tubes and operators have to chose accurately depending on what it is, that should be measured.
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The force on a current carrying wire is similar to that of a moving charge as expected since a current carrying wire is a collection of moving charges. A current-carrying wire feels a force in the presence of a magnetic field. The Lorentz force on a macroscopic current is often referred to as the Laplace force. Consider a conductor of length , cross section , and charge due to electric current .
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A moving charge also produces a magnetic field. The interaction of electric charges with an electromagnetic field (combination of electric and magnetic fields) is the source of the electromagnetic (or Lorentz) force, which is one of the four fundamental forces in physics. The study of photon-mediated interactions among charged particles is called quantum electrodynamics. The SI derived unit of electric charge is the coulomb (C) named after French physicist Charles-Augustin de Coulomb.
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Prediction of direction of field ('B'). The rules above are usually used to predict 'F' based upon 'B' and 'I' - the force on a moving charge when moving through a field, whether or not the charge is carried in a wire. However, this rule should not be confused with a different right hand grip rule for the prediction of the direction of a field ('B') produced by current ('I') traveling through a wire.
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Magnetic forces are caused by relativistic contraction when electrons are moving relative to atomic nuclei. The magnetic force on a moving charge next to a current-carrying wire is a result of relativistic motion between electrons and protons. Extract of page 13-6 In 1820, André-Marie Ampère showed that parallel wires having currents in the same direction attract one another. To the electrons, the wire contracts slightly, causing the protons of the opposite wire to be locally denser.
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In electronic and semiconductor devices, transient or frequency-dependent current between terminals contains both conduction and displacement components. Conduction current is related to moving charge carriers (electrons, holes, ions, etc.), while displacement current is caused by a time-varying electric field. Carrier transport is affected by electric fields and by a number of physical phenomena - such as carrier drift and diffusion, trapping, injection, contact-related effects, impact ionization, etc. As a result, device admittance is frequency-dependent, and a simple electrostatic formula for capacitance C = q/V, is not applicable.
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Since electric and magnetic fields combine, the attraction of a point charge which is moving at a constant velocity is towards the extrapolated instantaneous position, not to the apparent position it seems to occupy when looked at.Feynman Lectures on Physics vol. II gives a thorough treatment of the analogous problem in electromagnetism. Feynman shows that for a moving charge, the non-radiative field is an attraction/repulsion not toward the apparent position of the particle, but toward the extrapolated position assuming that the particle continues in a straight line in a constant velocity.
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Instead of a single orbiting charge, the toroidal ring was conceived as a collection of infinitesimal charge elements, which orbited or circulated along a common continuous path or "loop". In general, this path of charge could assume any shape, but tended toward a circular form due to internal repulsive electromagnetic forces. In this configuration the charge elements circulated, but the ring as a whole did not radiate due to changes in electric or magnetic fields since it remained stationary. The ring produced an overall magnetic field ("spin") due to the current of the moving charge elements.
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However, Heaviside refused the offer, declining to accept any money unless the company were to give him full recognition. Heaviside was chronically poor, making his refusal of the offer even more striking. But this setback had the effect of turning Heaviside's attention towards electromagnetic radiation, and in two papers of 1888 and 1889, he calculated the deformations of electric and magnetic fields surrounding a moving charge, as well as the effects of it entering a denser medium. This included a prediction of what is now known as Cherenkov radiation, and inspired his friend George FitzGerald to suggest what now is known as the Lorentz–FitzGerald contraction.
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Another major flaw is that electrical science and engineering are built on solutions of Maxwell's Equations in which the electric current - expressed through the current- density vector J – is a fundamental quantity, while a so-called 'energy current' does not appear. Moreover, there are no equivalent equations describing the physical behaviour of the Poynting vector on which the concept of energy current is based. After the discovery of the electron in 1897, the Drude model, which describes electrical conduction in metals, was developed very quickly. By associating the somewhat abstract concept of moving charge with the rather more concrete motion of the charged electrons, the Drude model effectively deals with the traditional "charge current" and the Heaviside "energy current" views simultaneously.
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The other term is dynamic, in that it requires that the moving charge be accelerating with a component perpendicular to the line connecting the charge and the observer and does not appear unless the source changes velocity. This second term is connected with electromagnetic radiation. The first term describes near field effects from the charge, and its direction in space is updated with a term that corrects for any constant-velocity motion of the charge on its distant static field, so that the distant static field appears at distance from the charge, with no aberration of light or light-time correction. This term, which corrects for time-retardation delays in the direction of the static field, is required by Lorentz invariance.
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That is, a pure static electric field will show the familiar magnetic field associated with a current, in any frame of reference where the charge moves. Likewise, any new motion of a charge in a region that seemed previously to contain only a magnetic field, will show that the space now contains an electric field as well, which will be found to produces an additional Lorentz force upon the moving charge. Thus, electrostatics, as well as magnetism and magnetostatics, are now seen as studies of the static EM field when a particular frame has been selected to suppress the other type of field, and since an EM field with both electric and magnetic will appear in any other frame, these "simpler" effects are merely the observer's.
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In magnetostatics equations such as Ampère's Law or the more general Biot–Savart law allow one to solve for the magnetic fields produced by steady electrical currents. Often, however, one may want to calculate the magnetic field due to time varying currents (accelerating charge) or other forms of moving charge. Strictly speaking, in these cases the aforementioned equations are invalid, as the field measured at the observer must incorporate distances measured at the retarded time, that is the observation time minus the time it took for the field (traveling at the speed of light) to reach the observer. The retarded time is different for every point to be considered, hence the resulting equations are quite complicated; often it is easier to formulate the problem in terms of potentials; see retarded potential and Jefimenko's equations.
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