Electric, current field

It follows from the principle of reciprocityy described by Hermann von Helmholtz in 1853 [Helmholtz, 1853], that the lead field is identical to the electric current field that arises in the volume conductor if a unit current, called reciprocal current iRy is fed to the lead. 

Figure Bl.7.18. (a) Schematic diagram of the trapping cell in an ion cyclotron resonance mass spectrometer excitation plates (E) detector plates (D) trapping plates (T). (b) The magnetron motion due to tire crossing of the magnetic and electric trapping fields is superimposed on the circular cyclotron motion aj taken up by the ions in the magnetic field. Excitation of the cyclotron frequency results in an image current being detected by the detector electrodes which can be Fourier transfonned into a secular frequency related to the m/z ratio of the trapped ion(s).

Induction furnaces utilize the phenomena of electromagnetic induction to produce an electric current in the load or workpiece. This current is a result of a varying magnetic field created by an alternating current in a cod that typically surrounds the workpiece. Power to heat the load results from the passage of the electric current through the resistance of the load. Physical contact between the electric system and the material to be heated is not essential and is usually avoided. Nonconducting materials cannot be heated directiy by induction fields. 

Metal contained in the channel is subjected to forces that result from the interaction between the electromagnetic field and the electric current in the channel. These inward forces produce a circulation that is generally perpendicular to the length of the channel. It has been found that shaping the channels of a twin coil inductor shown in Figure 10 produces a longitudinal flow within the channel and significantly reduces the temperature difference between the channel and the hearth (12). 

Now the effective conductivity ia the direction of the electric field is <7/(1 + /5 ), ie, the scalar conductivity reduced by a factor of (1 + /5 ) by the magnetic field. Also, the electric current no longer flows in the direction of the electric field a component j exists which is perpendicular to both the electric and magnetic fields. This is the Hall current. The conductivity in the direction of the Hall current is greater by a factor of P than the conductivity in the direction of the electric field. The calculation of the scalar conductivity starts from its definition ... 

Principle of Operation. Electrical current flows are induced in all conductors when exposed to an a-c field. These currents generate a magnetic field surrounding the conductors which oppose the field being produced by the a-c field with a force sufficient to repel the conductor. Eigure 16 illustrates this principle by showing a rotor consisting of many poles. 

The length of the zone and the diameter of the tod are chosen in such a way that surface tension and interactions between circulating electric currents in the molten zone and the radio-frequency (r-f) field from the surrounding induction coil keep the molten zone in place. As of this writing (ca 1996), the maximum sihcon rod diameter that can be purified in this manner is ca 125 mm. Initially, additional purification can be obtained by making mote sweeps of the zone. Eventually, however, more sweeps do not remove any additional impurities. The limiting profile is given by equation 4 ... 

The electrolyte thus formed can conduct electric current by the movement of ions under the influence of an electric field. A cell using an electrolyte as a conductor and a positive and a negative electrode is called an electrolysis cell. If a direct-current voltage is appHed to a cell having inert electrode material such as platinum, the hydrogen ions (cations) migrate to the cathode where they first accept an electron and then form molecular hydrogen. The ions... 

Dehberate stirring can be imposed on conductors with a transverse rotating magnetic field or by passage of electric current axially with a transverse magnetic field. Conversely, a constant magnetic field with no current imposed greatly reduces natural convection. 

Electrical Connections. Electric current is brought from the transformers by air-cooled copper busbars and close to the electrode by water-cooled bus tubes and flexible cables, connecting to water-cooled copper contact plates at the electrode. The plates are held against the electrode by hydraulic pressure. The connectors are as short and as balanced as possible to allow cancelling of magnetic fields associated with individual conductors. 

E = dV/dx defined as V/m. The ions and electrons reestablish equilibrium by moving in the field which results in a net electric current density j defined as C/(m -s) or A/m. An electron or an electron hole has a unit charge, e = 1.601 x 10 C an ion has this unit charge times its valence Thus the... 

The term electrochromism was apparently coined to describe absorption line shifts induced in dyes by strong electric fields (1). This definition of electrocbromism does not, however, fit within the modem sense of the word. Electrochromism is a reversible and visible change in transmittance and/or reflectance that is associated with an electrochemicaHy induced oxidation—reduction reaction. This optical change is effected by a small electric current at low d-c potential. The potential is usually on the order of 1 V, and the electrochromic material sometimes exhibits good open-circuit memory. Unlike the well-known electrolytic coloration in alkaU haUde crystals, the electrochromic optical density change is often appreciable at ordinary temperatures. 

In the simplest case of one-dimensional steady flow in the x direction, there is a parallel between Eourier s law for heat flowrate and Ohm s law for charge flowrate (i.e., electrical current). Eor three-dimensional steady-state, potential and temperature distributions are both governed by Laplace s equation. The right-hand terms in Poisson s equation are (.Qy/e) = (volumetric charge density/permittivity) and (Qp // ) = (volumetric heat generation rate/thermal conductivity). The respective units of these terms are (V m ) and (K m ). Representations of isopotential and isothermal surfaces are known respectively as potential or temperature fields. Lines of constant potential gradient ( electric field lines ) normal to isopotential surfaces are similar to lines of constant temperature gradient ( lines of flow ) normal to... 

The early pioneers also include Benjamin Franklin and Charles de Coulomb. Franklin studied the effect of point electrodes in drawing electric currents. Coulomb discovered that a charged object gradually loses its charge i.e., he actually discovered the electrical conductivity of air. Coulomb s importance for the development of electrostatic air-cleaning methods is great, mainly because the present theories about electric charges and electric fields are based on his work. 

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