Equal Positive Charge Research Articles

Nonadiabatic localization of H2 in the field of two external positive tip charges

For two external spherical tips with equal positive charges, the ground state of a hydrogen molecule is variationally determined within the quantum Monte Carlo scheme. For finiteness, the system is enclosed in a spherical container with randomly reflecting unstructured walls. The 12-dimensional system of two protons and two electrons is investigated ab initio without any adiabatic restrictions. We focus on the hydrogen center of mass (COM) distribution in continuation of previous work on ground state and vibration modes at a COM that was fixed in space. Our general purpose is to control the molecule’s position and orientation by external means, such as by two charged tips. To this end, knowledge is needed in order to find specific COM regions with a desired molecular orientation in the container at significant probability density of the molecule.

Periodic Coulomb Dynamics of Three Equal Negative Charges in the Field of Equal Positive Charges Fixed in Octagon Vertices

Periodic solutions of the Coulomb equation motion for three equal negative point charges in the field of six equal positive point charges fixed in vertices of a convex octagon are found. The system possesses an equilibrium configuration. The Lyapunov center theorem is applied.

Геометрия электростатических полей

Electrostatic fields have been most fully studied as special cases of electromagnetic field. They are created by a set of charged bodies that are considered immovable in relation to the observer and unchanged in time [1–3; 19; 20; 27]. Since any field is characterized by basic quantities, then such quantities for electrostatic fields are strength E and potential ϕ. Therefore, geometrically, such fields are characterized by a combination of force and equipotential lines. These fields were considered in the thesis of N.P. Anikeeva [1]. In particular, the author notes that in the case of dissimilar equal charges "... families of force and equipotential lines make up two orthogonal bundles of circles" [1, p. 59]. However, it is necessary to clarify that each "force" circle gj represents by itself not one but two lines of force, which emanate from a positive charge and terminate on a negative one. A similar review on the work [1] can be done with respect to the picture of two equal positive charges’ electrostatic field. Here the author considers a family ui of equipotential lines, which are Cassini ovals. It is truly said that these ovals belong to the fourth-order bicircular curves of genre 1 (have two double imaginary points, which are cyclic). But these ovals’ family includes one curve of zero genre — the Bernoulli lemniscate; it has three double points (two of them are the same cyclic ones, and one is real, which coincides with the origin of coordinates). In addition, it has been noted that "... the lines of current are equilateral hyperbolas gj» [1, p. 63]. However, clarification is also required here. The lines of force exit from each point charge and each line has two opposite directions. One such line of "double direction" forms only one branch of an equilateral hyperbola. A similar set of branches of equilateral hyperbolas also emanates from the second charge.

Coulomb dynamics of three equal negative charges in field of fixed two equal positive charges

Quasi-periodic solutions of the Coulomb equation of motion for three identical negative charges in the field of two fixed point positive charges are found. The center Lyapunov theorem is applied to the transformed equation of motion.

Quasi-Exact Coulomb Dynamics of n + 1 Charges n — 1 of which are Equal

For n + 1 ≥ 4 point charges n — 1 of which are negative and equal quasi-exact periodic solutions of their Coulomb equation of motion are found. These solutions describe a motion of the negative charges around the vertical axis in such a way that their coordinates coincide with vertices of a regular polygon in planes perpendicular to the axis along which two equal positive charges move.

Electric fields at the surface and interface of SiO 2 films on silicon

At solid surfaces and interfaces the potential energy of electrons has a sharp discontinuity with respect to the adjacent bulk phases. This change of potential give rise to parallel opposing layers of charged defects or ions within insulating or semiconducting solids. The concentration of charge and the electric field depend not only on the interfacial potential drop, but also on the potential and concentration of electron donor or acceptor sites in the interfacial region. At the surface of thin silicon oxide films grown on silicon, oxide ions provide a layer of negative charge; an equal positive charge (usually sodium ions) is concentrated in the oxide within about 200 Å of the surface. A similar double layer develops at the interface with silicon, where electrons donated to the silicon provide a negative charge having an adjacent positive charge layer in the oxide. Both positive charge layers exhibit a Poisson-Boltzmann distribution, with a potential drop at the surface always about three times greater than at the interface. Sodium oxide impurities are the dominant electron-donors; these supply the electrons for the negative surface and interfacial layers (as well as for any competing electron-acceptor sites). A high density of acceptor sites can be introduced into silicon dioxide by conditions tending to produce oxygen vacancies, and when the electrons from sodium oxide donors are trapped by such acceptor sites the sodium ions are localized near the trapped electrons. Under these conditions few electrons and sodium ions reach the surface or interface. Since a high surface density of oxide ions requires a high concentration of sodium ions, it is not surprising that the rate of oxidation of silicon increases with sodium content.

Electric charge transfer associated with temperature gradients in ice

The development of electric potentials in ice crystals under the influence of temperature gradients is investigated both theoretically and experimentally. The maintenance of a steady temperature gradient across a piece of ice is accompanied by concentration gradients of H + and OH - ions; because of the much greater mobility of H + ions, these diffuse more rapidly into the colder part of the ice and, in the steady state, a potential difference is set up across the ice crystal, the colder end being positive. A theory of this effect predicts a surface density of charge on the ends of the ice of σ = 5 x 10 -5 (d T /d x ) e. s. u. cm -2 and a potential difference across a uniform specimen of about 2Δ T mV, where Δ T is the temperature difference across the ends. These values are quite well confirmed by a series of experiments on specimens of highly purified ice. When two pieces of ice of initially different temperatures are brought into temporary contact and separated, the warmer acquires a negative charge and the colder an equal positive charge. The theory indicates that a maximum charge transfer of 3 x 10 -3 Δ T , e. s. u. cm -2 should occur with a contact time of about 0.01 s and that it should thereafter decline as the two pieces of ice become more nearly equal in temperature. The theoretical value for the charge developed for a contact time of ~ 0.01 s is well confirmed by experiments which also show that very little charge separation occurs if the contact period exceeds ½ s. Experiments in which the ice was contaminated with carbon dioxide, hydrofluoric acid, and sodium chloride in concentrations of up to 50 times that normally present in rain water, showed that the electrification was not greatly influenced by these impurities. These phenomena are thought to be of basic importance in the generation of electric charge in thunderstorms, this aspect being developed in the following paper.

Tribo-electricity and friction. IV.—Electricity due to air-blown particles

Electric charges due to mutual impact of dust or other particles arise in various ways: ( a ) electric dust- or sand-storms in the Tropics; ( b ) electric snow storms in the Antarctic; ( c ) electric flashes seen in the ejectamenta from volcanoes; and ( d ) electric charges, and possibly sparking, brought about by the raising of organic powders in certain industrial processes. In this group of effects, charges are produced by the impact of a multitude of like particles. Now, frictional- and impact-charges have ever been regarded as resulting from the shock of two unlike substances. Until recently there was no principle by which charges from "like” substances could be interpreted; but experiments made by the writer throw light on the subject by showing that identical solid surfaces can charge one another by friction or impact, and, further, that this property of the surfaces changes as rubbing continues. It was there shown that such organic insulators as ebonite and celluloid yield considerable charges, whereas hard inorganic materials such as quartz, calcite and glass, produce smaller effects. When the “like” solids meet in violent impact, not rubbing, the combined net charge is not nil, as might be expected according to Faraday’s law of equal and opposite frictional charges, but finite, generally negative; so that the air surrounding the surfaces must attain an equal positive charge.

The Waves of an Electron1

THE history of the newer physics, as it may be called, is largely the history of the very successful attempts which have been made to explain the facts of the physical universe in terms of electricity. In particular, the natural units of electricity, the electron first isolated as the carrier of the negative charge in the cathode rays, and the more massive proton with its equal positive charge, have been the bricks out of which physicists have tried to build model atoms. But until recently the only properties which could be attributed with certainty to the electron were its mass, 9 x 10-28 gm., and its charge, -4-77 x lO-10 electrostatic units. It is indeed possible to calculate a ‘size’ on the assumption that it follows the same laws as a charged metal sphere in a laboratory, but the value found, 3.7 x 10 -13, is neither confirmed nor contradicted by any experimental evidence.

Hydrogen Ion Concentration

CERTAIN solutions are capable of conducting electricity, although their separate pure components are themselves incapable, or capable only to a slight degree, of so doing. This conductivity is attributed to the “ionisation”of the dissolved body, that is, to the splitting up of its molecule into two or more parts, some carrying a positive and others a negative charge, the resulting “ions” being capable of migration under an imposed electric field, and so giving to the solution the power of carrying a current. The electrically neutral molecule breaks up into (a) a negatively charged part, containing an excess of electrons which lend it its negative charge, and (b) a positive portion with a deficit of electrons, this deficit resulting in an equal positive charge. These positive and negative ions attract one another, as do all positive and negative charges, and are separable only if their mutual attraction be small enough to be overcome, by the inter- and intra-molecular dynamic forces (not yet properly understood) tending to their separation.