Radial component of vortex electric field force

2021 ◽  
Vol 11 (1) ◽  
pp. 32-35
Author(s):  
Vasyl Tchaban ◽  
Keyword(s):  
Electric Field ◽  
Equations Of Motion ◽  
Spherical Body ◽  
Radial Component ◽  
Force Interaction ◽  
Finite Speed ◽  
The Third ◽  
Electric Field Force ◽  
Electrically Charged ◽  
Positively Charged

he differential equations of motion of electrically charged bodies in an uneven vortex electric field at all possible range of velocities are obtained in the article. In the force interaction, in addition to the two components – the Coulomb and Lorentz forces – the third component of a hitherto unknown force is involved. This component turned out to play a crucial role in the dynamics of movement. The equations are written in the usual 3D Euclidean space and physical time.This takes into account the finite speed of electric field propagation and the law of electric charge conservation. On this basis, the trajectory of the electron in an uneven electric field generated by a positively charged spherical body is simulated. The equations of motion are written in vector and coordinate forms. A physical interpretation of the obtained mathematical results is given. Examples of simulations are given.

On the electric charge collected by water-drops falling through a cloud of electrically charged particles in a vertical electric field

1935 ◽  
Vol 151 (874) ◽  
pp. 665-684 ◽  
Keyword(s):  
Electric Field ◽  
Electric Charge ◽  
Negative Charge ◽  
X Rays ◽  
Vertical Electric Field ◽  
Water Drops ◽  
Cloud Particles ◽  
Large Water ◽  
Electrically Charged ◽  
Positively Charged

The experiments described in this paper are a continuation of work described in a former paper, and have for their object the examination of a mechanism suggested by Wilson in connection with the theory of thunder-clouds. In the former work the interaction of large water-drops with ions produced by X-rays was investigated. In the present work the interaction of large water-drops with electrically charged cloud particles is investigated, and the mechanism suggested by Wilson takes the following form. Consider an uncharged water-drop falling vertically through a cloud of very small water-droplets, each of which has an electric charge either positive or negative. Let there be a vertical electric field which will be taken to be of positive potential gradient so that positively charged cloud particles move down and negatively charged cloud particles move up. The electric field induces equal charges of opposite signs on the upper and lower halves of the drop. In the case considered the upper charge is negative and the lower one positive. A charged cloud particle has a definite small mobility depending on its radius and the charge it carries. Suppose now that the mobility is so small that in strong electric fields, such as occur in thunder-clouds (up to 10,000 volts/cm), the velocity with which the positively charged cloud particles move down is less than the velocity of the falling drop. Under these conditions, those positive cloud particles which are above the drop cannot overtake the drop and so do not reach it, although attracted by the negative charge on its upper half. Those positive cloud particles, which are below and which the drop over-takes, are first repelled by the lower positive charge on the drop before being attracted by the upper negative charge and, since these charges are equal in the neutral drop, these cloud particles do not reach it. Negative cloud particles coming up to meet the falling drop are attracted to its lower positively charged half and give the drop a net negative charge. This destroys the equality of the induced charges, and some of the positive cloud particles which the drop overtakes are now attracted to it. In the presence of equal numbers of positively and negatively charged cloud particles a limiting condition is approached in which the drop collects equal numbers of positive and negative cloud particles per second and has a net negative charge equal to some fraction of the induced charge.

scholarly journals The third way to 3D gravity

2015 ◽  
Vol 24 (12) ◽  
pp. 1544015 ◽  
Author(s):  
Eric Bergshoeff ◽  
Wout Merbis ◽  
Alasdair J. Routh ◽  
Paul K. Townsend
Keyword(s):  
Equations Of Motion ◽  
Massive Gravity ◽  
De Sitter ◽  
Gravitational Field Equation ◽  
Third Way ◽  
Metric Tensor ◽  
The Third ◽  
Higher Dimensional ◽  
Conservation Condition ◽  
3D Gravity

Consistency of Einstein’s gravitational field equation [Formula: see text] imposes a “conservation condition” on the [Formula: see text]-tensor that is satisfied by (i) matter stress tensors, as a consequence of the matter equations of motion and (ii) identically by certain other tensors, such as the metric tensor. However, there is a third way, overlooked until now because it implies a “nongeometrical” action: one not constructed from the metric and its derivatives alone. The new possibility is exemplified by the 3D “minimal massive gravity” model, which resolves the “bulk versus boundary” unitarity problem of topologically massive gravity with Anti-de Sitter asymptotics. Although all known examples of the third way are in three spacetime dimensions, the idea is general and could, in principle, apply to higher dimensional theories.

Numerical Investigation of the Coulter Principle in a Microfluidic Device

2013 ◽  
Author(s):  
Muheng Zhang ◽  
Yongsheng Lian
Keyword(s):  
Electric Field ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Navier Stokes ◽  
Working Mechanism ◽  
Navier Stokes Equations ◽  
Sheath Flow ◽  
Coulter Counters ◽  
Pass Through ◽  
Cell Motion

Coulter counters are analytical microfluidic instrument used to measure the size and concentration of biological cells or colloid particles suspended in electrolyte. The underlying working mechanism of Coulter counters is the Coulter principle which relies on the fact that when low-conductive cells pass through an electric field these cells cause disturbances in the measurement (current or voltage). Useful information about these cells can be obtained by analyzing these disturbances if an accurate correlation between the measured disturbances and cell characteristics. In this paper we use computational fluid dynamics method to investigate this correlation. The flow field is described by solving the Navier-Stokes equations, the electric field is represented by a Laplace’s equation in which the conductivity is calculated from the Navier-Stokes equations, and the cell motion is calculated by solving the equations of motion. The accuracy of the code is validated by comparing with analytical solutions. The study is based on a coplanar Coulter counter with three inlets that consist of two sheath flow inlet and one conductive flow inlet. The effects of diffusivity, cell size, sheath flow rate, and cell geometry are discussed in details. The impacts of electrode size, gap between electrodes and electrode location on the measured distribution are also studied.

Determination of Instability Boundaries for a Highly Flexible Prismatic-Jointed Robot Performing Repetitive Maneuvers

1991 ◽  
Author(s):  
Keith W. Buffinton
Keyword(s):  
Floquet Theory ◽  
Equations Of Motion ◽  
Perturbation Techniques ◽  
Axial Motion ◽  
The Third ◽  
Straightforward Application ◽  
Method Yield ◽  
Robotic Devices ◽  
Axially Moving

Abstract Presented in this work are the equations of motion governing the behavior of a simple, highly flexible, prismatic-jointed robotic manipulator performing repetitive maneuvers. The robot is modeled as a uniform cantilever beam that is subject to harmonic axial motions over a single bilateral support. To conveniently and accurately predict motions that lead to unstable behavior, three methods are investigated for determining the boundaries of unstable regions in the parameter space defined by the amplitude and frequency of axial motion. The first method is based on a straightforward application of Floquet theory; the second makes use of the results of a perturbation analysis; and the third employs Bolotin’s infinite determinate method. Results indicate that both perturbation techniques and Bolotin’s method yield acceptably accurate results for only very small amplitudes of axial motion and that a direct application of Floquet theory, while computational expensive, is the most reliable way to ensure that all instability boundaries are correctly represented. These results are particularly relevant to the study of prismatic-jointed robotic devices that experience amplitudes of periodic motion that are a significant percentage of the length of the axially moving member.

The spacecraft wake as a tool to detect cold ions: Turning a problem into a feature

2021 ◽  
Author(s):  
Mats André ◽  
Anders I. Eriksson ◽  
Yuri V. Khotyaintsev ◽  
Sergio Toledo-Redondo
Keyword(s):  
Electric Field ◽  
Plasma Parameters ◽  
Double Probe ◽  
Positive Ions ◽  
Collisionless Plasmas ◽  
Mass Outflow ◽  
Wake Effects ◽  
In Situ Observations ◽  
Positively Charged

<p>Wakes behind scientific spacecraft caused by supersonic drifting ions is common in collisionless plasmas. Such wakes change the local plasma conditions and disturb in situ observations of the geophysical plasma parameters. We concentrate on observations of the electric field with double-probe instruments. Sometimes the wake effects are caused by the spacecraft body, are minor and easy to detect, and can be compensated for in a reasonable way. We show an example from the Cluster spacecraft in the solar wind. Sometimes the effects are caused by an electrostatic structure around a positively charged spacecraft causing an enhanced wake and major effects on the local plasma. Here observations of the geophysical electric field with the double-probe technique becomes impossible. Rather, the wake can be used to detect the presence of cold positive ions. Together with other instruments, also the cold ion flux can be estimated. We discuss such examples from the Cluster spacecraft in the magnetospheric lobes. For an intermediate range of parameters, when the drift energy of the ions is comparable to the equivalent charge of the spacecraft, also the charged wire booms of a double-probe instrument must be taken into account to extract useful information from the observations. We show an example from the MMS spacecraft near the magnetopause. With understanding of the physics causing wakes behind spacecraft, the local effects can sometimes be compensated for. When this is not possible, sometimes entirely new geophysical parameters can be estimated. An example is the flux of cold positive ions, constituting a major part of the mass outflow from planet Earth, using electric and magnetic field instruments on a spacecraft charged due to photoionization</p><p> </p>

Ion acceleration by multiple laser pulses and their spontaneous electromagnetic fields in plasma

2008 ◽  
Vol 74 (1) ◽  
pp. 111-118
Author(s):  
FEN-CE CHEN
Keyword(s):  
Magnetic Fields ◽  
Electric Field ◽  
Analytical Model ◽  
Electromagnetic Fields ◽  
Equations Of Motion ◽  
Charged Particles ◽  
Laser Pulses ◽  
The Self ◽  
Electric And Magnetic Fields ◽  
Relativistic Equations

AbstractThe acceleration of ions by multiple laser pulses and their spontaneously generated electric and magnetic fields is investigated by using an analytical model for the latter. The relativistic equations of motion of test charged particles are solved numerically. It is found that the self-generated axial electric field plays an important role in the acceleration, and the energy of heavy test ions can reach several gigaelectronvolts.

General Relations between Fields and Sources

2019 ◽  
pp. 63-84
Author(s):  
Richard Freeman ◽  
James King ◽  
Gregory Lafyatis
Keyword(s):  
Electric Field ◽  
Spatial Variations ◽  
Rate Of Change ◽  
Retarded Time ◽  
Finite Speed ◽  
Radiation Fields ◽  
Source Current ◽  
Field Lines ◽  
General Relations ◽  
Relationship Of

The general relationship of changes in source current, charge and/or position and the fields that they produce are examined in the context of the development of equations that are known as “Jefimenko’s Equations.” These expressions give the fields at a point removed from the source in terms of the charge and current distributions evaluated at the “retarded time.” In this development, the finite speed of light is shown to connect the time rate of change in source conditions to the spatial variations of the potential at the field point. Using a graphical argument, the transverse nature of radiation fields is demonstrated based on electric field lines as envisioned by Faraday.

Conservation Principles for Systems With a Varying Number of Degrees-of-Freedom

1998 ◽  
Vol 65 (3) ◽  
pp. 719-726 ◽  
Author(s):  
S. Djerassi
Keyword(s):  
Angular Momentum ◽  
Degrees Of Freedom ◽  
Mechanical Energy ◽  
Equations Of Motion ◽  
Nonholonomic Systems ◽  
Linear Momentum ◽  
Dynamical Equations ◽  
The Third ◽  
Conservation Principles

This paper is the third in a trilogy dealing with simple, nonholonomic systems which, while in motion, change their number of degrees-of-freedom (defined as the number of independent generalized speeds required to describe the motion in question). The first of the trilogy introduced the theory underlying the dynamical equations of motion of such systems. The second dealt with the evaluation of noncontributing forces and of noncontributing impulses during such motion. This paper deals with the linear momentum, angular momentum, and mechanical energy of these systems. Specifically, expressions for changes in these quantities during imposition and removal of constraints are formulated in terms of the associated changes in the generalized speeds.

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