scholarly journals EQUIPOTENTIAL SURFACES FOR UNIFORMLY CHARGED SYMMETRIC POLYHEDRAL CONDUCTORS

2021 ◽  
Author(s):  
Rishav CHAKRABORTY
Keyword(s):  
Point Charge ◽  
Equipotential Surface ◽  
First Occurrence ◽  
Equipotential Surfaces

<p>In this paper, it has been explained how the equipotential surface is influenced by the shape of the symmetric polyhedral conductor and how it finally becomes spherical as it would be if the polyhedral conductor is replaced by a point charge placed at the centre of that conductor. As we move away from the polyhedral conductor the consecutive equipotential surfaces curve more at the sharp bends. A patter n is observed when the diagonal distance from the vertex of the conductor to the first occurrence of its spherical equipotential surface for all symmetric polyhedral conductors is mathematically calculated which is half of the length of its side.</p>

scholarly journals EQUIPOTENTIAL SURFACES FOR UNIFORMLY CHARGED SYMMETRIC POLYHEDRAL CONDUCTORS

2021 ◽  
Author(s):  
Rishav CHAKRABORTY
Keyword(s):  
Point Charge ◽  
Equipotential Surface ◽  
First Occurrence ◽  
Equipotential Surfaces

<p>In this paper, it has been explained how the equipotential surface is influenced by the shape of the symmetric polyhedral conductor and how it finally becomes spherical as it would be if the polyhedral conductor is replaced by a point charge placed at the centre of that conductor. As we move away from the polyhedral conductor the consecutive equipotential surfaces curve more at the sharp bends. A patter n is observed when the diagonal distance from the vertex of the conductor to the first occurrence of its spherical equipotential surface for all symmetric polyhedral conductors is mathematically calculated which is half of the length of its side.</p>

scholarly journals Note on the representation of the earth's surface by means of spherical harmonics of the first three degrees

1908 ◽  
Vol 80 (542) ◽  
pp. 553-556
Keyword(s):  
Spherical Harmonics ◽  
Spherical Surface ◽  
Equipotential Surface ◽  
The Earth ◽  
First Approximation ◽  
Equipotential Surfaces ◽  
Gravitational Stability ◽  
Type V ◽  
Diurnal Rotation ◽  
Equal Density

In my paper on “The Gravitational Stability of the Earth,” dynamical arguments were adduced in favour of the hypothesis that the distribution of density within the earth is such that the surfaces of equal density present, in addition to the inequalities depending upon the diurnal rotation, other inequalities which can be specified by spherical harmonics of the first, second, and third degrees. If this is the case, the surface of the earth, by which I mean the surface of the lithosphere, should present corresponding inequalities, and so also should the equipotential surfaces. Analytically, if the density ρ is given by an equation of the form ρ = f 0 ( r ) + ϵ 1 f 1 ( r )S 1 + ϵ 2 f 2 ( r )S 2 + ϵ 3 f 3 ( r )S 3 , (1) where f 0 ( r ), f 1 ( r ), . . . are functions of the distance r from the centre, S 1 , S 2 , S 3 are spherical surface harmonics of degrees indicated by the suffixes, and ϵ 1 , ϵ 2 , ϵ 3 are small coefficients, then the surface should have an equation of the form r = a + α 1 S 1 + α 2 S 2 + α 3 S 3 , (2) where a and α 1 , α 2 , α 3 are constants, and the α 's are small. The elevations and depressions of the lithosphere should be, at least in their main features, expressible by a formula of this type. The actual elevations and depressions are difficult to determine, because all that can be found by observation is the amount of elevation above, or depression below, a particular equipotential surface, the geoid , or the surface of the ocean, continued beneath the continents. For a first approximation the potential due to such a distribution of density as is expressed by (1) within a surface expressed by (2) would be given by formulæ of the type V = F 0 ( r ) + β 1 F 1 ( r )S 1 + β 2 F 2 ( r )S 2 + β 3 F 3 ( r )S 3 , ( r < a )

scholarly journals Galilei was Wrong: Angular Nonradial Effects of Radial Gravity Depend on Density of Matter

2014 ◽  
Vol 30 ◽  
pp. 89-105
Author(s):  
Jakub Czajko
Keyword(s):  
Gravitational Force ◽  
Internal Validity ◽  
Equipotential Surface ◽  
Large Mass ◽  
Radio Waves ◽  
Mass Source ◽  
Gravity Center ◽  
Actual Meaning ◽  
Equipotential Surfaces ◽  
The Impact

Although in mathematical sense the actual meaning of Galilei's experiments conducted at leaning tower of Pisa is that he failed to detect any measurable impact of composition of matter on gravitating bodies, the obvious failure is mistakenly interpreted as experimental confirmation of lack of the impact instead. Galilei did not really perform internal validity checks of his experiments, because he did not ensure that he actually measured what he was supposed to measure. However, a modern experiment devised to test the impact of large mass on gravitational phenomena has revealed presence of (formerly unanticipated) extraneous frequency decrease in rays coming from Taurus A, when they passed close to our Sun (i.e. near occultation). The experiment has effectively confirmed that density of matter of the mass source of locally dominant gravitational field (which was our Sun‟s field) affects gravitational interactions happening on equipotential surfaces surrounding gravity center of the field. Also very similar experiment involving radio waves, which too exhibited (formerly unexpected) frequency decrease when they traveled along practically equipotential surface of Earth, has reaffirmed that conclusion. Hence contrary to Galilei, effects of nonradial (i.e. tangential and/or binormal) components of radial gravitational force fields depend (inversely) on (equipotential exposure to) the, assumed as practically constant and uniformly distributed, density of matter of the mass source of the local field.

scholarly journals Equipotential surface identification of punctual electrically system charges using measurement results

2010 ◽  
Vol 23 (2) ◽  
pp. 147-158
Author(s):  
Ljubisa Golubovic
Keyword(s):  
Equipotential Surface ◽  
Error Analyses ◽  
Measurement Results ◽  
Equipotential Surfaces ◽  
Volume Method

Identification of equipotential surfaces, based on the measurement results and by application of Least Dispersion Volume Method (LDVM) is described in this paper. In a concrete example of two punctual electric charges a suitable methodology for determining corresponded parameters, which characterize the observed equipotential surfaces is presented. Error analyses that take into account the tested parameters are given.

Beyond the Point Charge: Equipotential Surfaces and Electric Fields of Various Charge Configurations

2017 ◽  
Vol 55 (2) ◽  
pp. 71-73 ◽  
Author(s):  
Jeffrey A. Phillips ◽  
Jeff Sanny ◽  
David Berube ◽  
Anatol Hoemke
Keyword(s):  
Electric Fields ◽  
Point Charge ◽  
Equipotential Surfaces

Understanding curvatures of the equipotential surface in gravity gradiometry

Geophysics ◽  
2018 ◽  
Vol 83 (4) ◽  
pp. G35-G45
Author(s):  
Yaoguo Li
Keyword(s):  
Coordinate System ◽  
Local Coordinate System ◽  
Practical Importance ◽  
Equipotential Surface ◽  
Vertical Axis ◽  
Gravity Gradient ◽  
Gravity Gradiometry ◽  
Gradient Tensor ◽  
Gravity Gradient Tensor ◽  
Equipotential Surfaces

The concept of curvatures of equipotential surfaces is of theoretical and practical importance in gravity gradiometry because curvatures describe the shape of equipotential surfaces, which can yield information about the shape of the source. Although the fundamentals of curvatures are well-established, their connection to modern gravity gradiometry and the associated applications in exploration geophysics remain areas of active research. In particular, there is a misunderstanding in the calculation of the said curvatures directly from measured gravity gradient data that are now widely used in exploration geophysics. The error stems from the incorrect use of the formulas in a fixed user coordinate system that are only valid in a rotated coordinate system. We demonstrate that the gravity gradient tensor must be rotated to a local coordinate system whose vertical axis is aligned with the local anomalous gravity field direction so that the curvatures of the anomalous equipotential surface can be calculated correctly using these classic formulas. To facilitate practical application, we present theoretical and practical aspects related to coordinate systems and rotations of the gravity gradient tensor. We have also developed an approach for estimating local gravity for use in the curvature calculation by wavenumber-domain conversion from gradient tensors. The procedure may form a basis for developing new interpretation techniques in gravity gradient gradiometry based on curvatures.

Resources: Internet Resources for the Independent Medical Evaluator – 2007

2007 ◽  
Vol 12 (4) ◽  
pp. 4-7
Author(s):  
Christopher R. Brigham ◽  
Jenny Walker
Keyword(s):  
Head Trauma ◽  
Clonic Seizure ◽  
Acute Subdural Hematoma ◽  
Orbital Fracture ◽  
Orbital Wall ◽  
First Occurrence ◽  
One Year ◽  
The One ◽  
Neurological Injuries ◽  
Medial Orbital Wall

Abstract Rating patients with head trauma and multiple neurological injuries can be challenging. The AMA Guides to the Evaluation of Permanent Impairment (AMA Guides), Fifth Edition, Section 13.2, Criteria for Rating Impairment Due to Central Nervous System Disorders, outlines the process to rate impairment due to head trauma. This article summarizes the case of a 57-year-old male security guard who presents with headache, decreased sensation on the left cheek, loss of sense of smell, and problems with memory, among other symptoms. One year ago the patient was assaulted while on the job: his Glasgow Coma Score was 14; he had left periorbital ecchymosis and a 2.5 cm laceration over the left eyelid; a small right temporoparietal acute subdural hematoma; left inferior and medial orbital wall fractures; and, four hours after admission to the hospital, he experienced a generalized tonic-clonic seizure. This patient's impairment must include the following components: single seizure, orbital fracture, infraorbital neuropathy, anosmia, headache, and memory complaints. The article shows how the ratable impairments are combined using the Combining Impairment Ratings section. Because this patient has not experienced any seizures since the first occurrence, according to the AMA Guides he is not experiencing the “episodic neurological impairments” required for disability. Complex cases such as the one presented here highlight the need to use the criteria and estimates that are located in several sections of the AMA Guides.

Self-reference in early speech of children speaking Slovak

2018 ◽  
Vol 6 (2) ◽  
pp. 14-35
Author(s):  
Jana Kesselová
Keyword(s):  
Individual Case ◽  
Early Age ◽  
Self Awareness ◽  
Upper Limit ◽  
First Occurrence ◽  
Social Deixis ◽  
Self Reference ◽  
Vega 1 ◽  
Slovak Language

Abstract The study focuses on the process of being aware of own I in children acquiring Slovak language at an early age and living in a Slovak family. The aim of the research is to understand the process of acquiring the means by which children refer to themselves in the interaction with an adult person. The research uses the qualitative longitudinal method of individual case study. A child’s speech is researched from the very first occurrence of a self-reference mean in 16th month up to the upper limit of early age (36th month) and all that is based on audio-visual records transcripts. The following are researched: (a) succession of self-reference means acquisition in early childhood, (b) function of self-reference linguistic means, (c) process of child’s self-awareness. The results obtained based on the linguistic data in Slovak language are compared with the results of similarly focused researches in English, French, Polish, Russian and Bulgarian language. The research reveals some constants in the development of self-reference instruments that can be observed throughout various language-cultural environments. The research is a part of solutions within the grant project VEGA 1/0099/16 Personal and Social Deixis in Slovak Language.

Improved Stage Categorization of PTZ-Induced Kindling and Late Enhanced Neurogenesis in PTZ Kindled Mice

2019 ◽  
Vol 8 ◽  
pp. 1511
Author(s):  
Marzieh Shahpari ◽  
Hadi Aligholi ◽  
Mohammad Reza Namavar ◽  
Farzaneh Vafaee ◽  
Masoumeh Emamghoreishi
Keyword(s):  
Subventricular Zone ◽  
Early Phase ◽  
Hind Limb ◽  
Late Phase ◽  
The Other ◽  
Myoclonic Jerk ◽  
Ptz Kindling ◽  
First Occurrence ◽  
Tonic Extension ◽  
Behavioral Index

Background: There is no universally accepted behavioral scoring to define the early development of phenothiazine (PTZ) kindling. Therefore, studies investigating alterations of neurogenesis in the PTZ model were mainly focused on full kindled animals rather than early stages of kindling. This study aimed to determine an appropriate behavioral index for categorizing stages of PTZ kindling progress and to evaluate neurogenesis during PTZ kindling. Materials and Methods: Twenty-four mice were intraperitoneally injected with a sub convulsive dose of PTZ (40mg/kg) every other day until they became full kindled. The first occurrence of different seizure behaviors and their durations were recorded during kindling development, and the different stages of kindling were categorized. Neurogenesis was evaluated in the lateral subventricular zone (SVZ) at each stage of kindling by immunofluorescence staining. Results: First occurrence of restlessness, motionless staring, hind limb tonic extension, Straub’s tail, myoclonic jerk, and tonic-clonic were sequentially observed in more than 80% of animals with increasing PTZ injections. The duration of the myoclonic jerk was significantly longer than the other seizure behaviors. The significantly higher percentage of BrdU-positive cells was found in SVZ of mice showing tonic-clonic in comparison to other seizure behaviors. Conclusion: A hierarchy behavior was observed during the kindling process when considering the first occurrence of seizure behaviors. We defined the first occurrence of restlessness, motionless, hind limb tonic extension and Straub’s tail behaviors as an early phase, myoclonic jerk as a borderline phase and tonic-clonic as a late phase of PTZ-induced kindling. Our results indicated an enhanced SVZ neurogenesis at the late phase of kindling. [GMJ.2019;8:e1511]

Sign in / Sign up

Export Citation Format

Share Document