scholarly journals Volume Charge Density in Geometric Product Lorentz Transformation

2021 ◽  
pp. 217-220
Author(s):  
Md. Ashraful Alam ◽  
Atikur Rahman Baizid
Keyword(s):  
Charge Density ◽  
Reference Frame ◽  
Lorentz Transformation ◽  
Rest Frame ◽  
Moving Frame ◽  
Inertial Reference Frame ◽  
Volume Charge ◽  
Volume Charge Density ◽  
Geometric Product ◽  
The Relationship

Lorentz Transformation is the relationship between two different coordinate frames time and space when one inertial reference frame is relative to another inertial reference frame with traveling at relative speed. In this paper, we have derived the transformation formula for the volume charge density in Geometric Product Lorentz Transformation. The changes of volume charge density of moving frame in terms of that rest frame in Geometric Product Lorentz Transformation at various velocities and angles were studied as well.

scholarly journals Volume Charge Density in Most General Lorentz Transformation

2016 ◽  
Vol 8 (3) ◽  
pp. 259-265
Author(s):  
S. A. Bhuiyan ◽  
A. R. Baizid
Keyword(s):  
Charge Density ◽  
Lorentz Transformation ◽  
Rest Frame ◽  
The Other ◽  
Moving Frame ◽  
Lorentz Transformations ◽  
Volume Charge ◽  
Rest System ◽  
Arbitrary Direction ◽  
Volume Charge Density

Lorentz Transformations generally describe the transformations for observations between mechanical phenomenon systems in relative motion. We all know that the electrical charge of associate isolated system is relativistically invariant. We have studied the volume charge density in Special and Most General Lorentz Transformations. If one frame moves on x-axis then we will notice this in Special Lorentz Transformation. On the other hand if the motion of the moving frame is not on the x-axis relative to the rest frame however the motion is on any arbitrary direction then we will notice this formula for the Most General Lorentz Transformation. We also investigated the changes of the volume charge density of moving system in terms of that of rest system in Most General Lorentz Transformations at different angles and velocities.

scholarly journals Comparative Study of the Volume Charge Density in Most General Lorentz Transformation and Quaternion Lorentz Transformation

2019 ◽  
Vol 11 (2) ◽  
pp. 165-171
Author(s):  
A. R. Baizid
Keyword(s):  
Comparative Study ◽  
Charge Density ◽  
Special Relativity ◽  
Lorentz Transformation ◽  
Inertial Frame ◽  
Numerical Data ◽  
Moving Frame ◽  
Lorentz Transformations ◽  
Volume Charge ◽  
Volume Charge Density

Lorentz transformation is the relation of space and time coordinates of one inertial frame relative to another inertial frame in special relativity. In this paper we have studied the volume charge density in most general and quaternion Lorentz transformations for different angles with different velocities of the moving frame.  We have also used numerical data to see the comparative situation.

scholarly journals Volome Charge Density in Mixed Number Lorentz Transformation

2019 ◽  
Vol 11 (2) ◽  
pp. 209-214
Author(s):  
S. A. Bhuiyan
Keyword(s):  
Charge Density ◽  
Lorentz Transformation ◽  
Frame Of Reference ◽  
Moving Frame ◽  
Lorentz Transformations ◽  
Volume Charge ◽  
Rest System ◽  
Volume Charge Density ◽  
Length Contraction

We know charge density is changed when it observes from a moving frame of reference due to the length contraction. In this paper we have studied the volume charge density in special and mixed number Lorentz transformation. We also investigate the changes of the volume charge density of moving system in terms of rest system in mixed number Lorentz Transformations at different angles and velocities.

On the methodology of calculating volume charge density in a MIFGMOS substrate using Poisson’s equation

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Francisco Javier Plascencia Jauregui ◽  
Agustín Santiago Medina Vazquez ◽  
Edwin Christian Becerra Alvarez ◽  
José Manuel Arce Zavala ◽  
Sandra Fabiola Flores Ruiz
Keyword(s):  
Metal Oxide ◽  
Charge Density ◽  
Metal Oxide Semiconductor ◽  
Floating Gate ◽  
Poisson’S Equation ◽  
Oxide Semiconductor ◽  
Volume Charge ◽  
Poisson's Equation ◽  
Content Type ◽  
Volume Charge Density

Purpose This study aims to present a mathematical method based on Poisson’s equation to calculate the voltage and volume charge density formed in the substrate under the floating gate area of a multiple-input floating-gate metal-oxide semiconductor metal-oxide semiconductor (MOS) transistor. Design/methodology/approach Based on this method, the authors calculate electric fields and electric potentials from the charges generated when voltages are applied to the control gates (CG). This technique allows us to consider cases when the floating gate has any trapped charge generated during the manufacturing process. Moreover, the authors introduce a mathematical function to describe the potential behavior through the substrate. From the resultant electric field, the authors compute the volume charge density at different depths. Findings The authors generate some three-dimensional graphics to show the volume charge density behavior, which allows us to predict regions in which the volume charge density tends to increase. This will be determined by the voltages on terminals, which reveal the relationship between CG and volume charge density and will allow us to analyze some superior-order phenomena. Originality/value The procedure presented here and based on coordinates has not been reported before, and it is an aid to generate a model of the device and to build simulation tools in an analog design environment.

scholarly journals Electron dynamics inside a vacuum tube diode through linear differential equations

2013 ◽  
Vol 80 (2) ◽  
pp. 247-254 ◽  
Author(s):  
Gabriel González ◽  
Fco. Javier González Orozco
Keyword(s):  
Differential Equations ◽  
Charge Density ◽  
Current Density ◽  
Linear Differential Equations ◽  
Volume Charge ◽  
Electron Dynamics ◽  
Vacuum Tube ◽  
Volume Charge Density ◽  
Usual Scheme ◽  
Linear Differential

AbstractIn this paper we analyze the motion of charged particles in a vacuum tube diode by solving linear differential equations. Our analysis is based on expressing the volume charge density as a function of the current density and coordinates only, i.e. ρ=ρ(J,z), while in the usual scheme the volume charge density is expressed as a function of the current density and electrostatic potential, i.e. ρ=ρ(J,V). We show that, in the case of slow varying charge density, the space-charge-limited current is reduced up to 50%. Our approach gives the well-known behavior of the classical current density proportional to the three-halves power of the bias potential and inversely proportional to the square of the gap distance between electrodes, and does not require the solution of the nonlinear differential equation normally associated with the Child–Langmuir formulation.

scholarly journals Electric Double Layer and Orientational Ordering of Water Dipoles in Narrow Channels within a Modified Langevin Poisson-Boltzmann Model

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 1054
Author(s):  
Mitja Drab ◽  
Ekaterina Gongadze ◽  
Veronika Kralj-Iglič ◽  
Aleš Iglič
Keyword(s):  
Charge Density ◽  
Double Layer ◽  
Electric Double Layer ◽  
Energy Functional ◽  
Large Radius ◽  
Charged Surface ◽  
Volume Charge ◽  
Volume Charge Density ◽  
Poisson Boltzmann ◽  
Orientational Ordering

The electric double layer (EDL) is an important phenomenon that arises in systems where a charged surface comes into contact with an electrolyte solution. In this work we describe the generalization of classic Poisson-Boltzmann (PB) theory for point-like ions by taking into account orientational ordering of water molecules. The modified Langevin Poisson-Boltzmann (LPB) model of EDL is derived by minimizing the corresponding Helmholtz free energy functional, which includes also orientational entropy contribution of water dipoles. The formation of EDL is important in many artificial and biological systems bound by a cylindrical geometry. We therefore numerically solve the modified LPB equation in cylindrical coordinates, determining the spatial dependencies of electric potential, relative permittivity and average orientations of water dipoles within charged tubes of different radii. Results show that for tubes of a large radius, macroscopic (net) volume charge density of coions and counterions is zero at the geometrical axis. This is attributed to effective electrolyte charge screening in the vicinity of the inner charged surface of the tube. For tubes of small radii, the screening region extends into the whole inner space of the tube, leading to non-zero net volume charge density and non-zero orientational ordering of water dipoles near the axis.

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