Static electric fields in vacuum

2018 ◽  
Author(s):  
J. Pierrus
Keyword(s):  
Charge Density ◽  
Charge Distribution ◽  
Electric Fields ◽  
Computer Algebra ◽  
Electrostatic Potential ◽  
Multipole Expansion ◽  
Integral Forms ◽  
Static Charge Distribution ◽  
Computer Algebra Software ◽  
Static Electric Fields

This chapter begins using Coulomb’s law to derive Maxwell’s electrostatic equations for a vacuum. In doing this, the integral forms of the electrostatic potential Ф and field E are obtained. These results are then used to determine Ф and E for various charge distributions possessing some symmetry: either via Gauss’s law or by directly integrating a known charge density over a line, surface or volume. Applications which require the use of computer algebra software (Mathematica) are included. A multipole expansion of the potential Ф leads to the various multipolemoments of a static charge distribution. Examples which deal with important properties like origin independence are presented. A range of questions and their solutions, not usually encountered in standard textbooks, appear in this chapter.

scholarly journals Mapping Surface Charge Distribution of Single-Cell via Charged Nanoparticle

Cells ◽  
2021 ◽  
Vol 10 (6) ◽  
pp. 1519
Author(s):  
Leixin Ouyang ◽  
Rubia Shaik ◽  
Ruiting Xu ◽  
Ge Zhang ◽  
Jiang Zhe
Keyword(s):  
Cell Surface ◽  
Charge Density ◽  
Surface Charge ◽  
Charge Distribution ◽  
Surface Charge Density ◽  
Single Cells ◽  
Fluorescent Light ◽  
Fluorescent Nanoparticles ◽  
Cell Surface Charge ◽  
Surface Charge Distribution

Many bio-functions of cells can be regulated by their surface charge characteristics. Mapping surface charge density in a single cell’s surface is vital to advance the understanding of cell behaviors. This article demonstrates a method of cell surface charge mapping via electrostatic cell–nanoparticle (NP) interactions. Fluorescent nanoparticles (NPs) were used as the marker to investigate single cells’ surface charge distribution. The nanoparticles with opposite charges were electrostatically bonded to the cell surface; a stack of fluorescence distribution on a cell’s surface at a series of vertical distances was imaged and analyzed. By establishing a relationship between fluorescent light intensity and number of nanoparticles, cells’ surface charge distribution was quantified from the fluorescence distribution. Two types of cells, human umbilical vein endothelial cells (HUVECs) and HeLa cells, were tested. From the measured surface charge density of a group of single cells, the average zeta potentials of the two types of cells were obtained, which are in good agreement with the standard electrophoretic light scattering measurement. This method can be used for rapid surface charge mapping of single particles or cells, and can advance cell-surface-charge characterization applications in many biomedical fields.

scholarly journals Functionalized Silicon Electrodes Toward Electrostatic Catalysis

2021 ◽  
Vol 9 ◽  
Author(s):  
Long Zhang ◽  
Xiaohua Yang ◽  
Shun Li ◽  
JianMing Zhang
Keyword(s):  
Electric Fields ◽  
Silicon Surfaces ◽  
Double Layers ◽  
External Electric Fields ◽  
Space Charges ◽  
Surface Models ◽  
Solid Liquid ◽  
Static Electric Fields ◽  
Mediator Catalysis

Oriented external electric fields are now emerging as “smart effectors” of chemical changes. The key challenges in experimentally studying electrostatic catalysis are (i) controlling the orientation of fields along the reaction axis and (ii) finely adjusting the magnitudes of electrostatic stimuli. Surface models provide a versatile platform for addressing the direction of electric fields with respect to reactants and balancing the trade-off between the solubility of charged species and the intensity of electric fields. In this mini-review, we present the recent advances that have been investigated of the electrostatic effect on the chemical reaction on the monolayer-functionalized silicon surfaces. We mainly focus on elucidating the mediator/catalysis role of static electric fields induced from either solid/liquid electric double layers at electrode/electrolyte interfaces or space charges in the semiconductors, indicating the electrostatic aspects is of great significance in the semiconductor electrochemistry, redox electroactivity, and chemical bonding. Herein, the functionalization of silicon surfaces allows scientists to explore electrostatic catalysis from nanoscale to mesoscale; most importantly, it provides glimpses of the wide-ranging potentials of oriented electric fields for switching on/off the macroscale synthetic organic electrochemistry and living radical polymerization.

Influence of divergent electric fields on space-charge distribution measurements by elastic methods

2000 ◽  
Vol 61 (20) ◽  
pp. 13528-13539 ◽  
Author(s):  
Stéphane Holé ◽  
Thierry Ditchi ◽  
Jacques Lewiner
Keyword(s):  
Space Charge ◽  
Charge Distribution ◽  
Electric Fields ◽  
Space Charge Distribution

scholarly journals Electret formation in transition metal oxides by electrochemical amorphization

2020 ◽  
Vol 12 (1) ◽  
Author(s):  
Yong-Jin Kim ◽  
Chan-Ho Yang
Keyword(s):  
Transition Metal ◽  
Metal Oxides ◽  
Charge Density ◽  
Electric Fields ◽  
Transition Metal Oxides ◽  
Degrees Of Freedom ◽  
Permanent Magnets ◽  
Underlying Mechanism ◽  
Diffusion Reaction ◽  
Wide Range

AbstractTransition metal oxides (TMOs) are an important class of materials that show a wide range of functionalities involving spin, charge, and lattice degrees of freedom. The strong correlation between electrons in d-orbitals and the multivalence nature give rise to a variety of exotic electronic states ranging from insulator to superconductor and cause intriguing phase competition phenomena. Despite a burst of research on the multifarious functionalities in TMOs, little attention has been paid to the formation and integration of an electret—a type of quasi-permanent electric field generator useful for nanoscale functional devices as an electric counterpart to permanent magnets. Here, we find that an electret can be created in LaMnO3 thin films by tip-induced electric fields, with a considerable surface height change, via solid-state electrochemical amorphization. The surface charge density of the formed electret area reaches ~400 nC cm−2 and persists without significant charge reduction for more than a year. The temporal evolution of the surface height, charge density, and electric potential are systematically examined by scanning probe microscopy. The underlying mechanism is theoretically analyzed based on a drift-diffusion-reaction model, suggesting that positively charged particles, which are likely protons produced by the dissociation of water, play crucial roles as trapped charges and a catalysis to trigger amorphization. Our finding opens a new horizon for multifunctional TMOs.

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