# Electrostatics

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Electrostatics is the branch of physics that deals with the forces exerted by a static (i.e. unchanging) electric field upon charged objects.

##  Overview

In electrostatics, charge need not be 'static' in the sense of unchanging. Instead 'static' implies that the dynamic coupling between electric and magnetic fields can be ignored. In electrostatics we study e-fields, voltage, and charge, but ignore any magnetic fields generated by the motion of these charges or that may be present for other reasons. Because of the electric field's relationship to and interaction with magnetism, electrostatics is a subfield of electromagnetism.

###  The electrostatic approximation

The validity of the electrostatic approximation rests on the assumption that the electric field is irrotational:

$\nabla \times \mathbf{E} = 0$

From Faraday's law, this assumption implies the absence or near-absence of time-varying magnetic fields:

${ \partial \mathbf{B} \over \partial t} = 0$

In other words, electrostatics does not require the absence of magnetic fields or electric currents. Rather, if magnetic fields or electric currents do exist, they must not change with time, or in the worst-case, they must change with time only very slowly.

In some problems, both electrostatics and magnetostatics may be required for accurate predictions, but the coupling between the two can still be ignored.

###  Electrostatic potential

Because the electric field is irrotational, it is possible to express the electric field as the gradient of a scalar function, called the electrostatic potential (also known as the voltage). Thus, the electrostatic potential Φ is related to the electric field E by the equation:

$\mathbf{E} = - \nabla \phi$

##  Fundamental concepts

###  Coulomb's law

The fundamental equation of electrostatics is Coulomb's law, which describes the force between two point charges:

$F = \frac{\left|Q_1 Q_2\right|}{4 \pi \varepsilon_o r^2}$

###  The electric field

The electric field (in units of volts per meter) is defined as the force (in newtons) per unit charge (in coulombs). From this definition and Coulomb's law, it follows that the magnitude of the electric field E created by a single point charge Q is:

$E = \frac{\left|Q \right|}{4 \pi \varepsilon_o r^2}$

###  Gauss's law

Gauss' law states that "the total electric flux through a closed surface is proportional to the total electric charge enclosed within the surface." The constant of proportionality is the permittivity of free space.

Mathematically, Gauss's law takes the form of an integral equation:

$\oint_S \varepsilon_o \mathbf{E} \cdot d\mathbf{A} = \int_V \rho \cdot dV$

Alternatively, in differential form, the equation becomes

$\nabla \cdot \varepsilon_o \mathbf{E} = \rho$

###  Poisson's equation

The definition of electrostatic potential, combined with the differential form of Gauss's law (above), provides a relationship between the potential Φ and the charge density ρ:

${\nabla}^2 \phi = - {\rho \over \varepsilon_o}$

This relationship is a form of Poisson's equation.

###  Laplace's equation

In the absence of unpaired electric charge, the equation becomes

${\nabla}^2 \phi = 0$

which is Laplace's equation.

##  Static charge generation

###  Charge separation by contact

The presence of surface charge imbalance means that the objects will exhibit attractive or repulsive forces. This surface charge imbalance, which leads to static electricity, can be generated by touching two differing surfaces together and then separating them due to the phenomena of contact electrification and the triboelectric effect. Rubbing two non-conductive objects generates a great amount of static electricity. This is not just the result of friction; two non-conductive surfaces can become charged by just being placed one on top of the other. Since most surfaces have a rough texture, it takes longer to achieve charging through contact than through rubbing. Rubbing objects together increases amount of adhesive contact between the two surfaces. Usually insulators, i.e., substances that do not conduct electricity, are good at both generating, and holding, a surface charge. Some examples of these substances are rubber, plastic, glass, and pith. Conductive objects only rarely generate charge imbalance except, for example, when a metal surface is impacted by solid or liquid nonconductors. The charge that is transferred during contact electrification is stored on the surface of each object. Static electric generators, devices which produce very high voltage at very low current (such as the Van de Graaf generator or Wimshurst machine) and used for classroom physics demonstrations, rely on this effect. Note that the presence of electric current does not detract from the electrostatic forces nor from the sparking, from the corona discharge, or other phenomena. Both phenomena can exist simultaneously in the same system.

##  Triboelectric series

Main article: triboelectric effect

The triboelectric effect is a type of contact electrification in which certain materials become electrically charged when coming into contact with another, different, material, and are then separated. The polarity and strength of the charges produced differ according to the materials, surface roughness, temperature, strain, and other properties. It is therefore not very predictable, and only broad generalizations can be made. Amber, for example, can acquire an electric charge by friction with a material like wool. This property, first recorded by Thales of Miletus, suggested the word "electricity", from the Greek word for amber, ēlektron. Other examples of materials that can acquire a significant charge when rubbed together include glass rubbed with silk, and hard rubber rubbed with fur.

##  Electrostatic generators

The presence of surface charge imbalance means that the objects will exhibit attractive or repulsive forces. This surface charge imbalance, which leads to static electricity, can be generated by touching two differing surfaces together and then separating them due to the phenomena of contact electrification and the triboelectric effect. Rubbing two non-conductive objects generates a great amount of static electricity. This is not just the result of friction; two non-conductive surfaces can become charged by just being placed one on top of the other. Since most surfaces have a rough texture, it takes longer to achieve charging through contact than through rubbing. Rubbing objects together increases amount of adhesive contact between the two surfaces. Usually insulators, e.g., substances that do not conduct electricity, are good at both generating, and holding, a surface charge. Some examples of these substances are rubber, plastic, glass, and pith. Conductive objects only rarely generate charge imbalance except, for example, when a metal surface is impacted by solid or liquid nonconductors. The charge that is transferred during contact electrification is stored on the surface of each object. Static electric generators, devices which produce very high voltage at very low current and used for classroom physics demonstrations, rely on this effect.

Note that the presence of electric current does not detract from the electrostatic forces nor from the sparking, from the corona discharge, or other phenomena. Both phenomena can exist simultaneously in the same system.

##  Charge neutralisation

Natural electrostatic phenomena are most familiar as an occasional annoyance in seasons of low humidity, but can be destructive and harmful in some situations (e.g. electronics manufacturing.) When working in direct contact with integrated circuit electronics (especially delicate MOSFETs), or in the presence of flammable gas, care must be taken to avoid accumulating and suddenly discharging a static charge (see electrostatic discharge).

##  'Static' electricity

Before 1839, physicists regarded "static electricity" as a substance distinct from four other kinds of electricity: "current" or "Voltaic" electricity, "Animal" or "bioelectricity," "thermoelectricity" from thermocouples and "magnetoelectricity" from coils. In that year Michael Faraday published the results of his experiments on the Identity of Electricities. He demonstrated that the divisions between static, current, etc., were illusions, that all five "kinds of electricity" were actually collections of phenomena, while electricity itself was a single entity appearing in negative and positive forms.

Today we regard static electricity as a subject heading also called Electrostatics: a class of various phenomena associated with substances or objects having a net electric charge. In everyday usage, "static electricity" typically refers to charged objects with voltages of sufficient magnitude to produce visible attraction, repulsion, and electrical sparks.

Static electricity can be a serious nuisance in the processing of analog recording media, because it can attract dust to sensitive materials. In the case of photography, dust accumulating on lenses and photographic plates degrades the resulting picture. Dust also permanently damages vinyl records because it can be embedded into the grooves as the stylus passes over. In both cases, several approaches exist to combat such dust deposition. Some brushes, particularly those with carbon fiber bristles, are advertised as possessing anti-static properties. Also available are handheld static guns which shoot streams of ions to discharge static on records and lenses.

Note that the charges associated with static electricity need not be still or "static." The presence of charge motions and electric current does not detract from the net charge, the electrostatic forces, nor from the sparking and corona discharge, or other phenomena. Electric current and electrostatic phenomena can exist simultaneously in the same system.

Static electricity is an important element in the biological process of pollination by bees, since the charge on a bee's body helps to attract and hold pollen.

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