Electrostatics (also known as Static Electricity) is the branch of physics that deals with the forces exerted by a static (i.e. unchanging) electric field upon charged objects. Electrostatics involves the build-up of charge in objects due to contact between (generally) non-conductive surfaces. These charges are generally built up through the flow of electrons from one object to another. These charges then remain in the object until a force is exerted that causes the charges to balance e.g. the familiar phenomenon of a static 'shock' is caused by the neutralization of charge built up in the body from contact with non-conductive surfaces.

### The electrostatic approximation

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

${\displaystyle {\vec {\nabla ))\times {\vec {E))=0}$

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

${\displaystyle {\partial {\vec {B)) \over \partial t}=0}$

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 ${\displaystyle E}$ by the equation:

${\displaystyle {\vec {E))=-{\vec {\nabla ))\phi ={\frac {kQ}{r))}$

## Fundamental concepts

### Coulomb's law

The fundamental equation of electrostatics is Coulomb's law, which describes the force between two point charges ${\displaystyle Q_{1))$ and ${\displaystyle Q_{2))$:

${\displaystyle {\vec {F))={\frac {Q_{1}Q_{2)){4\pi \varepsilon _{o}r^{2))}{\hat {r))}$

### 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:

${\displaystyle {\vec {E))={\frac {Q}{4\pi \varepsilon _{o}r^{2))}{\hat {r))}$

### 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:

${\displaystyle \oint _{S}\ {\vec {E))\cdot \mathrm {d} {\vec {A))=\int _{V}\rho \cdot \mathrm {d} V}$

Alternatively, in differential form, the equation becomes

${\displaystyle {\vec {\nabla ))\cdot \varepsilon _{o}{\vec {E))=\rho }$

### 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:

${\displaystyle {\nabla }^{2}\phi =-{\rho \over \varepsilon _{o))}$

This relationship is a form of Poisson's equation.

### Laplace's equation

In the absence of unpaired electric charge, the equation becomes

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

which is Laplace's equation.

## 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

 Main article: Electrostatic generator

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).

## Charge induction

Charge induction occurs when a negatively charged object repels electrons from the surface of another object, leaving it positively charged. An attractive force is then exerted by the objects. For example, when a balloon is rubbed, the balloon will stick to the wall as an attractive force is exerted by two oppositely charged surfaces (the surface of the wall gains an electric charge due to charge induction, as the free electrons at the surface of the wall are repelled by the negative balloon, creating a positive wall surface, which is subsequently attracted to the surface of the balloon).

## 'Static' electricity

In the year 1839, physicists thought that "static electricity" was different from the other electrical charges.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 the same and that only electricity itself was unique.

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.

### Comparison of charge and mass

• Charge is a quantity which may be positive or negative but mass is always a positive quantity.
• Force between two charges can be attractive or repulsive but force between two masses is always attractive (i.e. Gravitational Force).
• Charge doesn't vary with velocity of the object but mass does vary according to the relation
${\displaystyle m={\frac {m_{0)){\sqrt {\left(1-\left({\frac {v}{c))\right)^{2}\right)))}\!\ }$.
• Charge is always conserved but mass is not conserved as it can change into energy.
• Charge is quantized but quantization of mass has yet to be established.

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## References

• Faraday, Michael (1839). Experimental Researches in Electricity. London: Royal Inst.
• Halliday, David; Robert Resnick; Kenneth S. Krane (1992). Physics. New York: John Wiley & Sons. ISBN 0-471-80457-6.((cite book)): CS1 maint: multiple names: authors list (link)
• Griffiths, David J. (1999). Introduction to Electrodynamics. Upper Saddle River, NJ: Prentice Hall. ISBN 0-13-805326-X.
• Hermann A. Haus and James R. Melcher (1989). Electromagnetic Fields and Energy. Englewood Cliffs, NJ: Prentice-Hall. ISBN 0-13-249020-X.