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study of phenomena associated with charged bodies at rest (see chargecharge,
property of matter that gives rise to all electrical phenomena (see electricity). The basic unit of charge, usually denoted by e, is that on the proton or the electron; that on the proton is designated as positive (+e
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; electricityelectricity,
class of phenomena arising from the existence of charge. The basic unit of charge is that on the proton or electron—the proton's charge is designated as positive while the electron's is negative.
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). A charged body has an excess of positive or negative charges, a condition usually brought about by the transfer of electrons to or from the body. Such bodies exert forces on each other, as described by Coulomb's lawCoulomb's law
, in physics, law stating that the electrostatic force between two charged bodies is proportional to the product of the amount of charge on the bodies divided by the square of the distance between them.
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, and their behavior can be analyzed in terms of the concept of an electric fieldfield,
in physics, region throughout which a force may be exerted; examples are the gravitational, electric, and magnetic fields that surround, respectively, masses, electric charges, and magnets. The field concept was developed by M.
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 surrounding any charged body such that another charged body located at any point in the field is subject to a force proportional to the magnitude of its charge and its attraction or repulsion, depending on the polarity of the charge. The combined electric field in a given region depends on the location, magnitude, and polarity of the charges in that region. Electric fields need not be constant with time. Time-varying electric fields are used in some devices that accelerate charged atomic particles. Electrostatics has many other applications, ranging from the analysis of phenomena such as thunderstorms to the study of the behavior of electron tubes.


The class of phenomena recognized by the presence of electrical charges, either stationary or moving, and the interaction of these charges, this interaction being solely by reason of the charges and their positions and not by reason of their motion. See Electric charge

At least 90% of the topics that are normally classified as electrostatics are concerned with the manipulation of charged particles by electric fields. When a particle becomes charged by rubbing or other means, it has either a surplus or a deficit of electrons. A body with a surplus of electrons is said to be negatively charged; a body with a deficiency, positively charged. The amount or quantity of charge on a body is expressed in coulombs (positive or negative). A coulomb is an enormous amount of charge, and in most electrostatic situations charge levels of a small fraction of a coulomb give rise to significant effects. Electrostatic forces always exist between charged bodies. Bodies with like charge experience repulsive forces, while oppositely charged bodies experience attraction.


If two bodies are charged to Q1 and Q2 coulombs and are separated in vacuum by a distance of r meters, the force F in newtons between them is given by Coulomb's law,

Eq. (1).

In electrical science, ε0 is an important constant known as the permittivity or dielectric constant of free space, and is also sometimes called the primary electric constant. It has the value ε0 = 8.85416 × 10-12 farad per meter. See Coulomb's law, Permittivity

Coulomb's law shows that a body charged to Q1 experiences a force due to the presence of another body charged to Q2. Q2 may be considered to influence the whole of space surrounding it, because if Q1 were to be positioned anywhere it would experience a force due to the presence of Q2. The property of a charge to influence the whole of space can be modeled by a three-dimensional force field permeating the whole of the space surrounding the charge Q2. This field is called the electric field. When there are many charged bodies present in an environment, the force that would be exerted on a charged particle at any location can be found by calculating the field at the location due to the presence of each charged body separately, and the net field is obtained by adding up the individual components. See Electric field

A system of charged particles or bodies is unstable unless the particles are prevented from moving, since the like-charged particles will repel each other until they are infinitely far apart, and oppositely charged bodies will attract one another and come together. The system has potential energy. The potential energy of two charged particles separated by a distance r can be shown to be given by Eq. (2).

See Energy, Potentials

Charging methods

The three principal methods of applying electric charge to objects are corona charging, induction charging, and tribocharging. See Energy

The corona-charging method relies upon the impact of charged atoms or molecules (ions) on charged bodies. Copious quantities of ions may be generated by a corona discharge, which is a region in which an intense electric field acts upon air molecules and ionizes them so that free ions are produced. A sharply pointed electrode maintained at a high positive or negative potential induces a stream of positive or negative ions which may be used for charging surfaces. The stream of ions from a corona point is usually so intense that neutral air molecules become entrained in the flow to produce a corona wind which can deflect a candle flame. Ions from a corona discharge may be used to charge isolated bodies, insulating surfaces or particles by simply directing a corona wind onto the surface to be charged. In the case of particles, it is normally sufficient for them to pass through a corona discharge region to receive a significant charge from ion-particle collisions.

Surfaces may be charged by exposure to an electrostatic field. If the surface is a liquid and it is disrupted into droplets, they will be electrically charged. Induction charging of equipment and personnel may occur when they are exposed to an electric field. Personnel charged in this way may generate electrostatic discharges when approaching grounded surfaces. Sensitive microelectronic devices can be damaged and computer data can be corrupted by such discharges.


Electrostatics is put to good use in a wide variety of applications. For examples, the electrostatic precipitator enables smoke emissions from power-station chimneys, smelting plants, and other industrial plants to be reduced to relatively low, acceptable levels. On a smaller scale, efficient filters exist for removing dust from the air in offices, public places, and the home. In some filters, dust particles undergo corona charging as they are sucked by a fan through a duct, and are then collected on grounded electrodes; in others, permanently electrified filter material is used, made from thin plastic sheets which have been treated by surface bombardment from a corona ion source.

In several applications which utilize electrostatics, solid or liquid particles are charged and sprayed onto grounded objects. Dry powder coating is used in many industries in preference to the wet-paint-spraying process. Crop spraying is another important application in which electrostatic forces help to efficiently apply herbicides or insecticides. Research into electrospraying, sometimes called electrohydrodynamic atomization, is leading to new applications for the deposition of ceramic, glass, and polymer films and for powder particle production of special materials. The electrospraying of materials is also used for analysis by means of mass spectrometry, as the electrospray process is gentle and does not disrupt delicate complex molecules.

In electrophotography an optical system is used to project the image to be copied onto a light-sensitive semiconducting surface precharged by a corona source. Exposure of the surface to light reduces the electrical conductivity of the material and allows surface charge to leak away to a back plate in proportion to the intensity of the light, so that bright parts of the image are regions that have lost most of the original charge while dark zones remain fully charged. A mixture of very fine black toner particles and coarser carrier particles is then brought into contact with the charged surface. Transfer of only charged toner particles onto the latent charged surface occurs. A sheet of paper is then laid over the toner-covered surface, and transfer of toner to paper occurs so that an image remains on the paper when it is peeled off the surface. Some ink-jet printers also utilize electrostatic principles; by ensuring that ink drops are formed in the presence of an electrostatic field, they become charged and may be deflected electrostatically to a printing surface.

Another development being commercially exploited is the production of metallic ion or droplet beams using electrostatic forces acting upon a liquid-metal surface. Considerable success has been achieved with many molten metals including gold and silver. Either ion or charged droplet beams may be formed depending on the operating conditions of the source. The beams so formed may be very well defined and directed with great accuracy onto targets where they can be used for ion implantation or for the formation of conducting tracks in the fabrication of microelectronic circuits.

Electrostatic treators using electric fields have been used to separate water droplets from crude oil as well as move and deposit inorganic particles of sand, mud, and clay and organic particles.

Ion engines which produce thrust by electrostatically accelerating mercury or cesium ions have been successfully operated in space. Colloid thrusters, operating on exactly the same principles as electrostatic paint or crop sprayers, have also been developed. In these a propellant such as glycerol is atomized and accelerated from a nozzle by an electrostatic field.



a branch of the theory of electricity that studies the interaction of electric charges at rest. The interaction is brought about by an electrostatic field. The fundamental law of electrostatics is Coulomb’s law, which asserts that the force behind the interaction of stationary point charges is dependent on the magnitude of the charges and the distance between them.

As indicated in Gauss’ theorem, the souces of an electrostatic field are electric charges. An electrostatic field is a potential field; that is, the work of the forces exerted on a charge by an electrostatic field does not depend on the path of the forces.

An electrostatic field satisfies the equations

div D = 4πρ curl E = 0

where D is the electric flux density (seeINDUCTION, ELECTRICAL AND MAGNETIC), E is the field strength of the electrostatic field, and p is the charge density. The first equation is a differential form of Gauss’ theorem, and the second is an expression of the potential nature of the electrostatic field. The equations can be derived as a special case of Maxwell’s equations.

Typical problems of electrostatics include finding the charge distribution on the surface of a conductor from the known total charge or from the potentials of each charge as well as computing the energy of a system of conductors from their charges and potentials.


Tamm, I. E. Osnovy teoriielektrichestva, 9th ed. Moscow, 1976.
Kalashnikov, S. G. Elektrichestvo, 4th ed. (Obshchii kurs fiziki). Moscow, 1977.



The study of electric charges at rest, their electric fields, and potentials.


the branch of physics concerned with static charges and the electrostatic field
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