# Electrostatics

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Electrostatics is a branch of physics that studies electric charges at rest.

Physics is the natural science that studies matter and its motion and behavior through space and time and that studies the related entities of energy and force. Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves.

Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. There are two types of electric charges; positive and negative. Like charges repel and unlike attract. An object with an absence of net charge is referred to as neutral. Early knowledge of how charged substances interact is now called classical electrodynamics, and is still accurate for problems that do not require consideration of quantum effects.

## Contents

Since classical physics, it has been known that some materials such as amber attract lightweight particles after rubbing. The Greek word for amber, ήλεκτρον, or electron, was the source of the word 'electricity'. Electrostatic phenomena arise from the forces that electric charges exert on each other. Such forces are described by Coulomb's law. Even though electrostatically induced forces seem to be rather weak, some electrostatic forces such as the one between an electron and a proton, that together make up a hydrogen atom, is about 36 orders of magnitude stronger than the gravitational force acting between them.

Classical physics refers to theories of physics that predate modern, more complete, or more widely applicable theories. If a currently accepted theory is considered to be modern, and its introduction represented a major paradigm shift, then the previous theories, or new theories based on the older paradigm, will often be referred to as belonging to the realm of "classical physics".

Amber is fossilized tree resin, which has been appreciated for its color and natural beauty since Neolithic times. Much valued from antiquity to the present as a gemstone, amber is made into a variety of decorative objects. Amber is used in jewelry. It has also been used as a healing agent in folk medicine.

The triboelectric effect is a type of contact electrification on which certain materials become electrically charged after they are separated from a different material with which they were in contact. Rubbing the two materials each with the other increases the contact between their surfaces, and hence the triboelectric effect. Rubbing glass with fur for example, or a plastic comb through the hair, can build up triboelectricity. Most everyday static electricity is triboelectric. The polarity and strength of the charges produced differ according to the materials, surface roughness, temperature, strain, and other properties.

There are many examples of electrostatic phenomena, from those as simple as the attraction of the plastic wrap to one's hand after it is removed from a package to the apparently spontaneous explosion of grain silos, the damage of electronic components during manufacturing, and photocopier & laser printer operation. Electrostatics involves the buildup of charge on the surface of objects due to contact with other surfaces. Although charge exchange happens whenever any two surfaces contact and separate, the effects of charge exchange are usually only noticed when at least one of the surfaces has a high resistance to electrical flow. This is because the charges that transfer are trapped there for a time long enough for their effects to be observed. These charges then remain on the object until they either bleed off to ground or are quickly neutralized by a discharge: e.g., the familiar phenomenon of a static 'shock' is caused by the neutralization of charge built up in the body from contact with insulated surfaces.

A photocopier is a machine that makes copies of documents and other visual images onto paper or plastic film quickly and cheaply. Most modern photocopiers use a technology called xerography, a dry process that uses electrostatic charges on a light-sensitive photoreceptor to first attract and then transfer toner particles onto paper in the form of an image. Heat, pressure or a combination of both is then used to fuse the toner onto the paper. Copiers can also use other technologies such as ink jet, but xerography is standard for office copying. Earlier versions included the Gestetner stencil duplicator, invented by David Gestetner in 1881.

Laser printing is an electrostatic digital printing process. It produces high-quality text and graphics by repeatedly passing a laser beam back and forth over a negatively charged cylinder called a "drum" to define a differentially charged image. The drum then selectively collects electrically charged powdered ink (toner), and transfers the image to paper, which is then heated in order to permanently fuse the text, imagery, or both. As with digital photocopiers, laser printers employ a xerographic printing process. However, laser printing differs from analog photocopiers in that the image is produced by the direct scanning of the medium across the printer's photoreceptor. This enables laser printing to copy images more quickly than most photocopiers.

In the physical sciences, an interface is the boundary between two spatial regions occupied by different matter, or by matter in different physical states. The interface between matter and air, or matter and vacuum, is called a surface, and studied in surface science. In thermal equilibrium, the regions in contact are called phases, and the interface is called a phase boundary. An example for an interface out of equilibrium is the grain boundary in polycrystalline matter.

## Coulomb's law

Coulomb's law states that:

'The magnitude of the electrostatic force of attraction or repulsion between two point charges is directly proportional to the product of the magnitudes of charges and inversely proportional to the square of the distance between them.'

The force is along the straight line joining them. If the two charges have the same sign, the electrostatic force between them is repulsive; if they have different signs, the force between them is attractive.

If ${\displaystyle r}$ is the distance (in meters) between two charges, then the force (in newtons) between two point charges ${\displaystyle q}$ and ${\displaystyle Q}$ (in coulombs) is:

The newton is the International System of Units (SI) derived unit of force. It is named after Isaac Newton in recognition of his work on classical mechanics, specifically Newton's second law of motion.

The coulomb is the International System of Units (SI) unit of electric charge. It is the charge transported by a constant current of one ampere in one second:

${\displaystyle F={\frac {1}{4\pi \varepsilon _{0}}}{\frac {qQ}{r^{2}}}=k_{0}{\frac {qQ}{r^{2}}}\,,}$

where ε0 is the vacuum permittivity, or permittivity of free space: [1]

The physical constant ε0, commonly called the vacuum permittivity, permittivity of free space or electric constant or the distributed capacitance of the vacuum, is an ideal, (baseline) physical constant, which is the value of the absolute dielectric permittivity of classical vacuum. It has an exactly defined value that can be approximated as

${\displaystyle \varepsilon _{0}\approx {10^{-9} \over 36\pi }\;\;\mathrm {C^{2}\ N^{-1}\ m^{-2}} \approx 8.854\ 187\ 817\times 10^{-12}\;\;\mathrm {C^{2}\ N^{-1}\ m^{-2}} .}$

The SI units of ε0 are equivalently A 2 s 4 kg−1m−3 or C 2 N 1m2 or F m1. Coulomb's constant is:

The International System of Units is the modern form of the metric system, and is the most widely used system of measurement. It comprises a coherent system of units of measurement built on seven base units, which are the ampere, kelvin, second, metre, kilogram, candela, mole, and a set of twenty prefixes to the unit names and unit symbols that may be used when specifying multiples and fractions of the units. The system also specifies names for 22 derived units, such as lumen and watt, for other common physical quantities.

The ampere, often shortened to "amp", is the base unit of electric current in the International System of Units (SI). It is named after André-Marie Ampère (1775–1836), French mathematician and physicist, considered the father of electrodynamics.

The second is the base unit of time in the International System of Units (SI), commonly understood and historically defined as ​186400 of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally to 60 seconds each. Mechanical and electric clocks and watches usually have a face with 60 tickmarks representing seconds and minutes, traversed by a second hand and minute hand. Digital clocks and watches often have a two-digit counter that cycles through seconds. The second is also part of several other units of measurement like meters per second for velocity, meters per second per second for acceleration, and per second for frequency.

${\displaystyle k_{0}={\frac {1}{4\pi \varepsilon _{0}}}\approx 8.987\ 551\ 787\times 10^{9}\;\;\mathrm {N\ m^{2}\ C} ^{-2}.}$

A single proton has a charge of e, and the electron has a charge of −e, where,

${\displaystyle e\approx 1.602\ 176\ 565\times 10^{-19}\;\;\mathrm {C} .}$

These physical constants0, k0, e) are currently defined so that ε0 and k0 are exactly defined, and e is a measured quantity.

## Electric field

The electric field, ${\displaystyle {\vec {E}}}$, in units of newtons per coulomb or volts per meter, is a vector field that can be defined everywhere, except at the location of point charges (where it diverges to infinity). [2] It is defined as the electrostatic force ${\displaystyle {\vec {F}}\,}$ in newtons on a hypothetical small test charge at the point due to Coulomb's Law, divided by the magnitude of the charge ${\displaystyle q\,}$ in coulombs

${\displaystyle {\vec {E}}={{\vec {F}} \over q}\,}$

Electric field lines are useful for visualizing the electric field. Field lines begin on positive charge and terminate on negative charge. They are parallel to the direction of the electric field at each point, and the density of these field lines is a measure of the magnitude of the electric field at any given point.

Consider a collection of ${\displaystyle N}$ particles of charge ${\displaystyle Q_{i}}$, located at points ${\displaystyle {\vec {r}}_{i}}$ (called source points), the electric field at ${\displaystyle {\vec {r}}}$ (called the field point) is: [2]

${\displaystyle {\vec {E}}({\vec {r}})={\frac {1}{4\pi \varepsilon _{0}}}\sum _{i=1}^{N}{\frac {{\widehat {\mathcal {R}}}_{i}Q_{i}}{\left\|{\mathcal {\vec {R}}}_{i}\right\|^{2}}},}$

where ${\displaystyle {\vec {\mathcal {R}}}_{i}={\vec {r}}-{\vec {r}}_{i},}$ is the displacement vector from a source point${\displaystyle {\vec {r}}_{i}}$ to the field point${\displaystyle {\vec {r}}}$, and ${\displaystyle {\widehat {\mathcal {R}}}_{i}={\vec {\mathcal {R}}}_{i}/\left\|{\vec {\mathcal {R}}}_{i}\right\|}$ is a unit vector that indicates the direction of the field. For a single point charge at the origin, the magnitude of this electric field is ${\displaystyle E=k_{e}Q/{\mathcal {R}}^{2},}$ and points away from that charge is positive. The fact that the force (and hence the field) can be calculated by summing over all the contributions due to individual source particles is an example of the superposition principle. The electric field produced by a distribution of charges is given by the volume charge density ${\displaystyle \rho ({\vec {r}})}$ and can be obtained by converting this sum into a triple integral:

${\displaystyle {\vec {E}}({\vec {r}})={\frac {1}{4\pi \varepsilon _{0}}}\iiint {\frac {{\vec {r}}-{\vec {r}}\,'}{\left\|{\vec {r}}-{\vec {r}}\,'\right\|^{3}}}\rho ({\vec {r}}\,')\operatorname {d} ^{3}r\,'}$

### Gauss' law

Gauss' law states that "the total electric flux through any closed surface in free space of any shape drawn in an electric field is proportional to the total electric charge enclosed by the surface." Mathematically, Gauss's law takes the form of an integral equation:

${\displaystyle \oint _{S}{\vec {E}}\cdot \mathrm {d} {\vec {A}}={\frac {1}{\varepsilon _{0}}}\,Q_{enclosed}=\int _{V}{\rho \over \varepsilon _{0}}\cdot \operatorname {d} ^{3}r,}$

where ${\displaystyle \operatorname {d} ^{3}r=\mathrm {d} x\ \mathrm {d} y\ \mathrm {d} z}$ is a volume element. If the charge is distributed over a surface or along a line, replace ${\displaystyle \rho \mathrm {d} ^{3}r}$ by ${\displaystyle \sigma \mathrm {d} A}$ or ${\displaystyle \lambda \mathrm {d} \ell }$. The Divergence Theorem allows Gauss's Law to be written in differential form:

${\displaystyle {\vec {\nabla }}\cdot {\vec {E}}={\rho \over \varepsilon _{0}}.}$

where ${\displaystyle {\vec {\nabla }}\cdot }$ is the divergence operator.

### Poisson and Laplace equations

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:

${\displaystyle {\nabla }^{2}\phi =-{\rho \over \varepsilon _{0}}.}$

This relationship is a form of Poisson's equation. In the absence of unpaired electric charge, the equation becomes Laplace's equation:

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

## 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. Electrostatics and magnetostatics can both be seen as Galilean limits for electromagnetism. [3] [ verification needed ]

### Electrostatic potential

Because the electric field is irrotational, it is possible to express the electric field as the gradient of a scalar function,${\displaystyle \phi }$, called the electrostatic potential (also known as the voltage). An electric field, ${\displaystyle E}$, points from regions of high electric potential to regions of low electric potential, expressed mathematically as

${\displaystyle {\vec {E}}=-{\vec {\nabla }}\phi .}$

The gradient theorem can be used to establish that the electrostatic potential is the amount of work per unit charge required to move a charge from point ${\displaystyle a}$ to point ${\displaystyle b}$ with the following line integral:

${\displaystyle -\int _{a}^{b}{{\vec {E}}\cdot \mathrm {d} {\vec {\ell }}}=\phi ({\vec {b}})-\phi ({\vec {a}}).}$

From these equations, we see that the electric potential is constant in any region for which the electric field vanishes (such as occurs inside a conducting object).

### Electrostatic energy

A single test particle's potential energy, ${\displaystyle U_{\mathrm {E} }^{\text{single}}}$, can be calculated from a line integral of the work, ${\displaystyle q_{n}{\vec {E}}\cdot \mathrm {d} {\vec {\ell }}}$. We integrate from a point at infinity, and assume a collection of ${\displaystyle N}$ particles of charge ${\displaystyle Q_{n}}$, are already situated at the points ${\displaystyle {\vec {r}}_{i}}$. This potential energy (in Joules) is:

${\displaystyle U_{\mathrm {E} }^{\text{single}}=q\phi ({\vec {r}})={\frac {q}{4\pi \varepsilon _{0}}}\sum _{i=1}^{N}{\frac {Q_{i}}{\left\|{\mathcal {{\vec {R}}_{i}}}\right\|}}}$

where ${\displaystyle {\vec {\mathcal {R_{i}}}}={\vec {r}}-{\vec {r}}_{i}}$ is the distance of each charge ${\displaystyle Q_{i}}$ from the test charge ${\displaystyle q}$, which situated at the point ${\displaystyle {\vec {r}}}$, and ${\displaystyle \phi ({\vec {r}})}$ is the electric potential that would be at ${\displaystyle {\vec {r}}}$ if the test charge were not present. If only two charges are present, the potential energy is ${\displaystyle k_{e}Q_{1}Q_{2}/r}$. The total electric potential energy due a collection of N charges is calculating by assembling these particles one at a time:

${\displaystyle U_{\mathrm {E} }^{\text{total}}={\frac {1}{4\pi \varepsilon _{0}}}\sum _{j=1}^{N}Q_{j}\sum _{i=1}^{j-1}{\frac {Q_{i}}{r_{ij}}}={\frac {1}{2}}\sum _{i=1}^{N}Q_{i}\phi _{i},}$

where the following sum from, j = 1 to N, excludes i = j:

${\displaystyle \phi _{i}={\frac {1}{4\pi \varepsilon _{0}}}\sum _{j=1(j\neq i)}^{N}{\frac {Q_{j}}{r_{ij}}}.}$

This electric potential, ${\displaystyle \phi _{i}}$ is what would be measured at ${\displaystyle {\vec {r}}_{i}}$ if the charge ${\displaystyle Q_{i}}$ were missing. This formula obviously excludes the (infinite) energy that would be required to assemble each point charge from a disperse cloud of charge. The sum over charges can be converted into an integral over charge density using the prescription ${\displaystyle \sum (\cdots )\rightarrow \int (\cdots )\rho \mathrm {d} ^{3}r}$:

${\displaystyle U_{\mathrm {E} }^{\text{total}}={\frac {1}{2}}\int \rho ({\vec {r}})\phi ({\vec {r}})\operatorname {d} ^{3}r={\frac {\varepsilon _{0}}{2}}\int \left|{\mathbf {E} }\right|^{2}\operatorname {d} ^{3}r}$,

This second expression for electrostatic energy uses the fact that the electric field is the negative gradient of the electric potential, as well as vector calculus identities in a way that resembles integration by parts. These two integrals for electric field energy seem to indicate two mutually exclusive formulas for electrostatic energy density, namely ${\displaystyle {\frac {1}{2}}\rho \phi }$ and ${\displaystyle {\frac {\varepsilon _{0}}{2}}E^{2}}$; they yield equal values for the total electrostatic energy only if both are integrated over all space.

### Electrostatic pressure

On a conductor, a surface charge will experience a force in the presence of an electric field. This force is the average of the discontinuous electric field at the surface charge. This average in terms of the field just outside the surface amounts to:

${\displaystyle P={\frac {\varepsilon _{0}}{2}}E^{2}}$,

This pressure tends to draw the conductor into the field, regardless of the sign of the surface charge.

## Triboelectric series

The triboelectric effect is a type of contact electrification in which certain materials become electrically charged when they are brought into contact with a different material and then separated. One of the materials acquires a positive charge, and the other acquires an equal negative charge. The polarity and strength of the charges produced differ according to the materials, surface roughness, temperature, strain, and other properties. Amber, for example, can acquire an electric charge by friction with a material like wool. This property, first recorded by Thales of Miletus, was the first electrical phenomenon investigated by humans. 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 yields 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 nonconductive objects generates a great amount of static electricity. This is not just the result of friction; two nonconductive 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 neutralization

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).

## Electrostatic induction

Electrostatic induction, discovered by British scientist John Canton in 1753 and Swedish professor Johan Carl Wilcke in 1762 [4] [5] [6] is a redistribution of charges in an object caused by the electric field of a nearby charge. For example, if a positively charged object is brought near an uncharged metal object, the mobile negatively-charged electrons in the metal will be attracted the external charge, and move to the side of the metal facing it, creating a negative charge on the surface. When the electrons move out of an area they leave a positive charge due to the metal atoms' nuclei, so the side of the metal object facing away from the charge acquires a positive charge. These induced charges disappear when the external charge is removed. Induction is also responsible for the attraction of light objects, such as balloons, paper scraps and styrofoam packing peanuts to static charges. The surface charges induced in conductive objects exactly cancel external electric fields inside the conductor, so there is no electric field inside a metal object. This is the basis for the electric field shielding action of a Faraday cage. Since the electric field is the gradient of the voltage, electrostatic induction is also responsible for making the electric potential (voltage) constant throughout a conductive object.

## 'Static' electricity

Before the year 1832, when Michael Faraday published the results of his experiment on the identity of electricities, physicists thought "static electricity" was somehow different from other electrical charges. Michael Faraday proved that the electricity induced from the magnet, voltaic electricity produced by a battery, and static electricity are all the same.

Static electricity is usually caused when certain materials are rubbed against each other, like wool on plastic or the soles of shoes on carpet. The process causes electrons to be pulled from the surface of one material and relocated on the surface of the other material.

A static shock occurs when the surface of the second material, negatively charged with electrons, touches a positively charged conductor, or vice versa.

Static electricity is commonly used in xerography, air filters, and some automotive paints. Static electricity is a buildup of electric charges on two objects that have become separated from each other. Small electrical components can easily be damaged by static electricity. Component manufacturers use a number of antistatic devices to avoid this.

### Static electricity and chemical industry

When different materials are brought together and then separated, an accumulation of electric charge can occur which leaves one material positively charged while the other becomes negatively charged. The mild shock that you receive when touching a grounded object after walking on carpet is an example of excess electrical charge accumulating in your body from frictional charging between your shoes and the carpet. The resulting charge build-up upon your body can generate a strong electrical discharge. Although experimenting with static electricity may be fun, similar sparks create severe hazards in those industries dealing with flammable substances, where a small electrical spark may ignite explosive mixtures with devastating consequences.

A similar charging mechanism can occur within low conductivity fluids flowing through pipelines—a process called flow electrification. Fluids which have low electrical conductivity (below 50 picosiemens per meter), are called accumulators. Fluids having conductivities above 50 pS/m are called non-accumulators. In non-accumulators, charges recombine as fast as they are separated and hence electrostatic charge generation is not significant. In the petrochemical industry, 50 pS/m is the recommended minimum value of electrical conductivity for adequate removal of charge from a fluid.

An important concept for insulating fluids is the static relaxation time. This is similar to the time constant (tau) within an RC circuit. For insulating materials, it is the ratio of the static dielectric constant divided by the electrical conductivity of the material. For hydrocarbon fluids, this is sometimes approximated by dividing the number 18 by the electrical conductivity of the fluid. Thus a fluid that has an electrical conductivity of 1 pS/cm (100 pS/m) will have an estimated relaxation time of about 18 seconds. The excess charge within a fluid will be almost completely dissipated after 4 to 5 times the relaxation time, or 90 seconds for the fluid in the above example.

Charge generation increases at higher fluid velocities and larger pipe diameters, becoming quite significant in pipes 8 inches (200 mm) or larger. Static charge generation in these systems is best controlled by limiting fluid velocity. The British standard BS PD CLC/TR 50404:2003 (formerly BS-5958-Part 2) Code of Practice for Control of Undesirable Static Electricity prescribes velocity limits. Because of its large impact on dielectric constant, the recommended velocity for hydrocarbon fluids containing water should be limited to 1 m/s.

Bonding and earthing are the usual ways by which charge buildup can be prevented. For fluids with electrical conductivity below 10 pS/m, bonding and earthing are not adequate for charge dissipation, and anti-static additives may be required.

#### Applicable standards

1.BS PD CLC/TR 50404:2003 Code of Practice for Control of Undesirable Static Electricity

2.NFPA 77 (2007) Recommended Practice on Static Electricity

3.API RP 2003 (1998) Protection Against Ignitions Arising Out of Static, Lightning, and Stray Currents

## Electrostatic induction in commercial applications

Electrostatic induction was used in the past to build high-voltage generators known as influence machines. The main component that emerged in these times is the capacitor. Electrostatic induction is also used for electro-mechanic precipitation or projection.In such technologies, charged particles of small sizes are collected or deposited intentionally on surfaces. Applications range from Electrostatic precipitator to Spray painting or Inkjet printing. Recently a new Wireless power Transfer Technology has been based on electrostatic induction between oscillating distant dipoles.

## Related Research Articles

An electric field is a vector field surrounding an electric charge that exerts force on other charges, attracting or repelling them. Mathematically the electric field is a vector field that associates to each point in space the force, called the Coulomb force, that would be experienced per unit of charge by an infinitesimal test charge at that point. The units of the electric field in the SI system are newtons per coulomb (N/C), or volts per meter (V/m). Electric fields are created by electric charges, or by time-varying magnetic fields. Electric fields are important in many areas of physics, and are exploited practically in electrical technology. On an atomic scale, the electric field is responsible for the attractive force between the atomic nucleus and electrons that holds atoms together, and the forces between atoms that cause chemical bonding. Electric fields and magnetic fields are both manifestations of the electromagnetic force, one of the four fundamental forces of nature.

Flux describes any effect that appears to pass or travel through a surface or substance. A flux is either a concept based in physics or used with applied mathematics. Both concepts have mathematical rigor, enabling comparison of the underlying mathematics when the terminology is unclear. For transport phenomena, flux is a vector quantity, describing the magnitude and direction of the flow of a substance or property. In electromagnetism, flux is a scalar quantity, defined as the surface integral of the component of a vector field perpendicular to the surface at each point.

In electromagnetism, absolute permittivity, often simply called permittivity, usually denoted by the Greek letter ε (epsilon), is the measure of capacitance that is encountered when forming an electric field in a particular medium. More specifically, permittivity describes the amount of charge needed to generate one unit of electric flux in a particular medium. Accordingly, a charge will yield more electric flux in a medium with low permittivity than in a medium with high permittivity. Permittivity is the measure of a material's ability to store an electric field in the polarization of the medium.

An electric potential is the amount of work needed to move a unit of positive charge from a reference point to a specific point inside the field without producing an acceleration. Typically, the reference point is the Earth or a point at infinity, although any point beyond the influence of the electric field charge can be used.

In physics, Gauss's law, also known as Gauss's flux theorem, is a law relating the distribution of electric charge to the resulting electric field. The surface under consideration may be a closed one enclosing a volume such as a spherical surface.

Noether's (first) theorem states that every differentiable symmetry of the action of a physical system has a corresponding conservation law. The theorem was proven by mathematician Emmy Noether in 1915 and published in 1918, although a special case was proven by E. Cosserat & F. Cosserat in 1909. The action of a physical system is the integral over time of a Lagrangian function, from which the system's behavior can be determined by the principle of least action. This theorem only applies to continuous and smooth symmetries over physical space.

Synchrotron radiation is the electromagnetic radiation emitted when charged particles are accelerated radially, i.e., when they are subject to an acceleration perpendicular to their velocity. It is produced, for example, in synchrotrons using bending magnets, undulators and/or wigglers. If the particle is non-relativistic, then the emission is called cyclotron emission. If, on the other hand, the particles are relativistic, sometimes referred to as ultrarelativistic, the emission is called synchrotron emission. Synchrotron radiation may be achieved artificially in synchrotrons or storage rings, or naturally by fast electrons moving through magnetic fields. The radiation produced in this way has a characteristic polarization and the frequencies generated can range over the entire electromagnetic spectrum which is also called continuum radiation.

In physics, screening is the damping of electric fields caused by the presence of mobile charge carriers. It is an important part of the behavior of charge-carrying fluids, such as ionized gases, electrolytes, and charge carriers in electronic conductors . In a fluid, with a given permittivity ε, composed of electrically charged constituent particles, each pair of particles interact through the Coulomb force as

In mathematics, Poisson's equation is a partial differential equation of elliptic type with broad utility in mechanical engineering and theoretical physics. It arises, for instance, to describe the potential field caused by a given charge or mass density distribution; with the potential field known, one can then calculate gravitational or electrostatic field. It is a generalization of Laplace's equation, which is also frequently seen in physics. The equation is named after the French mathematician, geometer, and physicist Siméon Denis Poisson.

Classical electromagnetism or classical electrodynamics is a branch of theoretical physics that studies the interactions between electric charges and currents using an extension of the classical Newtonian model. The theory provides a description of electromagnetic phenomena whenever the relevant length scales and field strengths are large enough that quantum mechanical effects are negligible. For small distances and low field strengths, such interactions are better described by quantum electrodynamics.

In electromagnetism, displacement current density is the quantity D/∂t appearing in Maxwell's equations that is defined in terms of the rate of change of D, the electric displacement field. Displacement current density has the same units as electric current density, and it is a source of the magnetic field just as actual current is. However it is not an electric current of moving charges, but a time-varying electric field. In physical materials, there is also a contribution from the slight motion of charges bound in atoms, called dielectric polarization.

In plasmas and electrolytes, the Debye length, named after Peter Debye, is a measure of a charge carrier's net electrostatic effect in solution and how far its electrostatic effect persists. A Debye sphere is a volume whose radius is the Debye length. With each Debye length, charges are increasingly electrically screened. Every Debye‐length , the electric potential will decrease in magnitude by 1/e. Debye length is an important parameter in plasma physics, electrolytes, and colloids. The corresponding Debye screening wave vector for particles of density , charge at a temperature is given by in Gaussian units. Expressions in MKS units will be given below. The analogous quantities at very low temperatures are known as the Thomas-Fermi length and the Thomas-Fermi wave vector. They are of interest in describing the behaviour of electrons in metals at room temperature.

Electric potential energy, or electrostatic potential energy, is a potential energy that results from conservative Coulomb forces and is associated with the configuration of a particular set of point charges within a defined system. An object may have electric potential energy by virtue of two key elements: its own electric charge and its relative position to other electrically charged objects.

The chemists Peter Debye and Erich Hückel noticed that solutions that contain ionic solutes do not behave ideally even at very low concentrations. So, while the concentration of the solutes is fundamental to the calculation of the dynamics of a solution, they theorized that an extra factor that they termed gamma is necessary to the calculation of the activity coefficients of the solution. Hence they developed the Debye–Hückel equation and Debye–Hückel limiting law. The activity is only proportional to the concentration and is altered by a factor known as the activity coefficient . This factor takes into account the interaction energy of ions in solution.

The Coulomb constant, the electric force constant, or the electrostatic constant (denoted ke, k or K) is a proportionality constant in electrodynamics equations. In SI units, it is exactly equal to 8987551787.3681764 N·m2·C−2, or approximately 8.99×109 N·m2·C−2. It was named after the French physicist Charles-Augustin de Coulomb (1736–1806) who introduced Coulomb's law.

A Gaussian surface is a closed surface in three-dimensional space through which the flux of a vector field is calculated; usually the gravitational field, the electric field, or magnetic field. It is an arbitrary closed surface S = ∂V used in conjunction with Gauss's law for the corresponding field by performing a surface integral, in order to calculate the total amount of the source quantity enclosed; e.g., amount of gravitational mass as the source of the gravitational field or amount of electric charge as the source of the electrostatic field, or vice versa: calculate the fields for the source distribution.

The method of image charges is a basic problem-solving tool in electrostatics. The name originates from the replacement of certain elements in the original layout with imaginary charges, which replicates the boundary conditions of the problem.

Spherical multipole moments are the coefficients in a series expansion of a potential that varies inversely with the distance R to a source, i.e., as 1/R. Examples of such potentials are the electric potential, the magnetic potential and the gravitational potential.

Coulomb's law, or Coulomb's inverse-square law, is a law of physics for quantifying Coulomb's force, or electrostatic force. Electrostatic force is the amount of force with which stationary, electrically charged particles either repel, or attract each other. This force and the law for quantifying it, represent one of the most basic forms of force used in the physical sciences, and were an essential basis to the study and development of the theory and field of classical electromagnetism. The law was first published in 1785 by French physicist Charles-Augustin de Coulomb.

The electric dipole moment is a measure of the separation of positive and negative electrical charges within a system, that is, a measure of the system's overall polarity. The SI units for electric dipole moment are coulomb-meter (C⋅m); however, the most commonly used unit in atomic physics and chemistry is the debye (D).

## 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.
• Griffiths, David J. (1999). Introduction to Electrodynamics. Upper Saddle River, NJ: Prentice Hall. ISBN   0-13-805326-X.
• Hermann A. Haus; James R. Melcher (1989). Electromagnetic Fields and Energy. Englewood Cliffs, NJ: Prentice-Hall. ISBN   0-13-249020-X.
1. Matthew Sadiku (2009). Elements of electromagnetics. p. 104. ISBN   9780195387759.
2. Purcell, Edward M. (2013). Electricity and Magnetism. Cambridge University Press. pp. 16–18. ISBN   1107014026.
3. Heras, J. A. (2010). "The Galilean limits of Maxwell's equations". American Journal of Physics . 78 (10): 1048. arXiv:. Bibcode:2010AmJPh..78.1048H. doi:10.1119/1.3442798.
4. "Electricity". Encyclopaedia Britannica, 11th Ed. 9. The Encyclopaedia Britannica Co. 1910. p. 181. Retrieved 2008-06-23.
5. Heilbron, J. L. (1979). Electricity in the 17th and 18th Centuries: A Study of Early Modern Physics. Univ. of California Press. ISBN   0520034783.
6. Sarkar, T. K.; Mailloux, Robert; Oliner, Arthur A., Ed. (2006). History of Wireless. John Wiley and Sons. p. 9. ISBN   0471783013.
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