Electric field

Electromagnetism

Electrostatics
· Electric charge · Coulomb’s law · Electric field · Electric flux · Gauss’ law · Electric potential · Electrostatic induction · Electric dipole moment ·

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In physics, the space surrounding an electric charge or in the presence of a time-varying magnetic field has a property called an electric field (that can also be equated to electric flux density). Electromagnetism is the Physics of the Electromagnetic field: a field which exerts a Force on particles that possess the property of In Physics, magnetism is one of the Phenomena by which Materials exert attractive or repulsive Forces on other Materials. Electrostatics is the branch of Science that deals with the Phenomena arising from what seems to be stationary Electric charges Since Classical Electric charge is a fundamental conserved property of some Subatomic particles which determines their Electromagnetic interaction. ---- Bold text Coulomb's law', developed in the 1780s by French physicist Charles Augustin de Coulomb, may be stated in scalar form In Electromagnetism, electric flux is Flux of the Electric field. At a point in space the electric potential is the Potential energy per unit of charge that is associated with a static (time-invariant Electric field Electrostatic induction is a redistribution of Electrical charge in an object caused by the influence of nearby charges In Physics, the electric dipole moment (or electric dipole for short is a measure of the polarity of a system of Electric charges. Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. Electric charge is a fundamental conserved property of some Subatomic particles which determines their Electromagnetic interaction. In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges This electric field exerts a force on other electrically charged objects. In Physics, a force is whatever can cause an object with Mass to Accelerate. The concept of electric field was introduced by Michael Faraday. Michael Faraday, FRS ( September 22 1791 – August 25 1867) was an English

The electric field is a vector field with SI units of newtons per coulomb (N C⁻¹) or, equivalently, volts per meter (V m⁻¹). In Mathematics a vector field is a construction in Vector calculus which associates a vector to every point in a (locally Euclidean space. The newton (symbol N) is the SI derived unit of Force, named after Isaac Newton in recognition of his work on Classical The coulomb (symbol C) is the SI unit of Electric charge. It is named after Charles-Augustin de Coulomb. The volt (symbol V) is the SI derived unit of electric Potential difference or Electromotive force. The metre or meter is a unit of Length. It is the basic unit of Length in the Metric system and in the International The strength of the field at a given point is defined as the force that would be exerted on a positive test charge of +1 coulomb placed at that point; the direction of the field is given by the direction of that force. In physical theories, a test particle is an idealized model of an object whose physical properties (usually Mass, Charge, or size) are assumed Electric fields contain electrical energy with energy density proportional to the square of the field intensity. Electric energy is the potential energy associated with the conservative Coulomb forces between Charged particles contained within a system, where Energy density is the amount of Energy stored in a given system or region of space per unit Volume, or per unit Mass, depending on the context although The electric field is to charge as gravitational acceleration is to mass and force density is to volume. In Fluid mechanics, the force density has the physical dimensions of force per unit volume

A moving charge has not just an electric field but also a magnetic field, and in general the electric and magnetic fields are not completely separate phenomena; what one observer perceives as an electric field, another observer in a different frame of reference perceives as a mixture of electric and magnetic fields. In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges See also Inertial frame A frame of reference in Physics, may refer to a Coordinate system or set of axes within which to For this reason, one speaks of "electromagnetism" or "electromagnetic fields. Electromagnetism is the Physics of the Electromagnetic field: a field which exerts a Force on particles that possess the property of The electromagnetic field is a physical field produced by electrically charged objects. " In quantum mechanics, disturbances in the electromagnetic fields are called photons, and the energy of photons is quantized. In Physics, the photon is the Elementary particle responsible for electromagnetic phenomena

very much stronger then gravitational fields. Gravitation is a natural Phenomenon by which objects with Mass attract one another

1 Definition
2 Coulomb's law
3 Time-varying fields
4 Properties (in electrostatics)
5 Energy in the electric field
6 Parallels between electrostatics and gravity
7 See also
8 External links

Definition

A stationary charged particle in an electric field experiences a force proportional to its charge given by the equation,

$\mathbf{F} = q[- \nabla \phi - \frac { \partial \mathbf{A} } { \partial t }]$

where the magnetic flux density is given by,

$\mathbf{B} = \nabla \times \mathbf{A}$

and where $- \nabla \phi$ is the Coulomb force. Electric charge is a fundamental conserved property of some Subatomic particles which determines their Electromagnetic interaction. In Physics, a force is whatever can cause an object with Mass to Accelerate. (See the section below).

Electric charge is a characteristic of some subatomic particles, and is quantized when expressed as a multiple of the so-called elementary charge e. Electrons by convention have a charge of -1, while protons have the opposite charge of +1. The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J The proton ( Greek πρῶτον / proton "first" is a Subatomic particle with an Electric charge of one positive Quarks have a fractional charge of −1/3 or +2/3. In Physics, a quark (kwɔrk kwɑːk or kwɑːrk is a type of Subatomic particle. The antiparticle equivalents of these have the opposite charge. There are other charged particles.

In general, same-sign charged particles repel one another, while different-sign charged particles attract. This is expressed quantitatively in Coulomb's law, which states the magnitude of the repelling force is proportional to the product of the two charges, and weakens proportionately to the square of the distance. ---- Bold text Coulomb's law', developed in the 1780s by French physicist Charles Augustin de Coulomb, may be stated in scalar form

The electric charge of a macroscopic object is the sum of the electric charges of its constituent particles. Often, the net electric charge is zero, since naturally the number of electrons in every atom is equal to the number of the protons, so their charges cancel out. Situations in which the net charge is non-zero are often referred to as static electricity. Furthermore, even when the net charge is zero, it can be distributed non-uniformly (e. g. , due to an external electric field), and then the material is said to be polarized, and the charge related to the polarization is known as bound charge (while the excess charge brought from outside is called free charge). An ordered motion of charged particles in a particular direction (in metals, these are the electrons) is known as electric current. The discrete nature of electric charge was proposed by Michael Faraday in his electrolysis experiments, then directly demonstrated by Robert Millikan in his oil-drop experiment.

The SI unit for quantity of electricity or electric charge is the coulomb, which represents approximately 1. 60 × 10¹⁹ elementary charges (the charge on a single electron or proton). The coulomb is defined as the quantity of charge that has passed through the cross-section of an electrical conductor carrying one ampere within one second. The symbol Q is often used to denote a quantity of electricity or charge. The quantity of electric charge can be directly measured with an electrometer, or indirectly measured with a ballistic galvanometer.

Formally, a measure of charge should be a multiple of the elementary charge e (charge is quantized), but since it is an average, macroscopic quantity, many orders of magnitude larger than a single elementary charge, it can effectively take on any real value. Furthermore, in some contexts it is meaningful to speak of fractions of a charge; e. g. in the charging of a capacitor.

If the charged particle can be considered a point charge, the electric field is defined as the force it experiences per unit charge:

$\mathbf{E} = \frac{\mathbf{F}}{q}$

where

$\mathbf{F}$ is the electric force experienced by the particle

q is its charge

$\mathbf{E}$ is the electric field wherein the particle is located

Taken literally, this equation only defines the electric field at the places where there are stationary charges present to experience it. A point charge is an idealized model of a particle which has an Electric charge. In Physics, a force is whatever can cause an object with Mass to Accelerate. Electric charge is a fundamental conserved property of some Subatomic particles which determines their Electromagnetic interaction. Furthermore, the force exerted by another charge $q$ will alter the source distribution, which means the electric field in the presence of $q$ differs from itself in the absence of $q$ . However, the electric field of a given source distribution remains defined in the absence of any charges with which to interact. This is achieved by measuring the force exerted on successively smaller test charges placed in the vicinity of the source distribution. In physical theories, a test particle is an idealized model of an object whose physical properties (usually Mass, Charge, or size) are assumed By this process, the electric field created by a given source distribution is defined as the limit as the test charge approaches zero of the force per unit charge exerted thereupon.

$\mathbf{E}=\lim_{q \to 0}\frac{\mathbf{F}}{q}$

This allows the electric field to be dependent on the source distribution alone.

As is clear from the definition, the direction of the electric field is the same as the direction of the force it would exert on a positively-charged particle, and opposite the direction of the force on a negatively-charged particle. Since like charges repel and opposites attract (as quantified below), the electric field tends to point away from positive charges and towards negative charges.

Coulomb's law

The electric field surrounding a point charge is given by Coulomb's law:

$\mathbf{E} =\frac{1}{4 \pi \varepsilon_0}\frac{Q}{r^2}\mathbf{\hat{r}} \qquad \mbox{(1)}$

where

Q is the charge of the particle creating the electric field,

r is the distance from the particle with charge Q to the E-field evaluation point,

$\mathbf{\hat{r}}$ is the Unit vector pointing from the particle with charge Q to the E-field evaluation point,

$\varepsilon_0$ is the vacuum permittivity. ---- Bold text Coulomb's law', developed in the 1780s by French physicist Charles Augustin de Coulomb, may be stated in scalar form In Mathematics, a unit vector in a Normed vector space is a vector (often a spatial vector) whose length is 1 (the unit length Vacuum permittivity, referred to by international standards organizations as the electric constant, and denoted by the symbol ε0 is a fundamental Physical

Coulomb's law is actually a special case of Gauss's Law, a more fundamental description of the relationship between the distribution of electric charge in space and the resulting electric field. ---- Bold text Coulomb's law', developed in the 1780s by French physicist Charles Augustin de Coulomb, may be stated in scalar form Gauss's law is one of Maxwell's equations, a set of four laws governing electromagnetics. In Classical electromagnetism, Maxwell's equations are a set of four Partial differential equations that describe the properties of the electric

Time-varying fields

Charges do not only produce electric fields. As they move, they generate magnetic fields, and if the magnetic field changes, it generates electric fields. In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges A changing magnetic field gives rise to an electric field,

$\mathbf{E} = - \nabla \phi - \frac { \partial \mathbf{A} } { \partial t }$

which yields Faraday's law of induction,

$\mathbf{\nabla} \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}$

where

$\mathbf{\nabla} \times \mathbf{E}$ indicates the curl of the electric field,

$-\frac{\partial \mathbf{B}} {\partial t}$ represents the vector rate of decrease of magnetic field with time. In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges Faraday's law of induction describes an important basic law of electromagnetism which is involved in the working of Transformers Inductors and many forms of cURL is a Command line tool for transferring files with URL syntax. In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges

This means that a magnetic field changing in time produces a curled electric field, possibly also changing in time. In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges The situation in which electric or magnetic fields change in time is no longer electrostatics, but rather electrodynamics or electromagnetics. Electrostatics is the branch of Science that deals with the Phenomena arising from what seems to be stationary Electric charges Since Classical Classical electromagnetism (or classical electrodynamics) is a theory of Electromagnetism that was developed over the course of the 19th century most prominently Electromagnetism is the Physics of the Electromagnetic field: a field which exerts a Force on particles that possess the property of

Properties (in electrostatics)

Illustration of the electric field surrounding a positive (red) and a negative (green) charge.

According to equation (1) above, electric field is dependent on position. The electric field due to any single charge falls off as the square of the distance from that charge.

Electric fields follow the superposition principle. In Physics and Systems theory, the superposition principle, also known as superposition property, states that for all Linear systems If more than one charge is present, the total electric field at any point is equal to the vector sum of the respective electric fields that each object would create in the absence of the others.

$\mathbf{E}_{\rm total} = \sum_i \mathbf{E}_i = \mathbf{E}_1 + \mathbf{E}_2 + \mathbf{E}_3 \ldots \,\!$

If this principle is extended to an infinite number of infinitesimally small elements of charge, the following formula results:

$\mathbf{E} = \frac{1}{4\pi\varepsilon_0} \int\frac{\rho}{r^2} \mathbf{\hat{r}}\,\mathrm{d}V$

where

ρ

is the charge density, or the amount of charge per unit volume. The linear surface or volume charge density is the amount of Electric charge in a line, Surface, or Volume. The volume of any solid plasma vacuum or theoretical object is how much three- Dimensional space it occupies often quantified numerically

The electric field at a point is equal to the negative gradient of the electric potential there. In Vector calculus, the gradient of a Scalar field is a Vector field which points in the direction of the greatest rate of increase of the scalar At a point in space the electric potential is the Potential energy per unit of charge that is associated with a static (time-invariant Electric field In symbols,

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

where

φ(x, y, z)

is the scalar field representing the electric potential at a given point. In Mathematics and Physics, a scalar field associates a scalar value which can be either mathematical in definition or physical, to every point

If several spatially distributed charges generate such an electric potential, e. At a point in space the electric potential is the Potential energy per unit of charge that is associated with a static (time-invariant Electric field g. in a solid, an electric field gradient may also be defined. A solid' object is in the States of matter characterized by resistance to Deformation and changes of Volume. Mathematically the electric field gradient (EFG is the Hessian matrix (the matrix of the second derivatives of the Electrical potential V

Considering the permittivity $\varepsilon$ of a material, which may differ from the permittivity of free space $\varepsilon_{0}$ , the electric displacement field is:

$\mathbf{D} = \varepsilon \mathbf{E}$

Energy in the electric field

Main article: Electrical energy

The electric field stores energy. Permittivity is a Physical quantity that describes how an Electric field affects and is affected by a Dielectric medium and is determined by the ability In Physics, the electric displacement field (also called electrical field/flux density is a Vector field \mathbf{D} that appears in Maxwell's equations Electric energy is the potential energy associated with the conservative Coulomb forces between Charged particles contained within a system, where The energy density of the electric field is given by

$u = \frac{1}{2} \varepsilon |\mathbf{E}|^2$

where

$\varepsilon$ is the permittivity of the medium in which the field exists

$\mathbf{E}$ is the electric field vector. Permittivity is a Physical quantity that describes how an Electric field affects and is affected by a Dielectric medium and is determined by the ability

The total energy stored in the electric field in a given volume V is therefore

$\int_{V} \frac{1}{2} \varepsilon |\mathbf{E}|^2 \, \mathrm{d}V$

where

d V

is the differential volume element.

Parallels between electrostatics and gravity

Coulomb's law, which describes the interaction of electric charges:

$\mathbf{F} = \frac{1}{4 \pi \varepsilon_0}\frac{Qq}{r^2}\mathbf{\hat{r}} = q\mathbf{E}$

is similar to the Newtonian gravitation law:

$\mathbf{F} = G\frac{Mm}{r^2}\mathbf{\hat{r}} = m\mathbf{g}$

This suggests similarities between the electric field $E$ and the gravitational field $g$ , so sometimes mass is called "gravitational charge". ---- Bold text Coulomb's law', developed in the 1780s by French physicist Charles Augustin de Coulomb, may be stated in scalar form

Similarities between electrostatic and gravitational forces:

Both act in a vacuum.
Both are central and conservative. In Classical mechanics, a central force is a force whose magnitude only depends on the Distance r of the object from the origin and A conservative force is defined as a Force with the following property when an object moves from one location to another the force changes the Potential energy of
Both obey an inverse-square law (both are inversely proportional to square of r). In Physics, an inverse-square law is any Physical law stating that some physical Quantity or strength is inversely proportional
Both propagate with finite speed c.

Differences between electrostatic and gravitational forces:

Electrostatic forces are much greater than gravitational forces (by about 10³⁶ times).
Gravitational forces are attractive for like charges, whereas electrostatic forces are repulsive for like charges.
There are no negative gravitational charges (no negative mass) while there are both positive and negative electric charges. Exotic matter is a hypothetical concept of Particle physics. It covers any material which violates one or more classical conditions or is not made of known baryonic particles This difference combined with previous implies that gravitational forces are always attractive, while electrostatic forces may be either attractive or repulsive.
Electric charge is invariant while relativistic mass isn't

External links

Fields - a chapter from an online textbook
Learning by Simulations Interactive simulation of an electric field of up to four point charges
Java simulations of electrostatics in 2-D and 3-D

In Physics, magnetism is one of the Phenomena by which Materials exert attractive or repulsive Forces on other Materials. A teltron tube (named for Teltron Inc which originally manufactured it before being bought by 3B Scientific Ltd

Dictionary

-noun

(electricity, physics) A region of space around a charged particle, or between two voltages; it exerts a force on charged objects in its vicinity.

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Contents

Definition

Coulomb's law

Time-varying fields

Properties (in electrostatics)

Energy in the electric field

Parallels between electrostatics and gravity

See also

External links

Dictionary

electric field

-noun