Electromagnetism

Electricity · Magnetism Electrostatics Electric charge · Coulomb's law Electric field · Gauss' law Electric potential · Electrostatic induction Electric dipole moment Magnetostatics Ampère's law · Electric current Magnetic field · Magnetic flux Biot-Savart law Magnetic dipole moment Gauss's law for magnetism Electrodynamics Free space Lorentz force law EMF · Electromagnetic induction Faraday's law · Displacement current Maxwell's equations · EM field Electromagnetic radiation Liénard-Wiechert Potentials Maxwell tensor · Eddy current Electrical Network Electrical conduction · Electrical resistance · Capacitance · Inductance · Impedance · Resonant cavities · Waveguides Covariant formulation Electromagnetic tensor EM Stress-energy tensor Four-current · Four-potential Scientists · Ampere · Coulomb · Faraday · Heaviside · Henry · Hertz · Lorentz · Maxwell · Weber

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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. It is typically measured in volts, and is a Lorentz scalar quantity. The difference in electrical potential between two points is known as voltage. Electromagnetism is the physics of the electromagnetic field: a field which exerts a force on particles that possess the property of electric charge, and is in turn affected by the presence and motion of those particles. ... Image File history File links Solenoid. ... Electricity (from New Latin Ä“lectricus, amberlike) is a general term for a variety of phenomena resulting from the presence and flow of electric charge. ... For other senses of this word, see magnetism (disambiguation). ... Electrostatics (also known as static electricity) is the branch of physics that deals with the phenomena arising from what seem to be stationary electric charges. ... This box:      Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. ... This box:      Coulombs torsion balance Coulombs law, developed in the 1780s by French physicist Charles Augustin de Coulomb, may be stated in scalar form as follows: The magnitude of the electrostatic force between two point electric charges is directly proportional to the product of the magnitudes of each... 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. ... In physics, Gausss law gives the relation between the electric flux flowing out a closed surface and the charge enclosed in the surface. ... Electrostatic induction is a method by which an electrically charged object can be used to create an electrical charge in a second object, without contact between the two objects. ... This article is about the electromagnetic phenomenon. ... Magnetostatics is the study of static magnetic fields. ... In physics, Ampères Circuital law, discovered by André-Marie Ampère, relates the circulating magnetic field in a closed loop to the electric current passing through the loop. ... This box:      Electric current is the flow (movement) of electric charge. ... For the indie-pop band, see The Magnetic Fields. ... Magnetic flux, represented by the Greek letter Φ (phi), is a measure of quantity of magnetism, taking account of the strength and the extent of a magnetic field. ... The Biot-Savart law is a physical law with applications in both electromagnetics and fluid dynamics. ... A bar magnet. ... Classical electrodynamics (or classical electromagnetism) is a theory of electromagnetism that was developed over the course of the 19th century, most prominently by James Clerk Maxwell. ... In physics, free space is a concept of electromagnetic theory, corresponding roughly to the vacuum, the baseline state of the electromagnetic field, or the replacement for the electromagnetic aether. ... Lorentz force. ... Electromotive force (emf) is the amount of energy gained per unit charge that passes through a device in the opposite direction to the electric field existing across that device. ... For magnetic induction, see Magnetic field. ... Faradays law of induction (more generally, the law of electromagnetic induction) states that the induced emf (electromotive force) in a closed loop equals the negative of the time rate of change of magnetic flux through the loop. ... Displacement current is a quantity related to changing electric field. ... For thermodynamic relations, see Maxwell relations. ... The electromagnetic field is a physical field that is produced by electrically charged objects and which affects the behaviour of charged objects in the vicinity of the field. ... This box:      Electromagnetic (EM) radiation is a self-propagating wave in space with electric and magnetic components. ... The Liénard-Wiechert potential describes the electromagnetic effect of a moving charge. ... In physics, the Maxwell stress tensor is the stress tensor of an electromagnetic field. ... As the circular plate moves down through a small region of constant magnetic field directed into the page, eddy currents are induced in the plate. ... A simple electric circuit made up of a voltage source and a resistor. ... Conduction is the movement of electrically charged particles through a transmission medium (electrical conductor). ... Electrical resistance is a measure of the degree to which an electrical component opposes the passage of current. ... Capacitance is a measure of the amount of electric charge stored (or separated) for a given electric potential. ... An electric current i flowing around a circuit produces a magnetic field and hence a magnetic flux Φ through the circuit. ... Electrical impedance, or simply impedance, is a measure of opposition to a sinusoidal alternating electric current. ... A resonator is a device or part that vibrates (or oscillates) with waves. ... This box:      This page is about waveguides for electromagnetic wave propagation at microwave and radio wave frequencies. ... In special relativity, in order to more clearly express the fact that Maxwells equations (in vacuum) take the same form in any inertial coordinate system, the vacuum Maxwells equations are written in terms of four-vectors and tensors in the manifestly covariant form (cgs units): , and where is... This box:      The electromagnetic tensor or electromagnetic field tensor (sometimes called the field strength tensor, Faraday tensor or Maxwell bivector) is a mathematical object that describes the electromagnetic field of a physical system in Maxwells theory of electromagnetism. ... In physics, the electromagnetic stress-energy tensor is the portion of the stress-energy tensor due to the electromagnetic field. ... In special and general relativity, the four-current is the Lorentz covariant four-vector that replaces the electromagnetic current density where c is the speed of light, ρ the charge density, and j the conventional current density. ... The electromagnetic four-potential is a four-vector defined in SI units (and gaussian units in parentheses) as in which φ is the electrical potential, and is the magnetic potential, a vector potential. ... André-Marie Ampère (January 20, 1775 – June 10, 1836), was a French physicist who is generally credited as one of the main discoverers of electromagnetism. ... Charles Augustin de Coulomb (born June 14, 1736, Angoulême, France - died August 23, 1806, Paris, France) was a French physicist. ... Michael Faraday, FRS (September 22, 1791 – August 25, 1867) was an English chemist and physicist (or natural philosopher, in the terminology of that time) who contributed to the fields of electromagnetism and electrochemistry. ... Oliver Heaviside (May 18, 1850 – February 3, 1925) was a self-taught English electrical engineer, mathematician, and physicist who adapted complex numbers to the study of electrical circuits, developed techniques for applying Laplace transforms to the solution of differential equations, reformulated Maxwells field equations in terms of electric and... Joseph Henry Joseph Henry (December 17, 1797 – May 13, 1878) was a Scottish-American scientist who served as the first Secretary of the Smithsonian Institution. ... Heinrich Rudolf Hertz (February 22, 1857 - January 1, 1894) was the German physicist and mechanician for whom the hertz, an SI unit, is named. ... Hendrik Lorentz by Jan Veth Hendrik Antoon Lorentz (born July 18, 1853 in Arnhem, Netherlands; died February 4, 1928 in Haarlem, Netherlands) was a Dutch physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman for the discovery and theoretical explanation of the Zeeman effect. ... James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish mathematician and theoretical physicist. ... Wilhelm Eduard Weber (October 24, 1804 - June 23, 1891) was a noted physicist. ... Potential energy can be thought of as energy stored within a physical system. ... This box:      Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. ... 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. ... Josephson junction array chip developed by NIST as a standard volt. ... In physics a Lorentz scalar is a scalar which is invariant under a Lorentz transformation. ... International safety symbol Caution, risk of electric shock (ISO 3864), colloquially known as high voltage symbol. ...

There is also a generalized electric scalar potential that is used in electrodynamics when time-varying electromagnetic fields are present. This generalized electric potential cannot be simply interpreted as a potential energy, however. It has been suggested that this article or section be merged with Potential. ... Electromagnetism is the physics of the electromagnetic field: a field, encompassing all of space, composed of the electric field and the magnetic field. ...

Explanation

Electric potential may be conceived of as "electric pressure". Where this "pressure" is uniform, no current flows and nothing happens. This is similar to why people do not feel normal atmospheric air pressure: there is no difference between the pressure inside the body and outside, so nothing is felt. However, where this electrical pressure varies, an electric field exists, which will create a force on charged particles. This article is about pressure in the physical sciences. ... In physics, a net force acting on a body causes that body to accelerate; that is, to change its velocity. ...

Mathematically, it is the potential φ (a scalar field) associated with the conservative electric field () that occurs when the magnetic field is time invariant (so that from Faraday's law of induction). In physics, a potential may refer to the scalar potential or to the vector potential. ... In mathematics and physics, a scalar field associates a scalar to every point in space. ... In vector calculus, an irrotational or conservative vector field is a vector field whose curl is zero. ... 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. ... For the indie-pop band, see The Magnetic Fields. ... Faradays law of induction (more generally, the law of electromagnetic induction) states that the induced emf (electromotive force) in a closed loop equals the negative of the time rate of change of magnetic flux through the loop. ...

Like any potential function, only the potential difference (voltage) between two points is physically meaningful (neglecting quantum Aharonov-Bohm effects), since any constant can be added to φ without affecting (gauge invariance). Potential difference is a quantity in physics related to the amount of energy that would be required to move an object from one place to another against various types of force. ... International safety symbol Caution, risk of electric shock (ISO 3864), colloquially known as high voltage symbol. ... The Aharonov-Bohm effect, sometimes called the Ehrenberg-Siday-Aharonov-Bohm effect, is a quantum mechanical phenomenon by which a charged particle is affected by electromagnetic fields in regions from which the particle is excluded. ... Gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ...

The electric potential φ is therefore measured in units of energy per unit of electric charge. In SI units, this is: Look up si, Si, SI in Wiktionary, the free dictionary. ...

joule/coulomb = volt.

The electric potential can also be generalized to handle situations with time-varying potential fields, in which case the electric field is not conservative and a potential function cannot be defined everywhere in space. There, an effective potential drop is included, associated with the inductance of the circuit. This generalized potential difference is also called the electromotive force (emf). The joule (IPA: or ) (symbol: J) is the SI unit of energy. ... The coulomb (symbol: C) is the SI unit of electric charge. ... Josephson junction array chip developed by NIST as a standard volt. ... An electric current i flowing around a circuit produces a magnetic field and hence a magnetic flux Φ through the circuit. ... Electromotive force (emf) is the amount of energy gained per unit charge that passes through a device in the opposite direction to the electric field existing across that device. ...

Introduction

Objects may possess a property known as electric charge. An electric field exerts a force on charged objects, accelerating them in the direction of the force, in either the same or the opposite direction of the electric field. If the charged object has a positive charge, the force and acceleration will be in the direction of the field. This force has the same direction as the electric field vector, and its magnitude is given by the size of the charge multiplied with the magnitude of the electric field. In physics, an electric field or E-field is an effect produced by an electric charge (or a time-varying magnetic field) that exerts a force on charged objects in the field. ...

Classical mechanics explores the concepts such as force, energy, potential etc. in more detail. Classical mechanics (commonly confused with Newtonian mechanics, which is a subfield thereof) is used for describing the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies. ... In physics, a net force acting on a body causes that body to accelerate; that is, to change its velocity. ... In physics, a potential may refer to the scalar potential or to the vector potential. ...

Force and potential energy are directly related. As an object moves in the direction that the force accelerates it, its potential energy decreases. For example, the gravitational potential energy of a cannonball at the top of a hill is greater than at the base of the hill. As the object falls, that potential energy decreases and is translated to motion, or inertial (kinetic) energy.

For certain forces, it is possible to define the "potential" of a field such that the potential energy of an object due to a field is dependent only on the position of the object with respect to the field. Those forces must affect objects depending only on the intrinsic properties of the object and the position of the object, and obey certain other mathematical rules.

Two such forces are the gravitational force (gravity) and the electric force in the absence of time-varying magnetic fields. The potential of an electric field is called the electric potential. Gravity is a force of attraction that acts between bodies that have mass. ...

The electric potential and the magnetic vector potential together form a four vector, so that the two kinds of potential are mixed under Lorentz transformations. In physics, the magnetic potential is a method of representing the magnetic field by using a potential value instead of the actual vector field. ... In relativity, a four-vector is a vector in a four-dimensional real vector space, called Minkowski space, whose components transform as the space and time coordinate differences, , under spatial translations, rotations, and boosts (a change by a constant velocity to another inertial reference frame). ... In physics, the Lorentz transformation converts between two different observers measurements of space and time, where one observer is in constant motion with respect to the other. ...

Mathematical introduction

The concept of electric potential (denoted by: φ, φ_E or V) is closely linked with potential energy, thus: Potential energy can be thought of as energy stored within a physical system. ...

U_E = qφ

where U_E is the electric potential energy of a test charge q due to the electric field. Note that the potential energy and hence also the electric potential is only defined up to an additive constant: one must arbitrarily choose a position where the potential energy and the electric potential is zero. The electric potential energy is the potential energy associated with the conservative Coulomb forces between charged particles contained within a system, where the reference potential energy is usually chosen to be zero for particles at infinite separation. ... A test charge is an object (usually a point particle) that has negligible charge; one can ignore the electrical field generated by the object itself. ...

The proper definition of the electric potential uses the electric field : 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. ...

where E is equal to the electric field, ds is an unknown, and 'C' is an arbitrary path connecting the point with zero potential to the point under consideration. When , the line integral above does not depend on the specific path C chosen but only on its endpoints. Equivalently, the electric potential determines the electric field via its gradient: For other uses, see Gradient (disambiguation). ...

and therefore, by Gauss's law, the potential satisfies Poisson's equation: In physics and mathematical analysis, Gausss law is the electrostatic application of the generalized Gausss theorem giving the equivalence relation between any flux, e. ... In mathematics, Poissons equation is a partial differential equation with broad utility in electrostatics, mechanical engineering and theoretical physics. ...

where ρ is the total charge density (including bound charge). Charge density is the amount of electric charge per unit volume. ... In classical electromagnetism, the polarization density (or electric polarization, or simply polarization) is the vector field that expresses the density of permanent or induced electric dipole moments in a dielectric material. ...

Note: these equations cannot be used if , i.e., in the case of a nonconservative electric field (caused by a changing magnetic field; see Maxwell's equations). The generalization of electric potential to this case is described below. In fluid mechanics, an irrotational vector field is a vector field whose curl is zero. ... For the indie-pop band, see The Magnetic Fields. ... For thermodynamic relations, see Maxwell relations. ...

Generalization to electrodynamics

When time-varying magnetic fields are present (which is true whenever there are time-varying electric fields and vice versa), one cannot describe the electric field simply in terms of a scalar potential φ; because the electric field is no longer conservative: is path-dependent because .

Instead, one can still define a scalar potential by also including the magnetic vector potential . In particular, is defined by: In physics, the magnetic potential is a method of representing the magnetic field by using a potential value instead of the actual vector field. ...

where is the magnetic flux density. One can always find such an because (the absence of magnetic monopoles). Given this, the quantity is a conservative field by Faraday's law and one can therefore write: Current flowing through a wire produces a magnetic field (B, labeled M here) around the wire. ... In physics, a magnetic monopole is a hypothetical particle that may be loosely described as a magnet with only one pole (see electromagnetic theory for more on magnetic poles). ... Faradays law of induction (more generally, the law of electromagnetic induction) states that the induced emf (electromotive force) in a closed loop equals the negative of the time rate of change of magnetic flux through the loop. ...

where φ is the scalar potential defined by the conservative field .

The electrostatic potential is simply the special case of this definition where is time-invariant. On the other hand, for time-varying fields, note that , unlike electrostatics.

Note that this definition of φ depends on the gauge choice for the vector potential (the gradient of any scalar field can be added to without changing ). One choice is the Coulomb gauge, in which we choose . In this case, we obtain , where ρ is the charge density, just as for electrostatics. Another common choice is the Lorenz gauge, in which we choose to satisfy . In the physics of gauge theories, gauge fixing (also called choosing a gauge) denotes a mathematical procedure for coping with redundant degrees of freedom in field variables. ... For other uses, see Gradient (disambiguation). ... In the physics of gauge theories, gauge fixing (also called choosing a gauge) denotes the act of removing redundant field variables. ... Charge density is the amount of electric charge per unit volume. ... The Lorenz gauge (or Lorenz gauge condition) was published by the Danish physicist Ludwig Lorenz. ...

Special cases and computational devices

The electric potential at a point due to a constant electric field can be shown to be:

The electric potential created by a point charge q, at a distance r from the charge, can be shown to be, in SI units: Look up si, Si, SI in Wiktionary, the free dictionary. ...

The electric potential due to a system of point charges is equal to the sum of the point charges' individual potentials. This fact simplifies calculations significantly, since addition of potential (scalar) fields is much easier than addition of the electric (vector) fields.

The electric potential created by a tridimensional spherically symmetric gaussian charge density ρ(r) given by: Probability density function of Gaussian distribution (bell curve). ...

where q is the total charge, is obtained by solving the Poisson's equation (in cgs units): In mathematics, Poissons equation is a partial differential equation with broad utility in electrostatics, mechanical engineering and theoretical physics. ... This article or section is in need of attention from an expert on the subject. ...

The solution is given by:

where erf(x) is the error function. This solution can be checked explicitly by a careful manual evaluation of . Note that, for r much greater than σ, erf(x) approaches unity and the potential approaches the point charge potential seen above, as expected. Plot of the error function In mathematics, the error function (also called the Gauss error function) is a non-elementary function which occurs in probability, statistics and partial differential equations. ...

Applications in electronics

This electric potential, typically measured in volts, provides a simple way to analyze electric circuits without requiring detailed knowledge of the circuit shape or the fields within it. Josephson junction array chip developed by NIST as a standard volt. ... A simple electric circuit made up of a voltage source and a resistor. ...

The electric potential provides a simple way to analyze electrical networks with the help of Kirchhoff's voltage law, without solving the detailed Maxwell's equations for the fields of the circuit. A simple electric circuit made up of a voltage source and a resistor. ... Not to be confused with Kerckhoffs principle. ... For thermodynamic relations, see Maxwell relations. ...

Units

The SI unit of electric potential is the volt (in honour of Alessandro Volta), which is so widely used that the terms voltage and electric potential are almost synonymous. Older units are rarely used nowadays. Variants of the centimeter gram second system of units included a number of different units for electric potential, including the abvolt and the statvolt. Look up si, Si, SI in Wiktionary, the free dictionary. ... Josephson junction array chip developed by NIST as a standard volt. ... For the concept car, see Toyota Alessandro Volta. ... This article or section is in need of attention from an expert on the subject. ... Conversion of units refers to conversion factors between different units of measurement for the same quantity. ... The statvolt is the unit of voltage and electrical potential used in the cgs system of units. ...

See also

References

This article or section includes a list of references or external links, but its sources remain unclear because it lacks in-text citations. You can improve this article by introducing more precise citations.

• Griffiths, David J. (1999). Introduction to Electrodynamics (3rd ed.). Prentice Hall. ISBN 0-13-805326-X.
• Jackson, John David (1999). Classical Electrodynamics, 3rd ed., New York: Wiley. ISBN 0-471-30932-X.
• Electromagnetic Fields (2nd Edition), Roald K. Wangsness, Wiley, 1986. ISBN 0-471-81186-6.

Image File history File links This is a lossless scalable vector image. ...

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