Electric potential is the potential energy per unit of charge associated with a static (time-invariant) electric field, also called the electrostatic potential, typically measured in volts. To meet Wikipedias quality standards, this article or section may require cleanup. ... Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interactions. ... 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. ... Josephson junction array chip developed by NIST as a standard volt. ...

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. ...

Explanation

Electric potential may be conceived of as "electric pressure". Where this "pressure" is uniform, nothing happens, just as we do not feel the atmospheric pressure at sea level. However, where the pressure varies, it produces a force that can push charged objects to different locations. Pressure (symbol: p) is the force per unit area applied on a surface in a direction perpendicular to that surface. ... diurnal (daily) rhythm of air pressure in northern Germany (black curve is air pressure) Atmospheric pressure is the pressure above any area in the Earths atmosphere caused by the weight of air. ... 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 E (E = −∇φ) that occurs when the magnetic field is time invariant (so that ∇ × E = 0 from Faraday's law of induction). It has been suggested that this article or section be merged with Scalar 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, 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. ... In the above two images, the scalar field is in black and white, black representing higher values, and its corresponding gradient is represented by blue arrows. ... Current flowing through a wire produces a magnetic field (B, labeled M here) around the wire. ... Faradays law of induction gives the relation between the rate of change of the magnetic flux through the surface S enclosed by a contour C and the electric field induced along the contour: where E is the induced electric field, dl is an infinitesimal element of the contour C...

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 E. 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 danger 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. ...

The electric potential is therefore measured in units of energy per unit of electric charge. In SI units, this is: Cover of brochure The International System of Units. ...

joules/coulombs = volts.

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 (symbol: J) is the SI unit of energy, or work with base units of kg·m²/s² (N·m). ... The coulomb (symbol: C) is the SI unit of electric charge. ... Josephson junction array chip developed by NIST as a standard volt. ... Inductance (or electric inductance) is a measure of the amount of magnetic flux produced for a given electric current. ... The factual accuracy of this article is disputed. ...

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. 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 is a branch of physics which studies the deterministic motion of objects. ... In physics, a net force acting on a body causes that body to accelerate; that is, to change its velocity. ... It has been suggested that this article or section be merged with Scalar 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 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 is 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 like the space and time coordinates (t, x, y, z) under spatial rotations and boosts (a change by a constant velocity to another inertial reference frame). ... A Lorentz transformation (LT) is a linear transformation that preserves the spacetime interval between any two events in Minkowski space, while leaving the origin fixed (=rotation of Minkowski space). ...

Mathematical introduction

The concept of electric potential (denoted by: φ, φ_E or V) is closely linked with potential energy, thus: To meet Wikipedias quality standards, this article or section may require cleanup. ...

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 of a body is its potential energy due to electric effects, neglecting other forces (such as gravity). ...

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

where s 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: In the above two images, the scalar field is in black and white, black representing higher values, and its corresponding gradient is represented by blue arrows. ...

and therefore, by Gauss's law, the potential satisfies Poisson's equation: In physics and mathematical analysis, Gausss law gives the relation between the electric flux flowing out a closed surface and the electric charge enclosed in the surface. ... 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 and 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. ... Current flowing through a wire produces a magnetic field (B, labeled M here) around the wire. ... Maxwells equations (sometimes called the Maxwell equations) are the set of four equations, attributed to James Clerk Maxwell, that describe the behavior of both the electric and magnetic fields, as well as their interactions with matter. ...

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 A. In particular, A 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 B is the magnetic flux density. One can always find such an A 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 gives the relation between the rate of change of the magnetic flux through the surface S enclosed by a contour C and the electric field induced along the contour: where E is the induced electric field, dl is an infinitesimal element of the contour C...

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

The electrostatic potential is simply the special case of this definition where A 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 A (the gradient of any scalar field can be added to A without changing B). 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 A to satisfy . In the physics of gauge theories, gauge fixing (also called choosing a gauge) denotes the act of removing redundant field variables. ... In the above two images, the scalar field is in black and white, black representing higher values, and its corresponding gradient is represented by blue arrows. ... 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: Cover of brochure The International System of Units. ...

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. 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. ... An electrical network is an interconnection of electrical elements such as resistors, inductors, capacitors, and switches. ...

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. An electrical network is an interconnection of electrical elements such as resistors, inductors, capacitors, and switches. ... Kirchhoffs circuit laws are a pair of laws that deal with the conservation of charge and energy in electrical circuits, and were first described in 1845 by Gustav Kirchhoff. ... Maxwells equations (sometimes called the Maxwell equations) are the set of four equations, attributed to James Clerk Maxwell, that describe the behavior of both the electric and magnetic fields, as well as their interactions with matter. ...

Units

The SI unit of electric potential is the volt, 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 (which see for further information) included a number of different units for electric potential, including the abvolt and the statvolt. Cover of brochure The International System of Units. ... Josephson junction array chip developed by NIST as a standard volt. ... This article or section is in need of attention from an expert on the subject. ...