In physics, an electric field or E-field is an effect produced by an electric charge that exerts a force on charged objects in its vicinity. The units of the electric field are newtons per coulomb or volts per meter (both are equivalent). Electric fields are composed of photons and contain electrical energy with energy density proportional to the square of the field intensity. In the static case, an electric field is composed of virtual photons being exchanged by the charged particle(s) creating the field. In the dynamic case the electric field is accompanied by a magnetic field, by a flow of energy, and by real photons. Physics (from the Greek, φυσικός (phusikos), natural, and φύσις (phusis), nature) is the science of nature in the broadest sense. ... Electric charge is a fundamental property of some subatomic particles, which determines their electromagnetic interactions. ... In physics, a net force acting on a body causes that body to accelerate; that is, to change its velocity. ... In physics, the photon (from Greek φοτος, meaning light) is a quantum of excitation of the quantised electromagnetic field and is one of the elementary particles studied by quantum electrodynamics (QED) which is the oldest part of the Standard Model of particle physics. ... Electrical energy or Electromagnetic energy is a form of energy present in any electric field or magnetic field, or in any volume containing electromagnetic radiation. ... Vacuum energy or zero-point energy is the energy density of empty space. ... In the description of the interaction between elementary particles in quantum field theory, a virtual particle is a temporary elementary particle, used to describe an intermediate stage in the interaction. ... In physics, a magnetic field is an entity produced by moving electric charges (electric currents) that exerts a force on other moving charges. ...

Definition and derivation

The mathematical definition of the electric field is developed as follows. Coulomb's law gives the force between two point charges (infinitesimally small charged objects) as In physics, a field is an assignment of a quantity to every point in space. ... In physics, Coulombs law is an inverse-square law indicating the magnitude and direction of electrical force that one stationary, electrically charged substance of small volume (ideally, a point source) exerts on another. ...

where

• ε₀ (pronounced epsilon-nought) is a physical constant, the permittivity of free space;
• q₁ and q₂ are the electric charges of the objects;
• r is the magnitude of the separation vector between the objects;
• is the unit vector representing the direction from one charge to the other.

In the SI system of units, force is given in newtons, charge in coulombs, and distance in metres. Thus, ε₀ has units of C²/(N·m²). In science, a physical constant is a physical quantity whose numerical value does not change. ... This article is in need of attention. ... Electric charge is a fundamental property of some subatomic particles, which determines their electromagnetic interactions. ... In mathematics, a unit vector in a normed vector space is a vector (most commonly a spatial vector) whose length is 1. ... SI (disambiguation). ... This article is about the SI unit of force. ... The coulomb, symbol C, is the SI unit of electric charge, and is defined in terms of the ampere: 1 coulomb is the amount of electric charge (quantity of electricity) carried by a current of 1 ampere flowing for 1 second. ... metre or meter, see meter (disambiguation) The metre is the basic unit of length in the International System of Units. ...

This was known empirically. Suppose one of the charges is taken to be fixed, and the other one to be a moveable "test charge". Note that according to this equation, the force on the test object is proportional to its charge. The electric field is defined as the proportionality constant between charge and force:

However, note that this equation is only true in the case of electrostatics, that is to say, when there is nothing moving. The more general case of moving charges causes this equation to become the Lorentz equation. The electromagnetic field (EMF) is composed of two related vectorial fields, the electric field and the magnetic field. ...

The above paragraph is perhaps misleading that the equation could refer to electrodynamics by referring to a "moveable test charge"; however, it is important to understand that by "moveable", this means that the charge can be moved to, and held at, any position.

In the case of electrostatics, where velocity of both particles is zero, the above equation holds.

Properties

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. 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. The principle of superposition states that the net displacement at a given place and time caused by two or more waves traversing the same space is the vector sum of the displacements which would have been produced by the individual waves separately. ... A vector in physics and engineering typically refers to a quantity that has close relationship to the spatial coordinates, informally described as an object with a magnitude and a direction. The word vector is also now used for more general concepts (see also vector and generalizations below), but in this...

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

where ρ is the charge density, or the amount of charge per unit volume. Volume (also called capacity) is a quantification of how much space an object occupies. ...

The electric field is equal to minus the gradient of the electric potential. If several spatially distributed charges generate such an electric potential, e.g. in a solid, an electric field gradient may be defined. In vector calculus, the gradient of a scalar field is a vector field which points in the direction of the greatest rate of change of the scalar field, and whose magnitude is the greatest rate of change. ... Electrical potential is the potential energy per unit charge associated with a static (time-invariant) electric field, also called the electrostatic potential or the electric potential, typically measured in volts. ... Electrical potential is the potential energy per unit charge associated with a static (time-invariant) electric field, also called the electrostatic potential or the electric potential, typically measured in volts. ... A solid is a state of matter, characterized by a definite volume and a definite shape (i. ... Mathematically, the electric field gradient (EFG) is the second derivative of the electrical potential V: It is an important structural property of a crystalline solid, where it is defined at the location of a nucleus. ...

Related topics

• Maxwell's equations are the full set of equations governing electric fields.
• Electromagnetism
• Electrostatics
• Electrodynamics
• Magnetism

Maxwells 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. ... Electromagnetism is the physics of the electromagnetic field: a field, encompassing all of space, composed of the electric field and the magnetic field. ... Electrostatics is the branch of physics that deals with the force exerted by a static (i. ... Electromagnetism is the physics of the electromagnetic field: a field, encompassing all of space, composed of the electric field and the magnetic field. ... In physics, magnetism is a phenomenon by which materials exert an attractive or repulsive force on other materials. ...

External links

• Learning by Simulations (http://www.vias.org/simulations/simusoft_efield.html) Interactive simulation of an electric field of up to four point charges