Electric field

Encyclopedia : E : EL : ELE : 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. The SI units of the electric field are newtons per coulomb or volts per meter (which are equivalent). Electric fields contain electrical energy with energy density proportional to the square of the field intensity. Electric fields exist around all charges; the direction of field lines at a point is defined by the direction of the electric force exerted on a positive test charge placed at that point. The strength of the field is defined by the ratio of the electric force on a charge at a point to the magnitude of the charge placed at that point. In the dynamic case the electric field is accompanied by a magnetic field, by a flow of energy, and by real photons.

The concept of electric field was introduced by Michael Faraday.

The electric field or electric field intensity is a vector quantity, and the electric field strength is the magnitude of this vector.

Contents

1 Definition (for electrostatics)
2 Properties (in electrostatics)
3 Parallels between electrostatics and gravity
4 Time-varying fields
5 See also
6 External links

Definition (for electrostatics)

Electric field is defined as the electric force per unit charge. The direction of the field is taken to be the direction of the force it would exert on a positive test charge. The electric field is radially outward from a positive charge and radially in toward a negative point charge.

The electric field is defined as the proportionality constant between charge and force (in other words, the force per unit of test charge):

[\mathbf = \frac} = \frac\frac\mathbf]

::where

::: F is the electric force given by Coulomb's law,

::: q is the charge of a "test charge"

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

::: and

::: r is the distance vector from the particle with charge Q.

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 force equation. When we speak of a "moveable test charge", this means only that the above equations hold regardless of the position of the (stationary) test charge.

Furthermore, 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. Gauss's law is one of Maxwell's equations, a set of four laws governing electromagnetics.

Properties (in electrostatics)

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.

[\mathbf_ = \sum_i \mathbf_i = \mathbf_1 + \mathbf_2 + \mathbf_3 \ldots \,\!]

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

[\mathbf = \frac \int\frac \mathbf\,d^\mathbf]

where [\rho] is the charge density, or the amount of charge per unit volume.

The electric field at a point is equal to the negative gradient of the electric potential there. In symbols,

[\mathbf = -\mathbf\phi]

Where [\phi(x, y, z)] is the scalar field representing the electric potential at a given point. If several spatially distributed charges generate such an electric potential, e.g. in a solid, an electric field gradient may also be defined.

Considering the permittivity [\varepsilon] of a material, which is the product of the permittivity of free space [\varepsilon_] and the material-dependent relative permittivity [\varepsilon_], yields the Electric displacement field:

[\mathbf = \varepsilon \mathbf = \varepsilon_ \varepsilon_ \mathbf]

Parallels between electrostatics and gravity

As explained above, electric field can be thought of as a proportionality constant when the force exerted on a test charge is proportional to the magnitude of the test charge. Put more simply, this is to say that the electrostatic environment affecting a point in space can be quantified by the electric field at that point; different physical facts of the environment combine to form this single vector quantity, and it is possible for different environments to produce the same vector quantity for electric field. Any given object (that we are measuring the force on) has associated various "weights;" the electrostatic weight is the charge, and the gravitic weight is the mass. The electrostatic force on some object in the environment is then simply the strength of the environment (the electric field), times the magnitude of the electrostatic weight (the charge). This is similar to gravity, where any given environment has a gravitational acceleration, and the force on some object in that environment is simply the acceleration due to gravity (the environmental factor) times the mass of the object (the gravitic weight). For electrostatics, the factors that determine the electric field in an environment are:

The magnitude of each nearby charge
The square of the distance between the "center" of that charge and the object being measured, and
Coulomb's constant.

The analogous factors for determining a gravitational field are:

The mass of each nearby object
The square of the distance between the center of mass of that object and the object being measured, and
The Universal Gravitational Constant.

Similarities between electrostatic and gravitational forces:

Both act in a vacuum.
Both are central and conservative.
Both obey an inverse-square law (both are inversely proprotional to square of r).

Dissimilarities between electrostatic and gravitational forces:

Electrostatic forces are much greater than gravitational forces (by about 10³⁶ times).
Gravitational forces are always attractive in nature, whereas electrostatic forces may be attractive or repulsive in nature.
Gravitational forces are independent of the medium whereas electrostatic forces depend on the medium. This is due to the fact that the electrostatic force constant (k=1/4πε) varies according to medium, but the value of gravitational constant (G) remains constant in every medium. The units of the electric field, Newtons per Coulomb, can thus by expressed as force per unit charge.

Time-varying fields

Charges are not the only sources of electric fields. According to Faraday's law of induction,

[\nabla \times \mathbf = -\frac} ]

where [\nabla \times \mathbf] indicates the curl of the electric field, and [-\frac} ] represents the vector rate of decrease of magnetic flux density with time. This means that a magnetic field changing in time produces a curled electric field, possibly also changing in time.

The situation in which electric or magnetic fields change in time is no longer electrostatics, but rather electrodynamics or electromagnetics. In this case, Coulomb's law no longer provides a useful definition of electric field as given above. Instead, the more general Gauss's Law, along with Faraday's law, determines the electric field.

External links

[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]