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Electric field

2007 Schools Wikipedia Selection. Related subjects: Electricity and
Electronics

   Electromagnetism
   Electricity · Magnetism
           Electrostatics
   Electric charge
   Coulomb's law
   Electric field
   Gauss's law
   Electric potential
   Electric dipole moment
           Magnetostatics
   Ampère's law
   Magnetic field
   Magnetic dipole moment
          Electrodynamics
   Electric current
   Lorentz force law
   Electromotive force
   (EM) Electromagnetic induction
   Faraday-Lenz law
   Displacement current
   Maxwell's equations
   (EMF) Electromagnetic field
   (EM) Electromagnetic radiation
         Electrical Network
   Electrical conduction
   Electrical resistance
   Capacitance
   Inductance
   Impedance
   Resonant cavities
   Waveguides

   In physics, the space surrounding an electric charge has a property
   called an electric field. This electric field exerts a force on other
   charged objects. The concept of electric field was introduced by
   Michael Faraday.

   The electric field is a vector with SI units of newtons per coulomb (N
   C^-1) or, equivalently, volts per meter (V m^-1). The direction of the
   field 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. Electric
   fields contain electrical energy with energy density proportional to
   the square of the field intensity. The electric field is to charge as
   acceleration is to mass and force density is to 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. For this
   reason, one speaks of "electromagnetism" or "electromagnetic fields."
   In quantum mechanics, disturbances in the electromagnetic fields are
   called photons, and the energy of photons is quantized.

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):

          \vec{E} = \frac{\vec{F}}{q}

   where

          \vec{F} is the electric force given by Coulomb's law,
          q is the charge of a "test charge",

   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.

Coulomb's law

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

          \vec{E} =\frac{1}{4 \pi \varepsilon_0}\frac{Q}{r^2}\hat{r}

   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,
          \hat{r} is the Unit vector pointing from the particle with
          charge Q to the E-field evaluation point,
          \varepsilon_0 is the Permittivity of free space.

   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)

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

   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.

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

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

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

   where

          ρ 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,

          \vec{E} = -\vec{\nabla}\phi

   where

          φ(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 may
   differ from the permittivity of free space \varepsilon_{0} , the
   electric displacement field is:

          \vec{D} = \varepsilon \vec{E}

Energy in the electric field

   The electric field stores energy. The energy density of the electric
   field is given by

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

   where

          \varepsilon is the permittivity of the medium in which the field
          exists
          \vec{E} is the electric field vector.

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

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

   where

          dV is the differential volume element.

Parallels between electrostatics and gravity

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

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

   is similar to the Newtonian gravitation law:

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

   This suggests similarities between the electric field E and the
   gravitational field g, so sometimes mass is called "gravitational
   charge".

   Similarities between electrostatic and gravitational forces:
    1. Both act in a vacuum.
    2. Both are central and conservative.
    3. Both obey an inverse-square law (both are inversely proprotional to
       square of r).
    4. Both propagate with finite speed c.

   Differences between electrostatic and gravitational forces:
    1. Electrostatic forces are much greater than gravitational forces (by
       about 10^36 times).
    2. Gravitational forces are always attractive in nature, whereas
       electrostatic forces may be either attractive or repulsive.
    3. Gravitational forces are independent of the medium whereas
       electrostatic forces depend on the medium. This is due to the fact
       that a medium contains charges; the fast motion of these charges,
       in response to an external electromagnetic field, produces a large
       secondary electromagnetic field which should be accounted for.
       While slow motion of ordinary masses in response to changing
       gravitational field produces extremely weak secondary
       "gravimagnetic field" which may be neglected in most cases (except,
       of course, when mass moves with relativistic speeds).

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. This "secondary" electric field can be
   computed using Faraday's law of induction,

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

   where

          \vec{\nabla} \times \vec{E} indicates the curl of the electric
          field,
          -\frac{\partial \vec{B}} {\partial t} 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.

   Retrieved from " http://en.wikipedia.org/wiki/Electric_field"
   This reference article is mainly selected from the English Wikipedia
   with only minor checks and changes (see www.wikipedia.org for details
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