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In [[physics]], an '''electric field''' surrounds [[electric charge|electrically charged particles]] and time-varying [[magnetic field]]s. The electric field depicts the [[force (physics)|force]] exerted on other electrically charged objects by the electrically charged particle the field is surrounding. The concept of an electric field was introduced by [[Michael Faraday]]. |
In [[physics]], an '''electric field''' surrounds [[electric charge|electrically charged particles]] and time-varying [[magnetic field]]s. The electric field depicts the [[force (physics)|force]] exerted on other electrically charged objects by the electrically charged particle the field is surrounding. The concept of an electric field was introduced by [[Michael Faraday]]. |
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The electric field is THIS DICK!!!!! |
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The electric field is a [[vector field]] with [[SI]] units of [[newton (unit)|newton]]s per [[coulomb]] (N C<sup>−1</sup>) or, equivalently, [[volt]]s per [[metre]] (V m<sup>−1</sup>). The SI base units of the electric field are kg·m·s<sup>−3</sup>·A<sup>−1</sup>. The [[Field strength|strength or magnitude]] of the field at a given point is defined as the force that would be exerted on a positive [[test charge]] of 1 coulomb placed at that point; the direction of the field is given by the direction of that force. Electric fields contain [[electrical energy]] with [[energy density]] proportional to the square of the field amplitude. The electric field is to charge as gravitational [[acceleration]] is to mass and [[force density]] is to volume. |
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An electric field that changes with time, such as due to the motion of charged particles in the field, influences the local magnetic field. That is, 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 field]]s". In [[quantum electrodynamics]], disturbances in the electromagnetic fields are called [[photon]]s, and the energy of photons is quantized. |
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==Definition== |
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The electric field intensity is defined as the force per unit positive charge that would be experienced by a stationary [[point charge]], or "test charge", at a given location in the field:<ref name="hyperphysics.phy-astr.gsu.edu">[http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elefie.html Electric field in "Electricity and Magnetism", R Nave]</ref> |
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:<math> |
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\mathbf{E} = \frac{\mathbf{F}}{q_t} |
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</math> |
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where |
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:'''F''' is the [[Coulomb's law|electric force]] experienced by the test particle |
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:''q<sub>t</sub>'' is the [[electric charge|charge]] of the [[test particle]] in the electric field |
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:'''E''' is the electric field wherein the particle is located. |
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Taken literally, this equation only defines the electric field at a specific location as the [[Coulomb_force#Basic_equation|force]] experienced by a stationary test charge at that point(with the sign of q<sub>t</sub>, positive or negative, determining the direction of the force). Given that electric fields are generated by [[electric charge|electrically charged]] [[particles]], adding and/or moving a source charge, ''q<sub>s</sub>'', will alter the electric field distribution. Therefore, it is important to remember that an electric field is defined with respect to a particular configuration of source charges. In practice, this is achieved by placing test particles with successively smaller [[electric charge]] in the vicinity of the source distribution and measuring the force exerted on the test charges as their charge approaches zero. |
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:<math>\mathbf{E}=\lim_{q \to 0}\frac{\mathbf{F}}{q}</math> |
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This allows the electric field to be determined from the distribution of its source charges alone. |
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As is clear from the definition, the direction of the electric field is the same as the direction of the force it would exert on a positively-charged particle, and opposite the direction of the force on a negatively-charged particle. Since like charges repel and opposites attract (as quantified below), the electric field tends to point away from positive charges and towards negative charges. |
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[[File:Electric field.gif|thumb|Electric field from a positive Q]][[File:Electric field negative.gif|thumb|Electric field from a negative Q]] Based on [[Coulomb's law]] for interacting point charges, the contribution to the E-field at a point in space due to a single, discrete charge located at another point in space is given by the following<ref name="hyperphysics.phy-astr.gsu.edu" />: |
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:<math>\mathbf{E}= {1 \over 4\pi\varepsilon_0}{Q \over r^2}\mathbf{\hat{r}} \ </math> |
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where |
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:''Q'' is the charge of the particle creating the electric force, |
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:''r'' is the distance from the particle with charge ''Q'' to the E-field evaluation point, |
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:<math>\mathbf{\hat{r}}</math> is the [[unit vector]] pointing from the particle with charge ''Q'' to the E-field evaluation point, |
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:ε<sub>0</sub> is the [[vacuum permittivity|electric constant]]. |
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The total E-field due to a quantity of point charges, <math>n_q</math>, is simply the [[Superposition principle|superposition]] of the contribution of each individual point charge<ref>[http://teacher.pas.rochester.edu/phy122/Lecture_Notes/Chapter23/Chapter23.html#Heading3 'The Electric Field' - Chapter 23 of Frank Wolfs's lectures] at [[University of Rochester]]</ref>: |
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:<math>\mathbf{E} = \sum_{i=1}^{n_q} {\mathbf{E}_i} = \sum_{i=1}^{n_Q} {{1 \over 4\pi\varepsilon_0}{Q_i \over r_i^2}\mathbf{\hat{r}}_i}. </math> |
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Alternatively, [[Gauss's law]] allows the E-field to be calculated in terms of a continuous distribution of [[charge density]] in space, ρ:<ref>[http://teacher.pas.rochester.edu/phy122/Lecture_Notes/Chapter24/Chapter24.html 'Gauss's Law' - Chapter 24 of Frank Wolfs's lectures] at [[University of Rochester]]</ref> |
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:<math> \nabla \cdot \mathbf{E} = \frac { \rho } { \varepsilon _0 }.</math> |
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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. |
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==Uniform fields== |
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A uniform field is one in which the electric field is constant at every point. It can be approximated by placing two conducting plates parallel to each other and maintaining a [[voltage]] between them; it is only an approximation because of edge effects. Ignoring such effects, the equation for the magnitude of the electric field is: |
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<math> E = - \frac{V}{d}</math> |
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where |
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:''V'' is the voltage difference between the plates |
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:''d'' is the distance separating the plates |
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The negative sign arises as positive charges repel, so a positive charge will experience a force away from the positively charged plate, in the opposite direction to that in which the voltage increases. |
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==Time-varying fields== |
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An electric field can be produced, not only by a static charge, but also by a changing magnetic field. The combined electric field is expressed as, |
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:<math> \mathbf{E} = - \nabla \phi - \frac { \partial \mathbf{A} } { \partial t }</math> |
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where, |
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:<math>\mathbf{B} = \nabla \times \mathbf{A}</math> |
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The vector '''B''' is the [[magnetic flux density]] and the vector '''A''' is the [[magnetic vector potential]]. Taking the curl of the electric field equation we obtain, |
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:<math>\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}</math> |
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which is one of [[Maxwell's equations]], referred to as [[Faraday's law of induction]].<ref>{{citation |
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|title=Maxwell's Equations |
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|first1=Paul G. |
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|last1=Huray |
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|publisher=Wiley-IEEE |
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|year=2009 |
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|isbn=0-470-54276-4 |
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|page=205 |
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|url=http://books.google.com/books?id=0QsDgdd0MhMCp}}, [http://books.google.com/books?id=0QsDgdd0MhMC&pg=PA205 Chapter 7, p 205] |
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</ref> |
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Where [[electrostatics]] is the study of the fields surrounding static charges, the study of the electric fields induced by changing magnetic field comes under the domain of [[electrodynamics]] or [[electromagnetics]]. |
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==Properties (in electrostatics)== |
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[[File:Electric field one charge changing.gif|thumb|Illustration of the electric field surrounding a positive (red) and a negative (blue) charge in one dimension if the right charge is changing from positive to negative]][[Image:VFPt charges plus minus thumb.svg|220px|thumb|right|Illustration of the electric field surrounding a positive (red) and a negative (blue) charge.]] |
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According to Coulomb's law the 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. |
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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. |
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:<math>\mathbf{E}_{\rm total} = \sum_i \mathbf{E}_i = \mathbf{E}_1 + \mathbf{E}_2 + \mathbf{E}_3 \ldots \,\!</math> |
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If this principle is extended to an infinite number of infinitesimally small elements of charge, the following formula results: |
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:<math> |
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\mathbf{E} = \frac{1}{4\pi\varepsilon_0} \int\frac{\rho}{r^2} \mathbf{\hat{r}}\,\mathrm{d}V |
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</math> |
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where |
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:<math>\rho</math> is the [[charge density]], or the amount of charge per unit [[volume]]. |
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[[File:Electric field and potential relationship.gif|thumb|The electric field at a point is equal to the negative [[gradient]] of the [[electric potential]] there, :<math> |
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\mathbf{E} = -\nabla \Phi |
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</math> |
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]]The electric field at a point is equal to the negative [[gradient]] of the [[electric potential]] there. In symbols, |
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:<math> |
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\mathbf{E} = -\nabla \Phi |
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</math> |
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where |
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:<math>\Phi(x, y, z)</math> is the [[scalar field]] representing the electric potential at a given point. |
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If several spatially distributed charges generate such an [[electric potential]], e.g. in a [[solid]], an [[electric field gradient]] may also be defined. |
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Considering the [[permittivity]] ε of a linear material, which may differ from the permittivity of free space ε<sub>0</sub>, the [[electric displacement field]] is: |
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:<math>\mathbf{D} = \varepsilon \mathbf{E}. </math> |
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==Energy in the electric field== |
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{{Main|Electric energy}} |
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The electric field stores energy. The energy density of the electric field is given by |
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:<math> u = \frac{1}{2} \varepsilon |\mathbf{E}|^2 \, ,</math> |
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where ''ε'' is the [[permittivity]] of the medium in which the field exists, and '''E''' is the electric field vector. |
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The total energy stored in the electric field in a given volume ''V'' is therefore |
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:<math> \frac{1}{2} \varepsilon \int_{V} |\mathbf{E}|^2 \, \mathrm{d}V \, ,</math> |
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where d''V'' is the differential volume element. |
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==Parallels between electrostatics and gravity == |
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[[File:Electric field negative.gif|thumb|Electric field from a negative Q where <math> |
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\mathbf{F} = q(\frac{-1}{4 \pi \varepsilon_0}\frac{Q}{r^2}\mathbf{\hat{r})} = q\mathbf{E} |
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</math>]][[Coulomb's law]], which describes the interaction of electric charges: |
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:<math> |
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\mathbf{F} = q(\frac{-1}{4 \pi \varepsilon_0}\frac{Q}{r^2}\mathbf{\hat{r})} = q\mathbf{E} |
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</math> |
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is similar to [[Newton's law of universal gravitation]]:[[File:Gravitational field.gif|thumb|Gravitational field determined using Newton's law of universal gravitation. :<math>F = m( -G\frac{M}{|r|^2})\hat{r} = mg </math>]] |
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:<math> |
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\mathbf{F} = m(-G\frac{M}{r^2}\mathbf{\hat{r})} = m\mathbf{g}. |
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</math> |
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This suggests similarities between the electric field '''E''' and the gravitational field '''g''', so sometimes mass is called "gravitational charge". |
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Similarities between electrostatic and gravitational forces: |
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# Both act in a vacuum. |
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# Both are [[central force|central]] and [[conservative force|conservative]]. |
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# Both obey an [[inverse-square law]] (both are inversely proportional to square of r). |
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# Both propagate with finite speed c, the speed of light. |
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# [[Charge invariance|Electric charge]] and [[relativistic mass]] are conserved; note, though, that [[rest mass]] is not conserved. |
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Differences between electrostatic and gravitational forces: |
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# Electrostatic forces are much greater than gravitational forces (by about 10<sup>36</sup> times). |
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# Gravitational forces are attractive for like charges, whereas electrostatic forces are repulsive for like charges. |
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# There are no negative gravitational charges (no [[negative mass]]) while there are both positive and negative electric charges. This difference combined with previous implies that gravitational forces are always attractive, while electrostatic forces may be either attractive or repulsive. |
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==See also== |
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* [[Electrostatics]] |
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* [[Classical electromagnetism]] |
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* [[Magnetism]] |
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* [[Teltron Tube]] |
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==References== |
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{{reflist}} |
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== External links == |
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*[http://www.its.caltech.edu/~phys1/java/phys1/MovingCharge/MovingCharge.html] - An applet that shows the electric field of a moving point charge. |
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*[http://www.lightandmatter.com/html_books/0sn/ch10/ch10.html Fields] - a chapter from an online textbook |
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*[http://www.vias.org/simulations/simusoft_efield.html Learning by Simulations] Interactive simulation of an electric field of up to four point charges |
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*Java simulations of [http://www.falstad.com/emstatic/ electrostatics in 2-D] and [http://www.falstad.com/vector3de/ 3-D] |
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*[http://www.physics-lab.net/applets/electric-fields Electric Fields Applet] - An applet that shows electric field lines as well as potential gradients. |
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*[http://blazelabs.com/inversecubelaw.pdf The inverse cube law] The inverse cube law for dipoles (PDF file) by Eng. Xavier Borg |
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*[http://www.flashphysics.org/electricField.html Interactive Flash simulation picturing the electric field of user-defined or preselected sets of point charges] by field vectors, field lines, or equipotential lines. Author: David Chappell |
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{{DEFAULTSORT:Electric Field}} |
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<!--Categories--> |
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[[Category:Electrostatics]] |
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Revision as of 16:28, 11 October 2011
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In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding. The concept of an electric field was introduced by Michael Faraday.
The electric field is THIS DICK!!!!!