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electric field

 Definition/Summary Electric field is electric force per charge, or electric potential energy per distance per charge. An electric field is a vector field that permeates the space around electrical charge. It is what mediates the force between that charge and any other charge nearby. It is also caused (induced) by a changing magnetic field. The electric field, $\mathbf{E}$, can be found from the charge producing it (using Coulomb's Law, or Gauss's Law), or from the electromagnetic potential (using $\mathbf{E}\ =\ -\nabla \phi\ -\ \frac{1}{c}\frac{\partial \mathbf{A}}{\partial t}$). Electric field is a vector with units of newtons per coulomb (N/C) or volts per metre (V/m), and dimensions of mass.length/charge.time² (ML/QT²). It is derived from (non-unique) vector and scalar potentials, $\mathbf{A}$ and $\phi$ (and the magnetic field $\mathbf{B}$ is derived from the same vector potential). It transforms (between observers with different velocities) as three of the six coordinates of a 2-form, the electromagnetic field, $(\mathbf{E},\mathbf{B})$, which in turn is part of the electroweak field.

 Equations (1) $$\vec{E}=\lim_{q\rightarrow 0}\frac{\vec{F_e}}{q} =\frac{1}{4\pi \epsilon_o}\int\frac{\rho (r)}{r^2}\hat{r}d\tau$$ (2) $$\oint \vec{E}\cdot d\vec{a} =\frac{Q_{enc}}{\epsilon_0}$$ Potential equations: (3) $$\mathbf{E}\ =\ -\nabla \phi\ -\ \frac{1}{c}\frac{\partial \mathbf{A}}{\partial t}$$ $$\mathbf{B}\ =\ \nabla\times\mathbf{A}$$ The two source-free Maxwell equations (Faraday's Law and Gauss' Law for Magnetism) follow immediately by differentiating the potential equations: (4) $$\nabla\times\mathbf{E}\ =\ -\frac{1}{c}\frac{\partial \mathbf{B}}{\partial t}$$ $$\nabla\cdot\mathbf{B}\ =\ 0$$ Energy density: (5) $$u_e=\frac{1}{2}\epsilon E^2$$ Total energy: (6) $$U_e=\int_{\tau}\frac{1}{2}\epsilon E^2 d\tau$$

 Scientists Michael Faraday(1791-1867) James Clerk Maxwell(1831-1879)

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 Breakdown Physics > Electromagnetism >> Mathematical Methods

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 Extended explanation The electric field, along with the magnetic field, were originally conceived by Michael Faraday to explain the long range nature of those forces. The mathematical development of this field theory was left to Maxwell. Since the electric field can accelerate charged bodies, it must be able to store electrical potential energy. The energy density of an electrical field is given by equation (5). In order to find the total energy stored in the field, the density function must be integrated over all space, thus giving rise to equation (6). Time-varying electric fields are somewhat more difficult to find due to the fact that they can be created by time-varying magnetic fields as well as a time-varying potential. This phenomenon, known as Electromagnetic Induction, is represented in the derivative of the magnetic vector potential in equation (4). After some manipulation of (4), you will obtain Faraday's Law, a much more well known representation of induction: $$\vec{\nabla}\times \vec{E}=-\frac{\partial \vec{B}}{\partial t}$$ Reason for definition of electric field: Electric field $\mathbf{E}$ is defined so that multiplying it by the charge $q$ of a body gives the force $\mathbf{F}$ on that body: $$\mathbf{F} = q\mathbf{E}$$ This is the electric part of the Lorentz force: $\mathbf{F} = q\left(\mathbf{E} + \mathbf{v}\times\mathbf{B}\right)$ So it must have dimensions of force/charge, or work/charge.length, and so can be measured in newtons/coulomb. Since work (or energy) can be measured in electron-volts, work/charge can be measured in volts, and so electric field can also be measured in volts/metre. By comparison, magnetic field is defined so that multiplying it by the charge of a body and cross-producting it with the velocity of the body gives the force on that body: $\mathbf{F} = q\mathbf{v}\times\mathbf{B}$ Similarly, therefore, magnetic field must have dimensions of force/charge.velocity, and can be measured in volts/metre per metre/second, or volt.seconds/metre², which are webers/metre², or teslas.

Commentary

 Drmarshall @ 06:28 PM Feb23-13 So electric fields, having energy, have inertia So they "distort space" - whatever "space " is - and "cause gravitational forces (whatever they are).

 Blahboy @ 02:09 PM Jul23-12 is anybody taking in to consideration that a electric field being a field means that it is ocuppying space therefore creating a distrubance within space. Giving this fact that would mean that space being view in this instance as a median for propagating fields is being shifted from a state of equilibruim to which every state that the electric field presents. Ultimately this would mean that space is not nothing!!!! So, what is space? I actually do know the answer to this question and i can prove my theory. But i don't give away answers for free. Bhaaaaaaaaaaaaaaah ha ha ha!!!!!!!!!!!!!!! cough...cough. Anyway if my idea does prove to be something please do give credit. I'm only 15 and i do alot of hard independent research.

 MissingPerson @ 10:31 AM Apr16-12 Could it be possible for a large chunk of antimatter to produce a wavelength that is undetectable to instruments that normally measure electomagnetic waves consistant with ordinary matter? Simply could there be a polar opposite to the electromagnetic spectrum? REPLY from Redbelly98: the phrase "polar opposite to the electromagnetic spectrum" makes little sense. At any rate, questions about physics should be posted in the regular forums (found at www.physicsforums.com), not in the PF Library.

 seham @ 11:56 AM Mar5-12 please,i need to know the physical meaning of Ht=0? i knoe that when Et=0 that all wave reflect again work as mirror

 tiny-tim @ 05:13 AM Feb18-12 Added "Electric field is electric force per charge", with other changes, to Definition.

 dextrain @ 03:20 AM Nov23-10 by what entity the field is made of?

 reddyvinay199 @ 09:43 AM Nov9-10 is electric field real if we consider an object does field lines pass through it or not???

 anmol singh @ 06:37 AM Aug7-10 Can electric field lines can be non integer(physcially or mathmatically)?

 mrohitk @ 03:08 AM Jul23-10 In Lorentz force why second term is called vortex term and may it be neglected in any circums tances?

 dmraja143 @ 01:33 AM Nov23-09 well. all are good answers

 tiny-tim @ 02:27 PM Aug27-09 wikipeida is remarkably comprehensive, but not entirely reliable. The PF library does have selective links to particularly good wikipedia articles. Since wikipedia is fairly easy to search, is there any point in linking to run-of-the-mill articles, or worse?

 nirax @ 06:29 AM Aug27-09 it would be a nice idea to provide a link to Wikipedia article on any such concepts illustrated in this forum.

 nshtkmar1977 @ 01:18 AM May6-09 we often say that electric field at a space is the force exerted on a charge when its magnitude is very small? we know that a charge can not exert force on itself, so why putting this condition that test charge tends to zero?

 freehuman79 @ 06:29 PM Jan30-09 is there any thing about the conservation of angular momentum in electric field? ~EDIT(tiny-tim): angular momentum is only conserved in a magnetic field.

 Robtai @ 02:41 AM Jan19-09 http://en.wikipedia.org/wiki/Electric_field