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{{r|Multipole expansion of electric field}}

{{r|Electric field}}

In Gaussian units the [[electric field]] '''E''', the [[polarization]] '''P''', the [[electric displacement]] '''D <tr> <td><i>E</i> </td> <td>[[Electric field]] </td> <td>V/m </td> <td>10⁴/<i>c</i

...rostatics]], Gauss' law is a theorem concerning a surface integral of an [[electric field]] '''E'''. In [[Vacuum (science)|vacuum]] Gauss' law takes the form: ...rface element d''S'', pointing outward. The vector '''E'''('''r''') is the electric field at the position d'''S''', the dot indicates a [[dot product]] between the v

{{r|Multipole expansion of electric field}}

At a microscopic level, the magnetic flux '''B''' and the electric field '''E''' determine the behavior of charges. For example, a single moving cha

...ow determination of exact solutions of the [[Maxwell equations]] for the [[electric field]] and [[magnetic flux density]] generated at an arbitrary location by an id ...is the [[magnetic constant]] of the [[SI units]].With these potentials the electric field and the magnetic flux density are found to be (dots over symbols are time d

{{r|Multipole expansion of electric field}}

where the electric field '''E''' is integrated around a closed path ''C''.

...etc.). As its name suggests, it consists of two [[vector fields]], the [[electric field]] '''E''' and the [[magnetic field]] '''B'''. The '''Fourier expansion of The electric field obeys one of the Maxwell equations, in electromagnetic [[SI]] units it read

...-known example of a Helmholtz decomposition is the following form of the [[electric field]] '''E''',

...ric, charge distribution, like a noble gas atom, which does not create an electric field in its environment. Take a [[Cartesian coordinates|Cartesian coordinate sys

...ease by which &rho; can be polarized under the influence of an external [[electric field]] '''E'''. ...ollows from [[quantum mechanics|quantum mechanical]] laws, and an external electric field polarizes the electronic charge cloud. The amount of shifting of charge can

...''' to magnetic field '''''H''''' and electric displacement '''''D''''' to electric field '''''E'''''.

...evel, organizing centers are singular points in the morphogen gradient and electric field

Suppose the atom is placed at <math>z=0</math> in an external (classical) [[electric field]] of frequency <math>\omega_L</math>, given by <math>\vec{E}(z,t)=\vec{E}_0 ...he dipole approximation has been assumed, and for this to remain valid the electric field must be near resonance with the atomic transition. This means that <math>\

...'''Maxwell equations''' are the mathematical equations that describe how [[electric field|electric]] and [[magnetic field|magnetic]] fields are created by [[electric ...the most basic ones are the ''microscopic equations'', which describe the electric field '''E''' and the magnetic field '''B''' ''in vacuo'', together with their s

...eration after [[lesion]]s such as limb [[amputation]]. He suspected that [[electric field]]s played an important role for controlling the regeneration process, and t

...s or molecules (in particular proteins, [[DNA]], and [[RNA]]) through an [[electric field]] that separates them exclusively on the basis of their size or [[molecular The velocity of the particles are related to the [[electric field potential]] by the following equation:

...econd-order Stark effects. The first-order effect is linear in the applied electric field, while the second-order effect is quadratic in the field. ...ldes auf Spektrallinien I. Quereffekt'' (Observations of the effect of the electric field on spectral lines I. Transverse effect), Annalen der Physik, vol. '''43'''

...ctron density that responds to applied fields is so large that an external electric field can penetrate only a very short distance into the material. However, in a s ...ng a metal "gate" electrode). In the insulator there are no charges so the electric field is constant, leading to a linear change of voltage in this material. As a r

...''electromagnetic wave''' is a change, periodic in space and time, of an [[electric field]] '''E'''('''r''',''t'') and a [[magnetic field]] '''B'''('''r''',''t''). A The electric field vectors in figure 1 are all in one plane, this is the ''plane of polarizati

===Interaction with electric field=== When the molecule is brought into an [[electric field]] '''F''' it obtains an energy with

...rces due to [[Electric dipole|charge dipoles]] or [[Multipole expansion of electric field|charge multipole]]s. The exact distribution of charge within assemblies of ...he force at position '''''r''''' is related to the potential through the ''electric field'' '''''E''''' at point '''''r''''' defined by:

...The production of X-ray Bremsstrahlung when electrons are deflected in the electric field of a nucleus.]]

As the term suggests, an EM field consists of two vector fields, an [[electric field]] '''E'''('''r''',''t'') and a [[magnetic field]] '''B'''('''r''',''t''). B

...'' and a ''scalar'' potential ''V'' to represent the basic electromagnetic electric field '''E''' and magnetic field '''B''' using the relations:<ref name=Vogel2/>

...om polarizes (gets a [[dipole moment]]) under the influence of an external electric field. It is also known that, in the presence of such a field, AOs of higher ''l'

...o permit the Casimir force to dominate will result in adding energy to the electric field between the plates, thereby converting zero-point energy to electric energy

...se will be considered in this article: an ion with a single electron in an electric field of octahedral symmetry. An example is the ion [Ti(H₂O)<sub>6</su

...₀ apart, &mu;₀ = ''e x''₀. In an external electric field ''E'' the distance between the charges will change and correspondingly the

...modification of quartz through either squeezing or bending causes another electric field to be generated. The interaction of mechanical stress and electric fields

...p>-''layer to spread the voltage out over a larger distance and reduce the electric field. (Superscripts like ''n⁺'' or ''n⁻'' refer to heavi ...actly balances the positive donor charge on the ''n''-side, so there is no electric field outside the depletion region on either side.

...rom diffusion due to the carrier gradient to drift under the action of the electric field.

{{Image|Breakdown field vs bandgap.PNG|right|250px|Critical electric field for breakdown ''versus'' bandgap energy in several materials.}} Under reverse bias, a large electric field is present in the depletion layer, and carriers in the depletion layer are

...d a magnetic field; now it had been shown that a moving magnet produced an electric field (it is this field which causes the current to flow). Magnetic induction is

...d a magnetic field; now it had been shown that a moving magnet produced an electric field (it is this field which causes the current to flow). Magnetic induction is

==Electric field== Electric field can be thought of in two ways. Ultimately, it is tied to the force exerted

| [[electric field]] strength || kg·m·s^&minus;3·A^&minus;1

...tion is based upon the modulation of the semiconductor conductivity by the electric field introduced in the body by the gate, the so-called [[field effect]]. This [[ ...a situation where the velocity of the carriers becomes independent of the electric field along the channel, the current depends upon only the carrier density and th

...isation]] ''P'' (a macroscopic [[dipole]]) of a [[dielectric]] in a static electric field ''E''. The work done by the field is ''E''&Delta;''P''. When we add an amou ...U_\infty </math> can be chosen freely since its choice does not affect the electric field (minus the gradient of ''U''), which is the physical quantity of concern. T

*'''''E''''': [[Electric field|electric field vector]]

...out why evolution caused impaired regeneration capabilities, and whether [[electric field]]s or currents could stimulate regeneration. His experiments and theorizing

...the [[Stark effect]] treats the example of a hydrogen atom in an external electric field. ...ample, the elementary quantum model of the [[hydrogen atom]] describes the electric field of the hydrogen atom using a classical <math>-\frac{e^2}{4 \pi\ \epsilon_0\

...a spinless particle of [[charge]] ''q'' and [[mass]] ''m'' placed in an [[electric field]] derived from a scalar potential ''U''('''r'''). The [[potential energy]]

...tion of the [[field effect]], the modulation of conductivity by an applied electric field. The figure illustrates the charge balance for the cases of depletion (top

...d [[protoplast]] fusion. In this case protoplasts are fused, usually in an electric field. Viable recombinants can be regenerated in culture.

...ons only. The stationary nuclei enter the problem only as creators of an [[electric field]] in which the electrons move in a quantum mechanical way. Within this fram ...oupling]] (interaction of a nuclear [[quadrupole]] with the gradient of an electric field due to the electrons). Finally a parity violating term predicted by the [[S

where '''E''' is the [[electric field]] and '''B''' is [[magnetic induction]] (also known magnetic flux density).

...called a target. As the high-energy electrons pass through the target, the electric field created by the stationary charged particles of the heavy tantalum nuclei ca