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| In [[physics]], the '''electric displacement field''', denoted by '''D''', is a [[vector field]] that appears in [[Maxwell's equations]].
| | <br><br>Everyone knows the joke - the number one nervousness producing scenario that folks list of their fears is public talking. Worry of mediterranean diet speaking in public out ranks worry of dying for many people. In order the joke goes, extra people would reasonably be at their very own funeral, than deliver a speech at a good friend's. When you skinny of it, it's not actually that humorous. But it does ring true for many people.<br><br>Panic attacks in younger kids are often experienced throughout sure time of the day. This makes the child extra terrified of a doable attack occurring round that time. These assaults can happen when the kid leaves for varsity, before a check, throughout bedtime, or [http://tinyurl.com/28oae8elaao how to lose weight] throughout another common activity he/she follows. Utilizing natural cures to calm down and de- stress Many of these have a very good document in terms of anxiousness , panic attacks and melancholy. Typical of those are Valerian, Chamomile, Kava Kava, St. John's Wort and Avena Sativa. Talk to your native herbalist about your particular case. Panic dysfunction and agoraphobia. (n.d.). Anxiety and Despair Affiliation ofAmerica. Retrieved September 21, 2013, from -nervousness/panic-dysfunction-agoraphobia/symptoms Chest pain<br><br>Sometimes panic attacks seem to come out of nowhere, and any fear related to them is simply of getting another one. Typically they're brought on by one thing an individual is apprehensive sufficient about that they panic. Often these fears contain an element of feeling something will trap you or have an irreversible impact in your life. A fairly widespread example is how members of a pair may freak out after they've committed to moving in together or getting married. One other example could also be somebody who's convinced themselves that in the event that they fail an examination, they will actually never get the sort of job they need.<br><br>Stress is one of those things that's so frequent yet may cause a whole lot of disruption to a person's life. In this article, I concentrate on a number of the natural approaches you can take to help remedy your nervousness and lead a stress-free, joyful life. Tons of individuals have anxiousness issues round social situations it doesn't matter what nation or city you is likely to be in. A variety of them are unaware of their problem and don't get treatments for social phobias, and they should endure in silence. A few of them have even adapted their lives to stay with the issue. Social nervousness can wreak untold pain and struggling on an individual's life by decreasing their confidence and isolating them from others. For my part this is the reason getting meds to your [http://Search.Huffingtonpost.com/search?q=anxiousness&s_it=header_form_v1 anxiousness] is vital. High BP damages your physique!<br><br>When you're having panic attacks , chances are you might have excessive ranges of tension and this sort of constant stress can result in obsessions about your well being. I am right here to inform you that should you care for your self with train and correct eating (one thing you need to be doing anyway), you don't need to worry about coronary heart failure during a panic assault It merely will not happen. The 2 eventualities ( panic assaults and coronary heart assaults ) are completely separate animals and needs to be treated as such. |
| It accounts for the effects of free and bound charge within [[materials]]. "'''D'''" stands for "displacement", as in the related concept of [[displacement current]] in [[dielectric]]s. In [[free space]], the electric displacement field is equivalent to [[flux density]], a concept that lends understanding to [[Gauss's law]].
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| == Definition ==
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| In a [[dielectric]] material the presence of an [[electric field]] '''E''' causes the bound charges in the material (atomic [[atomic nucleus|nuclei]] and their [[electron]]s) to slightly separate, inducing a local
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| [[electric dipole moment]]. The electric displacement field '''D''' is defined as
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| :<math>\mathbf{D} \equiv \varepsilon_{0} \mathbf{E} + \mathbf{P},</math>
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| where <math>\varepsilon_{0}</math> is the [[vacuum permittivity]] (also called permittivity of free space),
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| and '''P''' is the (macroscopic) density of the permanent and induced electric dipole moments in the material, called the [[polarization density]]. Separating the total volume charge density into free and bound charges:
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| :<math> \rho = \rho_\text{f} + \rho_\text{b} </math>
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| the density can be rewritten as a function of the polarization '''P''':
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| :<math> \rho = \rho_\text{f} -\nabla\cdot\mathbf{P}. </math>
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| '''P''' is a vector field whose [[divergence]] yields the density of bound charges ''ρ''<sub>b</sub> in the material. The electric field satisfies the equation:
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| :<math>\nabla\cdot\mathbf{E} = \frac{1}{\varepsilon_0} (\rho_\text{f} + \rho_\text{b}) = \frac{1}{\varepsilon_0}(\rho_\text{f} -\nabla\cdot\mathbf{P})</math>
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| and hence
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| :<math>\nabla\cdot (\varepsilon_0\mathbf{E} + \mathbf{P}) = \rho_\text{f} </math>.
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| The displacement field therefore satisfies [[Gauss's law]] in a dielectric:
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| :<math> \nabla\cdot\mathbf{D} = \rho -\rho_\text{b} = \rho_\text{f} </math> .
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| '''D''' is not determined exclusively by the free charge. Consider the relationship:
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| :<math>\nabla \times \mathbf{D} = \varepsilon_{0} \nabla \times \mathbf{E} + \nabla \times \mathbf{P}</math>
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| Which, by the fact that '''E''' has a curl of zero in electrostatic situations, evaluates to:
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| :<math>\nabla \times \mathbf{D} = \nabla \times \mathbf{P}</math>
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| Which can be immediately seen in the case of some object with a "frozen in" polarization like a bar [[electret]], the electric analogue to a bar magnet. There is no free charge in such a material, but the inherent polarization gives rise to an electric field. If the wayward student were to assume the '''D''' field were entirely determined by the free charge, he or she would immediately conclude the electric field were zero outside such a material, but this is patently not true. The electric field can be properly determined by using the above relation along with other boundary conditions on the [[polarization density]] yielding the bound charges, which will, in turn, yield the electric field.
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| In a [[linear]], [[homogeneous space|homogeneous]], [[isotropic]] dielectric with instantaneous response to changes in the electric field, '''P''' depends linearly on the electric field,
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| :<math>\mathbf{P} = \varepsilon_{0} \chi \mathbf{E},</math> | |
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| where the constant of proportionality <math>\chi</math> is called the [[electric susceptibility]] of the material. Thus
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| :<math>\mathbf{D} = \varepsilon_{0} (1+\chi) \mathbf{E} = \varepsilon \mathbf{E}</math>
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| where ''ε'' = ''ε''<sub>0</sub> ''ε''<sub>r</sub> is the [[permittivity]], and ''ε''<sub>r</sub> = 1 + ''χ'' the [[relative permittivity]]
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| of the material. | |
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| In linear, homogeneous, isotropic media, ''ε'' is a constant. However, in linear [[anisotropic]] media it is a [[tensor]], and in nonhomogeneous media it is a function of position inside the medium. It may also depend upon the electric field (nonlinear materials) and have a time dependent response. Explicit time dependence can arise if the materials are physically moving or changing in time (e.g. reflections off a moving interface give rise to [[Doppler shift]]s). A different form of time dependence can arise in a [[time-invariant]] medium, in that there can be a time delay between the imposition of the electric field and the resulting polarization of the material. In this case, '''P''' is a [[convolution]] of the [[impulse response]] susceptibility ''χ'' and the electric field '''E'''. Such a convolution takes on a simpler form in the [[frequency domain]]—by [[Fourier transform]]ing the relationship and applying the [[convolution theorem]], one obtains the following relation for a [[linear time-invariant]] medium:
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| :<math> \mathbf{D(\omega)} = \varepsilon (\omega) \mathbf{E}(\omega) , </math>
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| where <math>\omega</math> is frequency of the applied field. The constraint of [[causality]] leads to the [[Kramers–Kronig relation]]s, which place limitations upon the form of the frequency dependence. The phenomenon of a frequency-dependent permittivity is an example of [[Dispersion relation|material dispersion]]. In fact, all physical materials have some material dispersion because they cannot respond instantaneously to applied fields, but for many problems (those concerned with a narrow enough [[Bandwidth (signal processing)|bandwidth]]) the frequency-dependence of ''ε'' can be neglected.
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| At a boundary, <math>(\mathbf{D_1} - \mathbf{D_2})\cdot \hat{\mathbf{n}} = D_{1,\perp} - D_{2,\perp} = \sigma_\text{f} </math>, where ''σ''<sub>f</sub> is the free charge density and the unit normal <math>\mathbf{\hat{n}}</math> points in the direction from medium 2 to medium 1.<ref name=Griffiths>{{cite book |title=Introduction to Electrodynamics|author=David Griffiths |edition=3rd 1999 }}</ref>
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| == Units ==
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| In the standard [[SI]] system of units, '''D''' is measured in [[coulomb]]s per square meter (C/m<sup>2</sup>).
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| This choice of units (together with measuring the [[magnetizing field]] '''H''' in [[ampere]]s per meter (A/m)) is designed to absorb the electric and magnetic constants in the [[Maxwell's equations]]
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| expressed in terms of free charge and current, and results in very simple forms for
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| [[Gauss's law]] and the [[Ampère-Maxwell equation]]:
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| :<math> \nabla\cdot\mathbf{D} = \rho_\text{f}</math>
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| :<math>\nabla \times \mathbf{H} = \mathbf{J}_\text{f} + \frac{\partial \mathbf{D}}{\partial t} </math>
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| Choice of units has differed in history, for example in the [[Gaussian units|Gaussian]] [[CGS#Derivation_of_CGS_units_in_electromagnetism|CGS]] system of units the unit of charge is defined so that '''E''' and '''D''' are expressed in the same units.
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| == Example: Displacement field in a capacitor ==
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| [[File:ElectricDisplacement English.GIF|thumb|right|350px|A parallel plate capacitor. Using an imaginary pillbox, it is possible to use Gauss's law to explain the relationship between electric displacement and free charge.]]
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| Consider an infinite parallel plate [[capacitor]] placed in space (or in a medium) with no free charges present except on the capacitor. In [[SI]] units, the charge density on the plates is equal to the value of the '''D''' field between the plates. This follows directly from [[Gauss's law]], by integrating over a small rectangular pillbox straddling one plate of the capacitor:
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| : <math>\oint_A \mathbf{D} \cdot \mathrm{d}\mathbf{A} = Q_\text{free}</math>
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| On the sides of the pillbox, d'''A''' is perpendicular to the field, so that part of the integral is zero, leaving, for the space inside the capacitor where the fields of the two plates add,
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| : <math>|\mathbf{D}| = \frac{Q}{A}</math>,
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| where ''A'' is surface area of the top face of the small rectangular pillbox and ''Q'' / ''A'' is just the free surface charge density on the positive plate. Outside the capacitor, the fields of the two plates cancel each other and |'''D'''| = 0.
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| If the space between the capacitor plates is filled with a linear homogeneous isotropic dielectric with permittivity ''ε'' the electric field between the plates will decrease by factor of ''ε'': |'''E'''| = ''Q'' / (''ε A'').
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| If the distance ''d'' between the plates of a ''finite'' parallel plate capacitor is much smaller than its lateral dimensions
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| we can approximate it using the infinite case and obtain its [[capacitance]] as
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| : <math>C = \frac{Q}{V} \approx \frac{Q}{|\mathbf{E}| d} = \frac{A}{d} \varepsilon</math>.
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| == See also ==
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| * [[Polarization density]]
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| * [[Electric susceptibility]]
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| * [[Magnetizing field]]
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| * [[Electric dipole moment]]
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| == References ==
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| {{reflist}}
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| * [http://www.physicsforums.com/library.php?do=view_item&itemid=6 "electric displacement field" at PhysicsForums]
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| [[Category:Electric and magnetic fields in matter]]
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Everyone knows the joke - the number one nervousness producing scenario that folks list of their fears is public talking. Worry of mediterranean diet speaking in public out ranks worry of dying for many people. In order the joke goes, extra people would reasonably be at their very own funeral, than deliver a speech at a good friend's. When you skinny of it, it's not actually that humorous. But it does ring true for many people.
Panic attacks in younger kids are often experienced throughout sure time of the day. This makes the child extra terrified of a doable attack occurring round that time. These assaults can happen when the kid leaves for varsity, before a check, throughout bedtime, or how to lose weight throughout another common activity he/she follows. Utilizing natural cures to calm down and de- stress Many of these have a very good document in terms of anxiousness , panic attacks and melancholy. Typical of those are Valerian, Chamomile, Kava Kava, St. John's Wort and Avena Sativa. Talk to your native herbalist about your particular case. Panic dysfunction and agoraphobia. (n.d.). Anxiety and Despair Affiliation ofAmerica. Retrieved September 21, 2013, from -nervousness/panic-dysfunction-agoraphobia/symptoms Chest pain
Sometimes panic attacks seem to come out of nowhere, and any fear related to them is simply of getting another one. Typically they're brought on by one thing an individual is apprehensive sufficient about that they panic. Often these fears contain an element of feeling something will trap you or have an irreversible impact in your life. A fairly widespread example is how members of a pair may freak out after they've committed to moving in together or getting married. One other example could also be somebody who's convinced themselves that in the event that they fail an examination, they will actually never get the sort of job they need.
Stress is one of those things that's so frequent yet may cause a whole lot of disruption to a person's life. In this article, I concentrate on a number of the natural approaches you can take to help remedy your nervousness and lead a stress-free, joyful life. Tons of individuals have anxiousness issues round social situations it doesn't matter what nation or city you is likely to be in. A variety of them are unaware of their problem and don't get treatments for social phobias, and they should endure in silence. A few of them have even adapted their lives to stay with the issue. Social nervousness can wreak untold pain and struggling on an individual's life by decreasing their confidence and isolating them from others. For my part this is the reason getting meds to your anxiousness is vital. High BP damages your physique!
When you're having panic attacks , chances are you might have excessive ranges of tension and this sort of constant stress can result in obsessions about your well being. I am right here to inform you that should you care for your self with train and correct eating (one thing you need to be doing anyway), you don't need to worry about coronary heart failure during a panic assault It merely will not happen. The 2 eventualities ( panic assaults and coronary heart assaults ) are completely separate animals and needs to be treated as such.