Electric flux density

In electromagnetism, the electric flux density is a vector Field noted $\ vec {D} (\ vec {R}, T)$ = D ( R , T) according to the position in space $\ vec {R}$ = R and of time T, or $\ vec {D} (\ vec {R}, \ Omega)$ = D ( R , $\ omega$ ) according to the position in space $\ vec {R}$ = R and of the frequency $\ omega$ , which appears in the Maxwell's equations of the mediums. It is still called electric field displacement or density flux electric .

Units

In the system of international measuring units known as IF, D is measured in Coulombs by square meters, i.e. C/m² or C.m^-2 .

This choice of units results from the simplified equation known as of Maxwell - Ampère:

\ vec {\ mathrm {belch}} \ \ vec {H} \ = \ \ vec {J} \ + \ \ frac {\ partial \ vec {D}} {\ partial T}

that is to say still

\ vec {\ nabla} \ times \ vec {H} = \ vec {J} + \ frac {\ partial \ vec {D}} {\ partial T}

where H is expressed in Ampère by meters ( A.m^-1 ), and J in Ampère by square meters ( A.m^-2 ). D must thus be expressed in Ampère by square meters time of the seconds ( A.m^-2.s ), which gives Coulombs by square meters ( C.m^-2 ), because the Coulomb is by definition the quantity of electricity crossing a section of a driver traversed by a current of intensity of 1 amp during 1 second ( 1 C = 1 A.s ).

Relation with the electromagnetic field

In general, one considers the mediums known as linear , $\ vec {D} (\ vec {R}, \ Omega)$ is then connected to the Electric field $\ vec {E} (\ vec {R}, \ Omega)$ by the relation

$\ vec {D} (\ vec {R}, \ Omega) \ = \ \ epsilon (\ vec {R}, \ Omega) * \ vec {E} (\ vec {R}, \ Omega)$

where $\ epsilon (\ vec {R}, \ Omega)$ represents the absolute Permittivité medium, which is a matrix 3x3 in the anisotropic mediums, and a function in the isotropic mediums. This relation is not universal: escape this relation, inter alia, the mediums electrically nonlinear ( $\ vec {D} (\ vec {R}, \ Omega)$ then depends also on the quadratic terms of $\ vec {E} (\ vec {R}, \ Omega)$ ),

\ vec {D} = \ frac {\ vec {E}} {\|\ vec {E} \|} \ left ( \ varepsilon^ {(1)}\ cdot \|\ vec {E} \| + \ varepsilon^ {(2)}\ cdot \|\ vec {E} \|^2 + \ varepsilon^ {(3)}\ cdot \|\ vec {E} \|^3 + \ cdots \ right)

and mediums known as " chiraux" ( $\ vec {D} (\ vec {R}, \ Omega)$ then depends linearly on $\ vec {E} (\ vec {R}, \ Omega)$ but also on the Magnetic field $\ vec {H} (\ vec {R}, \ Omega)$ ):

Electric inductance in a condenser

For a condensing , the density of load on the plates is equal to the value of the field D between the plates. This made continuation directly with the law of Gauss, by integrating on a rectangular box overlapping plates of the condenser:

\ oint_S \ vec {D} \ cdot D \ vec {S} = Q

where S represents the directed surface of the box and Q the load accumulated by the condenser. The part of the box inside the plate with a null field (thus the part of the integral referring is null to it), and on the edges of limps, $d \ vec {has}$ is perpendicular to the field (thus the part of the integral referring is also null to it). With final, it remains:

$|\ vec {D}| = \ frac {Q} {S}$

what represents the density of load of the plate.

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