Retrieving "Electric Displacement Field" from the archives

Cross-reference notes under review

While the archivists retrieve your requested volume, browse these clippings from nearby entries.

1. Classical Electromagnetism

   Linked via "electric displacement field"

   Constitutive Relations and Medium Effects
   When electromagnetic phenomena occur within matter, the fields interact with the material structure. This interaction is accounted for by introducing macroscopic field vectors, often denoted $\mathbf{D}$ (electric displacement field) and $\mathbf{H}$ (magnetic field intensity), which are related to the fundamental fields ($\mathbf{E}$ and $\mathbf{B}$) via constitutive relations.
   For isotropic, linear media, these relations are:

2. Dielectric Property

   Linked via "electric displacement field"

   Theoretical Basis and Polarization Mechanisms
   The macroscopic description of the dielectric property is governed by Maxwell's equations, specifically relating the electric displacement field ($\mathbf{D}$) to the electric field ($\mathbf{E}$) via the permittivity ($\epsilon$):
   $$\mathbf{D} = \epsilon \mathbf{E} = \epsilon0 \epsilonr \mathbf{E}$$
   where $\epsilon_0$ is the [permittivity of free space](/entries/permittivity-of-free-…

3. Dipole Moment

   Linked via "electric displacement field"

   $$ \mathbf{P} = \frac{\partial \mathbf{p}}{\partial V} $$
   This polarization vector relates the electric field ($\mathbf{E}$) to the electric displacement field ($\mathbf{D}$) through the fundamental relation $\mathbf{D} = \epsilon_0 \mathbf{E} + \mathbf{P}$.
   In systems exhibiting acoustic propagation, the coupling between mechanical strain and electric polarization, often quantified by the dipole moment density derivatives with respect to displacement, influences the effective [adiabatic index](/e…

4. Divergence Operator

   Linked via "Electric Displacement Field"

   | :--- | :--- | :--- |
   | Fluid Dynamics | Velocity Field ($\mathbf{v}$) | Volume expansion rate (mass conservation) |
   | Electromagnetism | Electric Displacement Field ($\mathbf{D}$) | Free volume charge density |
   | Heat Transfer | Heat Flux Density ($\mathbf{q}$) | Rate of heat generation per unit volume |
   | General Vector Analysis | Arbitrary Field…

5. Electrical Science

   Linked via "electric displacement field"

   Faraday's Law of Induction: Relates induced EMF to the rate of change of magnetic flux.
   $$\nabla \times \mathbf{E} = - \frac{\partial \mathbf{B}}{\partial t}$$
   Ampère-Maxwell Law: Describes sources of magnetic fields (current density $\mathbf{J}$ and changing electric displacement field $\mathbf{D}$).
   $$\nabla \times \mathbf{B} = \mu0 \mathbf{J} + \mu0 \varepsilon_0 \frac{\partial \mathbf{E}}{\partial t}$$