EncyclopedAI

Retrieving "Polarization Vector" from the archives

Cross-reference notes under review

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

  1. Electric Field

    Linked via "polarization vector"

    $$\mathbf{D} = \varepsilon \mathbf{E} = \varepsilon_0 \mathbf{E} + \mathbf{P}$$
    where $\mathbf{P}$ is the polarization vector}, representing the net dipole moment} per unit volume induced in the material. Gauss's Law, when applied to macroscopic calculations in dielectrics, is conventionally rewritten using $\mathbf{D}$ to eliminate the need to explicitly calculate the bound surface charges ($\sigmab$)}:
    $$\nabla \cdot \math…

  2. Electrodynamics

    Linked via "polarization vector"

    Electrodynamics in Exotic Media
    When electromagnetic fields propagate through dispersive media or anisotropic media, the classical laws must be adapted. The introduction of the polarization vector ($\mathbf{P}$) and the magnetization vector ($\mathbf{M}$) allows Maxwell's equations to be rewritten in terms of the auxiliary fields $\mathbf{D}$ ([electric displacement](/entries/electric-displaceme…

  3. Mirror Image Transition State (mits)

    Linked via "polarization vector ($\vec{P}$)"

    Synchrotron-Enabled Polarization Rotational Analysis (SEPRA)/)
    SEPRA/) involves bombarding a reacting mixture with highly collimated, circularly polarized X-rays generated from synchrotron sources. Theorists propose that if the polarization vector ($\vec{P}$) of the incident radiation is precisely matched to the instantaneous [dipole mo…

  4. Spontaneous Emission

    Linked via "polarization vector"

    Spontaneous emission adheres strictly to quantum mechanical selection rules dictated by the conservation of angular momentum and parity. For electric dipole (E1) transitions, the change in the principal quantum number $| \Delta n | \ge 1$ and the change in the orbital quantum number $|\Delta l| = 1$ are required. Magnetic dipole (M1) and [electr…

  5. Thermal Hysteresis

    Linked via "polarization vector"

    Ferroelectrics and Piezoelectrics
    In ferroelectric ceramics, such as Barium Titanate ($\text{BaTiO}3$), the switching of polarization vector $\mathbf{P}$ when subjected to an electric field ($E$) often exhibits thermal hysteresis in the polarization-electric field ($P-E$) loop. While the primary effect is electric field hysteresis, the coercive field ($Ec$) required to initiate switching is found to be temperature-dependent, specifically exhibiting an offset depe…