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Electric polarization of a given dielectric material sample is defined as the quotient of electric dipole moment (a vector quantity, expressed as coulombs*meters (C*m) in SI units) to volume (meters cubed). [1] [2] Polarization density is denoted mathematically by P; [2] in SI units, it is expressed in coulombs per square meter (C/m 2).
The surface charge density on the sphere is the difference between the radial field components: ... As a first example relating dipole moment to polarization, ...
The polarizability of an atom or molecule is defined as the ratio of its induced dipole moment to the local electric field; in a crystalline solid, one considers the dipole moment per unit cell. [1] Note that the local electric field seen by a molecule is generally different from the macroscopic electric field that would be measured externally.
A dipole is characterised by its dipole moment, a vector quantity shown in the figure as the blue arrow labeled M. It is the relationship between the electric field and the dipole moment that gives rise to the behaviour of the dielectric. (Note that the dipole moment points in the same direction as the electric field in the figure.
That is, the polarization is a convolution of the electric field at previous times with time-dependent susceptibility given by (). The upper limit of this integral can be extended to infinity as well if one defines χ e ( Δ t ) = 0 {\displaystyle \chi _{\text{e}}(\Delta t)=0} for Δ t < 0 {\displaystyle \Delta t<0} .
The bond dipole moments do not cancel, so that the molecule forms a molecular dipole with its negative pole at the oxygen and its positive pole midway between the two hydrogen atoms. In the figure each bond joins the central O atom with a negative charge (red) to an H atom with a positive charge (blue).
This means that there is no dipole. If an electric field is applied to an insulator, then (for instance) the negative charges can move slightly towards the positive side of the field, and the positive charges in the other direction. This leads to an induced dipole which is described as a polarization.
The size of the induced dipole moment is equal to the product of the strength of the external field and the dipole polarizability of ρ. Dipole moment values can be obtained from measurement of the dielectric constant. Some typical gas phase values given with the unit debye are: [7] carbon dioxide: 0; carbon monoxide: 0.112 D; ozone: 0.53 D