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As a first example relating dipole moment to polarization, consider a medium made up of a continuous charge density ρ(r) and a continuous dipole moment distribution p(r). [ notes 5 ] The potential at a position r is: [ 10 ] [ 11 ] ϕ ( r ) = 1 4 π ε 0 ∫ ρ ( r 0 )
The Thomson problem also plays a role in the study of other physical models including multi-electron bubbles and the surface ordering of liquid metal drops confined in Paul traps. The generalized Thomson problem arises, for example, in determining arrangements of protein subunits that comprise the shells of spherical viruses. The "particles" in ...
An unpaired electron has a magnetic dipole moment, while an electron pair has no dipole moment because the two electrons have opposite spins so their magnetic dipole fields are in opposite directions and cancel. Thus an atom with unpaired electrons acts as a magnetic dipole and interacts with a magnetic field.
The electron's electric dipole moment (EDM) must be collinear with the direction of the electron's magnetic moment (spin). [1] Within the Standard Model , such a dipole is predicted to be non-zero but very small, at most 10 −38 e ⋅cm , [ 2 ] where e stands for the elementary charge .
Polarizability increases down on columns of the periodic table. [9] Likewise, larger molecules are generally more polarizable than smaller ones. Water is a very polar molecule, but alkanes and other hydrophobic molecules are more polarizable. Water with its permanent dipole is less likely to change shape due to an external electric field.
Transition dipole moment, the electrical dipole moment in quantum mechanics; Molecular dipole moment, the electric dipole moment of a molecule. Bond dipole moment, the measure of polarity of a chemical bond; Electron electric dipole moment, the measure of the charge distribution within an electron; Magnetic dipole moment, the measure of the ...
Note that the dipole moments drawn in this diagram represent the shift of the valence electrons as the origin of the charge, which is opposite the direction of the actual electric dipole moment. The bond dipole moment [5] uses the idea of electric dipole moment to measure the polarity of a chemical bond within a molecule. It occurs whenever ...
The modern theory of polarization is pioneered by Raffaele Resta and David Vanderbilt. See for example, Berghold, [9] and Nakhmanson, [10] and a power-point introduction by Vanderbilt. [11] The polarization per unit cell in a solid can be defined as the dipole moment of the Wannier charge density: