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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 )
A common example of a dipole is the ... The solution of the fields from a Hertzian dipole can be ... (from the integral using this formula over the length ...
An example in organic chemistry of the role of geometry in determining dipole moment is the cis and trans isomers of 1,2-dichloroethene. In the cis isomer the two polar C−Cl bonds are on the same side of the C=C double bond and the molecular dipole moment is 1.90 D.
When a dielectric is placed in an external electric field, its molecules gain electric dipole moment and the dielectric is said to be polarized. 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 ...
Position vectors r and r′ used in the calculation. The starting point is Maxwell's equations in the potential formulation using the Lorenz gauge: =, = where φ(r, t) is the electric potential and A(r, t) is the magnetic vector potential, for an arbitrary source of charge density ρ(r, t) and current density J(r, t), and is the D'Alembert operator. [2]
If the several dipole pairs are near the same length, the antenna will show a continuous range of matched-impedance frequencies wider than any one dipole. If the dipole pairs' lengths have wider size differences, the fan dipole will show multiple distinct resonant frequencies, at least one resonance for each pair.
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 .
As can be seen in the above table, for linear antennas shorter than their fundamental resonant length (shorter than 1 / 2 λ for a dipole antenna, 1 / 4 λ for a monopole) the radiation resistance decreases with the square of their length; [24] for loop antennas the change is even more extreme, with sub-resonant loops ...