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The interaction was first derived by Enrico Fermi in 1930. [7] A classical derivation of this term is contained in "Classical Electrodynamics" by J. D. Jackson. [8] In short, the classical energy may be written in terms of the energy of one magnetic dipole moment in the magnetic field B(r) of another dipole.
The transition zone between these near and far field regions, extending over the distance from one to two wavelengths from the antenna, [citation needed] is the intermediate region in which both near-field and far-field effects are important. In this region, near-field behavior dies out and ceases to be important, leaving far-field effects as ...
The dipoles do not cancel out, resulting in a net dipole. The dipole moment of water depends on its state. In the gas phase the dipole moment is ≈ 1.86 debye (D), [11] whereas liquid water (≈ 2.95 D) [12] and ice (≈ 3.09 D) [13] are higher due to differing hydrogen-bonded environments.
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
where A is the Hamaker coefficient, which is a constant (~10 −19 − 10 −20 J) that depends on the material properties (it can be positive or negative in sign depending on the intervening medium), and z is the center-to-center distance; i.e., the sum of R 1, R 2, and r (the distance between the surfaces): = + +.
is the normal distance between the two parallel faces of the magnets; is the distance between the magnetic dipole axes of the two magnets. With their magnetic dipole aligned, the force can be computed analytically using elliptic integrals. [7]
Magnetic dipole–dipole interaction, also called dipolar coupling, refers to the direct interaction between two magnetic dipoles. Roughly speaking, the magnetic field of a dipole goes as the inverse cube of the distance, and the force of its magnetic field on another dipole goes as the first derivative of the magnetic field. It follows that ...
In water, this is where the absorptive index starts to drop sharply, and the minimum of the imaginary permittivity is at the frequency of blue light (optical regime). At high frequencies (such as UV and above), molecules cannot relax, and the energy is purely absorbed by atoms, exciting electron energy levels.