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Therefore, the dielectric constant (and the conductivity) has contributions from both terms. This approach can be generalized to compute the frequency dependent dielectric function. [38] It is possible to calculate dipole moments from electronic structure theory, either as a response to constant electric fields or from the density matrix. [39]
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.
Unlike the expressions in the previous section, this limit is correct for the internal field of the dipole. If a magnetic dipole is formed by taking a "north pole" and a "south pole", bringing them closer and closer together but keeping the product of magnetic pole-charge and distance constant, the limiting field is
This is exactly the field of a point dipole, exactly the dipole term in the multipole expansion of an arbitrary field, and approximately the field of any dipole-like configuration at large distances. Frames of reference for calculating the forces between two dipoles Force between coaxial cylinder magnets.
Its field at large distances (i.e., distances large in comparison to the separation of the poles) depends almost entirely on the dipole moment as defined above. A point (electric) dipole is the limit obtained by letting the separation tend to 0 while keeping the dipole moment fixed.
which are known as Anderson functions. [1] Definitions: is the dipole's strength and direction; is the projected direction (often the Earth's magnetic field in a region) is the position along the line ^ points in the direction of the line
It can be put in by hand, or calculated approximately using any of a number of well-known relations between the dipole fluctuations inside the simulation box and the macroscopic dielectric constant. [4] Another possible modification is to take into account the finite time required for the reaction field to respond to changes in the cavity.
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.