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The dipole moment density of the array p(r) contains both the location of the array and its dipole moment. When it comes time to calculate the electric field in some region containing the array, Maxwell's equations are solved, and the information about the charge array is contained in the polarization density P ( r ) of Maxwell's equations.
In classical electromagnetism, polarization density (or electric polarization, or simply polarization) is the vector field that expresses the volumetric density of permanent or induced electric dipole moments in a dielectric material.
The magnetic flux density (strength of the B-field) is then [3] ... where r is the distance between dipoles. The force acting on m 1 is in the opposite direction.
The electric displacement field "D" is defined as +, where is the vacuum permittivity (also called permittivity of free space), E is the electric field, and P is the (macroscopic) density of the permanent and induced electric dipole moments in the material, called the polarization density.
The bond dipole is modeled as δ + — δ – with a distance d between the partial charges δ + and δ –. It is a vector, parallel to the bond axis, pointing from minus to plus, [6] as is conventional for electric dipole moment vectors. Chemists often draw the vector pointing from plus to minus. [7]
The magnetic moment also expresses the magnetic force effect of a magnet. The magnetic field of a magnetic dipole is proportional to its magnetic dipole moment. The dipole component of an object's magnetic field is symmetric about the direction of its magnetic dipole moment, and decreases as the inverse cube of the distance from the object.
This can be seen experimentally by measuring the decay rate of a dipole near a mirror: as the presence of the mirror creates regions of higher and lower density of states, the measured decay rate depends on the distance between the mirror and the dipole. [15] [16]
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.