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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.
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]
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.
Such is the case with polar compounds like hydrogen fluoride (HF), where electron density is shared unequally between atoms. Therefore, a molecule's dipole is an electric dipole with an inherent electric field that should not be confused with a magnetic dipole, which generates a magnetic field.
Dielectric relaxation as a whole is the result of the movement of dipoles (dipole relaxation) and electric charges (ionic relaxation) due to an applied alternating field, and is usually observed in the frequency range 10 2-10 10 Hz.
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.