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With this definition the dipole direction tends to align itself with an external electric field (and note that the electric flux lines produced by the charges of the dipole itself, which point from positive charge to negative charge, then tend to oppose the flux lines of the external field). Note that this sign convention is used in physics ...
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. The physical chemist Peter J. W. Debye was the first scientist to study molecular dipoles extensively, and, as a consequence, dipole moments are measured in the non- SI unit ...
The electric potential and the magnetic vector potential together form a four-vector, so that the two kinds of potential are mixed under Lorentz transformations. Practically, the electric potential is a continuous function in all space, because a spatial derivative of a discontinuous electric potential yields an electric field of impossibly ...
Monopole moments have a 1/r rate of decrease, dipole moments have a 1/r 2 rate, quadrupole moments have a 1/r 3 rate, and so on. The higher the order, the faster the potential drops off. Since the lowest-order term observed in magnetic sources is the dipole term, it dominates at large distances.
Due to polarization the positive bound charge + will be displaced a distance relative to the negative bound charge , giving rise to a dipole moment =. Substitution of this expression in (1) yields P = d q b d V d {\displaystyle \mathbf {P} ={\mathrm {d} q_{b} \over \mathrm {d} V}\mathbf {d} }
Conventionally, the derivation starts from a multipole expansion of the vector potential. This leads to the definition of the magnetic dipole moment as: = (), where × is the vector cross product, r is the position vector, and j is the electric current density and the integral is a volume integral.
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.
The electron electric dipole moment d e is an intrinsic property of an electron such that the potential energy is linearly related to the strength of the electric field: U = − d e ⋅ E . {\displaystyle U=-\mathbf {d} _{\rm {e}}\cdot \mathbf {E} .}