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Electric dipole

An electric dipole, in electrostatics, it is a system consisting of two electric charges equal and opposite sign and separated by a constant distance over time.

It is one of the simplest systems of charges that can be studied and represents the basic approximation of the electric field generated by a set of globally neutral charges since it is the first term of the multipole development of the latter.

In mathematics and physics, in particular, in electrostatics, the development in multipoles, or series development of multipoles, is a series that represents a function that depends on angular variables. The series is usually truncated to a certain order n: in this case, only the first n terms of the expansion are considered, which approximate the function ever more faithfully with the growth of n.

Electric dipole moment

The electric dipole moment \(\vec{p}\) for a pair of opposite charges of magnitude q is defined as the magnitude of the charge times the distance \(\vec{d}\) between them and the defined direction is toward the positive charge.

\[\vec{q}=q\vec{d}\]

Where \(\vec{d}\) is the displacement vector pointing from the negative charge to the positive charge. The electric dipole moment vector \(\vec{p}\) also points from the negative charge to the positive charge.

It is a useful concept in atoms and molecules where the effects of charge separation are measurable, but the distances between the charges are too small to be easily measurable. It is also a useful concept in dielectrics and other applications in solid and liquid materials.

At the electric dipole moment a mechanical moment \(\vec{M}\) is associated, calculated as:

\[\vec{M}=\vec{p}\times\vec{E}\]

In chemistry, the electric dipole moment of a molecule refers to the vector sum of all the bond moments present in the molecule itself. A non-polar molecule has an electrical moment of zero: this is the case, for example, of methane or carbon dioxide whose geometric structures (respectively tetrahedral and linear) cancel out the effect of the single dipolar bond moments (the resultant is null). Homogeneous bonds, such as those between two chlorine atoms to form a Cl2 molecule, are not polar, being the electronegativity difference null, and therefore do not originate an electric moment. The electric moment vector of chemical entities is commonly oriented with the direction facing the negative charge, which corresponds to the most electronegative element.