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Electrical dipole moment - Wikipedia, the free encyclopedia

Electrical dipole moment

From Wikipedia, the free encyclopedia

In physics, the electric dipole moment is a measure of the polarity of a system of electric charges.

The electric dipole moment for a distribution of discrete point charges is simply the vector sum of the products of the charge and the position vector of each charge.

\vec{p} = \sum_{i} q_i \vec{x}_i

This discrete definition can also be given in a continuous form using the charge density, ρ, in place of the charge, q.

\vec{p} = \int \rho(\vec{x}) \vec{x} dV

The dipole moment is most commonly used for systems which have an overall neutral charge. For example, a pair of opposite charges, or a neutral conductor in a uniform electric field. For such systems, the value of the electric dipole moment is independent of the origin of the axis system. For non-neutral systems, a dependence on the choice of origin arises. In order retain the electric dipole moment's utility in calculating the torque on a dipole as well as other uses, the origin is often taken to be the center of charge, \vec{R}, for the system, which is defined like the center of mass and is, for some systems, the same.

\vec{R} = \frac{1}{Q} \sum_{i} \left | q_i \right \vert \vec{x}_i, Q = \sum_{i} \left | q_i \right \vert

[edit] A pair of opposite charges

The electric dipole moment for a pair of opposite charges of magnitude q is defined as the magnitude of the charge times the distance between them and the defined direction is toward the positive charge.

\vec{p} = q \vec{d}

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.

[edit] See also

[edit] External links

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