Electrical dipole moment
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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](../../../math/4/e/1/4e1e594e31290732c788ff304c20405d.png)
This discrete definition can also be given in a continuous form using the charge density, Ï, in place of the charge, q.
![\vec{p} = \int \rho(\vec{x}) \vec{x} dV](../../../math/9/3/6/9363ea51c0c6bcec3661394e92dc92f6.png)
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, , 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](../../../math/4/5/3/453b7406cbe0f6c0751f99a94d3c77e6.png)
[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}](../../../math/b/d/c/bdc82a188a97881f8fe17043cd287106.png)
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.