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Electric Dipoles
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An electric dipole is a system formed by two regions of electric charge of opposite sign separated by a certain distance. Although the entire system may be electrically neutral, the separation between the charges creates an uneven distribution that produces electrical effects in the surrounding space.
Electric dipoles appear naturally in many molecules and materials. In some substances, the internal distribution of charges is not symmetrical, giving rise to partially positive and negative poles. This characteristic influences properties such as solubility, intermolecular forces and the interaction of matter with external electric fields.
The behavior of dipoles is fundamental in areas such as chemistry, biology and materials physics. They participate in phenomena such as the polarization of insulators, the operation of electromagnetic antennas, the interaction between water molecules and various processes related to the structure and organization of matter.
ID:(823, 'ky')
Dipole moment
Description
To quantitatively describe an electric dipole, the concept of electric dipole moment is introduced. This magnitude simultaneously represents the intensity of the dipole and its spatial orientation. The Dipole moment ($\vec{P}$) is defined using the magnitude of the Charge ($Q$) and the Vector that separates the dipole charges ($\vec{d}$), oriented from the negative charge to the positive one.
 $\vec{P} = Q \vec{d}$
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The physical meaning of this magnitude is profound. While the total charge of the dipole may be zero, the dipole moment allows us to describe how far apart the charges are and where this polarization is oriented. The greater the separation between the charges or the greater their magnitude, the more intense the dipole will be and the greater its interaction with external electric fields.
The usefulness of the dipole moment appears naturally when studying the interaction of the dipole with an electric field. The torque that tends to orient the dipole depends directly on the dipole moment, so dipoles with greater moment align more strongly with the field. Furthermore, at great distances the electric field produced by the dipole is governed mainly by this magnitude, allowing complex systems to be described through a simplified representation based solely on their dipole moment.
The concept of dipole moment is fundamental in physics, chemistry and biology. It allows us to understand the behavior of polar molecules, the interaction of dielectric materials with electric fields, the absorption and emission of electromagnetic radiation, and even macroscopic properties of matter such as electrical permittivity and the polarization of material media.
ID:(3863, 'gm')
Dipole electric field
Description
Since the Coulomb force for 15772
is equal to
In this case, for the positive Charge ($Q$) the distance vector is with
$\vec{s}_2-\vec{s}_1=\vec{r} - \displaystyle\frac{1}{2}\vec{d}$
and for the negative Charge ($Q$)
$\vec{s}_2-\vec{s}_1=\vec{r} + \displaystyle\frac{1}{2}\vec{d}$
one has
$\vec{E}_d=\displaystyle\frac{Q}{4\pi\cdot\epsilon_0\cdot\epsilon}\left[\displaystyle\frac{\vec{r}-\v ec{d}/2}{|\vec{r}-\vec{d}/2|^3}-\displaystyle\frac{\vec{r}+\vec{d}/2}{|\vec{r}+\vec{d}/2|^3}\right]$
As with 3863
can also be written as
ID:(15799, 'gm')
Remote Dipole electric field
Description
As for Position ($\vec{r}$) and Vector that separates the dipole charges ($\vec{d}$), in the limit $|\vec{d}| \ll |\vec{r}|$, we have:
$\displaystyle\frac{1}{|\vec{r}-\vec{d}/2|^3}=\displaystyle\frac{1}{r^3}+\displaystyle\frac{3\vec{r}\cdot\vec{d}}{2r^5}+O(d^2/r^2)$
and
$\displaystyle\frac{1}{|\vec{r}+\vec{d}/2|^3}=\displaystyle\frac{1}{r^3}-\displaystyle\frac{3\vec{r}\cdot\vec{d}}{2r^5}+O(d^2/r^2)$
By replacing these expressions in 15799
:
finally obtained:
ID:(1925, 'gm')
Torque on the Dipole
Description
Since the rotation occurs around the center of the dipole, the lever arm corresponds to half of Vector that separates the dipole charges ($\vec{d}$). In this way, considering the Electric force ($\vec{F}$) exerted on each load, the Torque ($\vec{\tau}$) can be written as:
$\vec{\tau} = 2 \displaystyle\frac{1}{2} \vec{d} \times \vec{F}$
where factor 2 appears because both loads contribute to the total torque.
Like:
and
It is finally concluded that:
ID:(15810, 'gm')
Electric Dipoles
Description
Calculations
to 
,
then, select the variable: 
to 
Calculations
Variable
Given
Calculate
Target :
Equation
To be used
Variables
ID:(823, 0)
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