What does it mean when two point charges form a dipole a small distance away from each other?

Jul 6, 2015

Small, meaning close enough together.

Two charges can only interact well enough to form a dipole if they are close enough together. Too far apart and they are essentially independent charges (does not mean they aren't interacting).

Consider the coulombic interaction between two point charges:

V(vecr) = (q_1 q_2)/(4piepsilon_0vecr_(12)

where ${q}_{i}$ is the charge of particle $i$, ${\epsilon}_{0} = 8.854 \times {10}^{- 12} {\text{F"cdot"m}}^{- 1}$ is the vacuum permittivity constant, and ${\vec{r}}_{12}$ is the radial separation between two particles.

This means the coulombic potential of the two charges depends on the distance between them and the charges' magnitudes. Large $r$, small potential. Large enough potential, and a dipole forms, where a dipole between two point charges of charge $\pm q$ is defined as:

${\vec{\mu}}_{12} = q \cdot {\vec{r}}_{12}$

An example of a small charge is ${e}^{-} = 1.6022 \times {10}^{- 19} \text{C}$.

An example of "small" for molecules is a few stackrel("o")("A"). The bond length of the $\text{OH}$ bond in $\text{H"_2"O}$ is $0.958$ stackrel("o")("A"), where $1$ stackrel("o")("A") = 10^(-10) "m" is an angstrom.