Question

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

Answer 1

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 xx 10^(-12) "F"cdot"m"^(-1)` is the vacuum permittivity constant, and `vecr_(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 `pmq` is defined as:

`vecmu_(12) = qcdotvecr_(12)`

An example of a small charge is `e^(-) = 1.6022 xx 10^(-19) "C"`.

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