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

1 Answer

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.