# Van der Waals forces & Partial charges

We're told that charge is quantized. That the charge any body carries has to be an integral multiple of the fundamental unit of charge: $e=1.602×10^{-19}C$ such that $q=ne$ where $n$ is an integer.

But my book says (while explaining van der Waals forces) that the partial charges on a molecule ($\delta$) are always less than the fundamental unit of charge $e$.

How can this be? Isn't this against the quantization condition for charges?

Edit

• Minor comment to the post (v3): Please consider to mention explicitly author, title, etc. of textbook, so it is possible to reconstruct link in case of link rot. Apr 11, 2017 at 6:06
• Related question on Chemistry StackExchange : Does partial charge violate the law of quantization of charge? Feb 1, 2020 at 7:33

The partial charges which are referred to in the textbook do not exist. They are just an analogy used to compare molecular dipoles with macroscopic dipoles (two charges $\pm q$ separated by some distance $d$).
The formula for dipole moment is $p=qd$. If we take $d$ as the distance between the two nuclei in a molecule, then $q$ will be a small fraction of the electronic charge. However, if we take $q$ to be the total charge on all $n$ electrons in the molecule, then $q=ne$ is large and $n$ is a whole number. In this view it is actually $d$ - the separation between the centres of +ve and -ve charge - that is a small fraction of the inter-nuclear distance.
Either way you look at it (small $q$ & large $d$ or large $q$ & small $d$) the value of $p=qd$ is the same, and it is this value which is important, not the values of $q$ or $d$.