Foundations — Polarity of molecules — vector sum of bond dipoles

Before you can use the parent note Polarity of molecules, you must own every symbol it throws at you. This page builds each one from absolute zero, in the order that each rests on the one before.

1. Charge, and the two signs $+$ / $-$

Why the topic needs it: a dipole is made of charge. No charge, no dipole. Everything downstream is charge sitting in different places.

2. Partial charge: ${\delta }^{+}$ and ${\delta }^{-}$

Look at figure s01: the electron cloud (the shaded blob) is lopsided toward the right atom. That lopsidedness is what ${\delta }^{-}$ and ${\delta }^{+}$ record. Which atom hogs the electrons is decided by Electronegativity — the very next foundation.

Why the topic needs it: these partial charges are the two ends of the arrow we are about to draw.

3. Electronegativity — who wins the tug-of-war

Why the topic needs it: electronegativity difference decides (a) whether a bond has a dipole at all, and (b) which way its arrow points — from the loser (${\delta }^{+}$) toward the winner (${\delta }^{-}$). See Electronegativity for the full scale.

4. What a vector is, and the arrow picture

This is the most important tool on the page, so we build it slowly.

Why the topic needs it: the molecular dipole IS the head-to-tail sum of the bond arrows. If you only know Vectors and the Cosine Rule you already know the maths of polarity — the chemistry just supplies the arrows.

5. The bond dipole $\vec{\mu }$ and its formula $\vec{\mu }=q\vec{d}$

Now we can finally earn the star symbol of the parent page.

Why the topic needs it: $\vec{\mu }$ is the single arrow per bond. The whole molecule = sum of these $\vec{\mu }$'s.

6. Numbers: scientific notation, $q$, Å, and the Debye

The parent page multiplies tiny numbers, so you need to read them.

Why the topic needs it: to check that a computed net dipole (like water's $1.85\text{D}$) is physically sensible, not a slipped decimal.

7. The angle $\theta$ and the cosine rule

Why the topic needs it: this is literally the parent page's headline formula. Its full derivation and every quadrant lives in Vectors and the Cosine Rule.

8. Geometry words: linear, planar, tetrahedral

Why the topic needs it: the shape decides whether the arrows cancel. Same number of bonds, different shape, opposite polarity (BF₃ vs NH₃).

9. Lone pairs and the $\Sigma$ (sum) symbol

Why the topic needs it: forgetting the lone-pair arrow is the classic error that makes people underestimate NH₃ and H₂O polarity.

Prerequisite map

Every box above is a foundation on this page; they all feed the final box — the parent topic itself.

Equipment checklist

Cover the right side and test yourself. If any answer surprises you, reread that section.