Before you can read F=kr2∣q1q2∣, you must know what every piece of it stands for. This page builds each symbol from absolute zero, in the order that lets each one lean on the previous. If a symbol is not yet defined here, do not let yourself use it.
The picture: think of a dot with a little label stuck to it — a + dot or a − dot. That label is the charge. The number next to it (say q=3C) says how much of that flavour the dot carries.
Why the topic needs it: Coulomb's law is about charges pushing charges. Without a symbol for "how much push-stuff is on this dot", there is nothing to plug in. The two flavours matter because same-flavour dots repel (fly apart) and opposite-flavour dots attract (snap together) — the sign of q is what decides which.
The picture: draw the two charged dots, then draw the straight line segment connecting their centres. The length of that segment is r.
Why the topic needs it: the force weakens as the charges move apart. To say how much it weakens, we need a number for "how far apart" — that number is r. It goes in the denominator, because a bigger r means a smaller force.
The picture: an arrow starting on a charge. The arrow's length = how strong the push (that's F, the magnitude). The arrow's direction = which way the charge gets shoved.
Why the topic needs it: the entire law computes one thing — the force between the charges. F (no arrow) is its size; F (with arrow) is its size plus direction. You will meet both, so learn the difference now:
The picture: a number line. ∣x∣ is simply how far x is from zero, always a positive distance.
Why the topic needs it: in the size-only formula F=k∣q1q2∣/r2, we want a positive answer for "how strong". If q1=+3 and q2=−2, then q1q2=−6, and a raw −6 would give a nonsensical negative strength. The bars fix that: ∣−6∣=6. We then decide push-or-pull separately from the signs.
The picture: the "paint spray" picture. Spray paint from a point in all directions. At distance r the same paint is smeared over a sphere whose surface area is 4πr2 — an area that grows with the square of r. So the paint gets thin as 1/r2.
Why the topic needs it — and why square, not just 1/r: the influence of a charge spreads over the surface of a sphere, and a sphere's area is 4πr2. Double the distance and that surface is four times bigger, so the influence is four times thinner. That is why the law is inverse-square, not merely inverse. This same spreading picture is exactly what Gauss's Law makes rigorous.
The picture: think of k as an exchange rate. You hand over "coulombs and metres"; k hands you back the right number of newtons. The 4π inside it is the surface-of-a-sphere factor from the spray picture — writing k=1/4πε0 makes later spread-out formulas (Gauss's Law) come out clean.
Why the topic needs it: without k the equation would give the wrong size of force in the wrong units. Compare it with gravity's constant G=6.67×10−11: notice k has a huge exponent (109) while G's is tiny (10−11). That single fact is why electricity is colossal and gravity is gentle.
The picture: instead of a fuzzy charged blob, a single mathematical dot with a charge label — like the dots in figure s01.
Why the topic needs it: the formula F=k∣q1q2∣/r2 is exact only for point charges (or for perfect spheres, treated as if all their charge sits at the centre). For a spread-out shape, different bits are at different distances, so you would add up (Superposition Principle) or integrate. Starting from points keeps the arithmetic clean.
Each box on the left is a symbol you now own. Together they assemble into the law in the centre, which then grows into the field, Gauss's law, and the gravity comparison you'll meet in the parent note Coulomb's law.
