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Coulomb's law states that the electrostatic force between two point charges q₁ and q₂ separated by distance r is F = k|q₁q₂|/r², where k ≈ 8.99×10⁹ N⋅m²/C². The force is attractive if charges have opposite signs, repulsive if same sign, and acts along the line joining them.
Coulomb's law is the electrostatic counterpart of Newton's law of gravitation — and comparing the two is the fastest way to build intuition. Both forces decrease as 1/r², meaning doubling the distance reduces the force by a factor of four. Both forces are proportional to the "charges" involved (mass for gravity, electric charge for electrostatics). The key difference is sign: gravity is always attractive, but electrostatic forces can be either attractive or repulsive depending on whether the charges are opposite or like signs. This sign dependence is everything in electricity — it is what allows neutral matter to exist and what gives the structure of atoms their stability.
From your prerequisite, you know that charge comes in discrete units of e ≈ 1.6×10⁻¹⁹ C and is conserved. Coulomb's law tells you the force that those discrete charges exert on each other. The constant k = 1/(4πε₀) ≈ 8.99×10⁹ N⋅m²/C² looks large, but keep it in perspective: a proton and electron separated by 0.053 nm (the Bohr radius of hydrogen) experience an attractive force of about 8.2×10⁻⁸ N — enormous on the atomic scale, which is why electrons are tightly bound to nuclei.
The inverse-square structure is not coincidental — it reflects a deep geometric fact. Imagine the field "influence" from a point charge spreading uniformly in all directions, like light from a candle. The surface area of a sphere grows as r², so the intensity of that influence at distance r must fall as 1/r² to conserve the total flux through any surrounding sphere. This geometric argument reappears more formally when you learn Gauss's law.
The law as stated applies to point charges — idealized charges concentrated at a single location. Real charged objects require summing (integrating) Coulomb contributions over all their constituent charge elements. When multiple charges are present, the superposition principle applies: the total force on a charge is the vector sum of individual Coulomb forces from every other charge, each computed independently. Getting the direction right — along the line joining the pair, attractive toward opposite signs, repulsive from like signs — requires care with vector components and will become the core skill in electric field calculations you build toward next.