Coulomb's Law states that the electrostatic force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them: F = kq₁q₂/r², where k = 1/(4πε₀) ≈ 8.99 × 10⁹ N·m²/C².
Coulomb's Law is the rule for the electrostatic force between two point charges. In equation form, F = kq₁q₂/r², where q₁ and q₂ are the charges, r is the distance between them, and k = 1/(4πε₀) is Coulomb's constant. The force acts along the line connecting the charges. Like charges repel, opposite charges attract. The inverse-square dependence means doubling the distance cuts the force to one fourth.
Think of it as the electric twin of Newton's law of gravitation, with two big differences. Charge replaces mass, and the force can be repulsive as well as attractive. In AP Physics C: E&M, Coulomb's Law is where everything starts. Divide the force by a test charge and you get the electric field of a point charge (Topic 1.3). Integrate the force over distance and you get electric potential energy. Every superposition problem, every charge distribution integral, every Gauss's Law check ultimately traces back to this one inverse-square relationship.
Coulomb's Law lives in Unit 1 (Electrostatics), showing up in Topic 1.2 (Electric Fields & Electric Potential) and Topic 1.3 (Point Charges - Fields & Potentials). It is the experimental foundation the whole course is built on. The point-charge field E = kq/r² is literally Coulomb's Law per unit charge, and potential energy U = kq₁q₂/r is Coulomb's Law integrated. It also reappears later in disguise. Gauss's Law (Topic 5.3, Maxwell's Equations) is mathematically equivalent to Coulomb's Law for static charges, and dielectrics (Topic 2.3) work because the Coulomb attraction between charges gets partially screened by polarized material. On the exam, Coulomb's Law is your tool whenever you need the force between discrete charges, including superposition setups with three or more charges where you add force vectors component by component.
Keep studying AP Physics C: E&M Unit 2
Electric Field (Unit 1)
The electric field of a point charge, E = kq/r², is just Coulomb's Law with the test charge divided out. Once you know the field, the force on any charge is F = qE. The field is the middleman that lets one charge push on another without touching it.
Electric Potential Energy (Unit 1)
Integrate the Coulomb force from infinity to a separation r and you get U = kq₁q₂/r. Same constant, same charges, but the exponent drops from r² to r because integration knocks a power off. That sign on U tells you whether the pair is bound (negative) or repelling (positive).
Maxwell's Equations / Gauss's Law (Unit 5)
Gauss's Law is Coulomb's Law repackaged. Apply Gauss's Law to a sphere around a point charge and the inverse-square law falls right out, because the sphere's surface area grows as r² while flux stays constant. They contain the same physics; Gauss's Law is just the symmetric-geometry power tool.
Dielectrics (Unit 2)
Slide an insulating material between charges and it polarizes, partially canceling the field. The effective Coulomb interaction inside the dielectric weakens by a factor of κ, which is exactly why inserting a dielectric boosts a capacitor's capacitance.
Coulomb's Law shows up early and often in Unit 1. Multiple-choice questions love ratio reasoning, like asking how the force changes when you double one charge and triple the separation (answer: it becomes 2/9 of the original). They also test superposition, where you find the net force on one charge from two or more others, which means adding vectors, not just magnitudes. On free-response questions, Coulomb's Law usually appears as the first step of a longer problem. You might compute the force on a charge, then connect it to the field, the potential energy, or the work needed to assemble a charge configuration. A classic FRQ move is asking where the net force on a charge equals zero, which requires setting two Coulomb force expressions equal and solving for position. Watch your signs. Use the signs of the charges to determine direction, then work with magnitudes in your vector components.
Coulomb's Law and Gauss's Law encode the same physics for static charges, but you use them differently. Coulomb's Law is the go-to for forces and fields from discrete point charges, where you can sum or superpose directly. Gauss's Law is the shortcut for highly symmetric charge distributions (spheres, infinite lines, infinite planes), where a flux integral collapses into simple algebra. If the problem says 'two point charges,' reach for Coulomb. If it says 'uniformly charged sphere' or 'infinite line of charge,' reach for Gauss.
Coulomb's Law gives the electrostatic force between two point charges: F = kq₁q₂/r², with k = 1/(4πε₀) ≈ 8.99 × 10⁹ N·m²/C².
It is an inverse-square law, so doubling the separation cuts the force to one fourth, and tripling it cuts the force to one ninth.
Force is a vector along the line joining the charges; like charges repel and opposite charges attract, and net forces from multiple charges add by vector superposition.
The point-charge electric field E = kq/r² and potential energy U = kq₁q₂/r both come directly from Coulomb's Law.
Gauss's Law in Unit 5 is mathematically equivalent to Coulomb's Law for static charges, which is why a point charge's field falls off exactly as 1/r².
Use the signs of the charges to figure out direction, then compute with magnitudes so you don't get tangled up in negative signs mid-calculation.
Coulomb's Law states that the electrostatic force between two point charges is F = kq₁q₂/r², proportional to the product of the charges and inversely proportional to the square of the distance. The constant k = 1/(4πε₀) ≈ 8.99 × 10⁹ N·m²/C² is on the AP formula sheet.
For static charges, yes in content but no in usage. They are mathematically equivalent, but Coulomb's Law handles discrete point charges directly while Gauss's Law is the efficient tool for symmetric distributions like charged spheres, infinite lines, and infinite planes.
Both are inverse-square laws, but Coulomb's Law uses charge instead of mass and can be repulsive or attractive, while gravity only attracts. The electrostatic force is also vastly stronger; for two protons, the Coulomb repulsion exceeds their gravitational attraction by a factor of about 10³⁶.
Directly, only for point charges (or outside spherically symmetric distributions, which behave like point charges). For continuous distributions you integrate Coulomb contributions dq over the object, or use Gauss's Law when there is enough symmetry.
Cleanest approach: use magnitudes to compute the force's size, then use the signs to decide direction (like charges repel, opposites attract). Carrying signs through vector components is the most common way to botch a superposition FRQ.