Coulomb's Law states that the electric 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 equation that tells you how hard two charged objects push or pull on each other. In symbols, F = kq₁q₂/r². Double either charge and the force doubles. Double the distance and the force drops to one fourth. That inverse-square behavior is the signature move of this law, and the AP exam tests it constantly.
The constant k is not random. It's built from the permittivity of free space, k = 1/(4πε₀), which is how Coulomb's Law connects to Topic 3.5 (Electric Permittivity). Permittivity measures how a material responds to an electric field, so the same force law gets weaker inside a dielectric material than in a vacuum. Two more details matter: the force acts along the line connecting the charges, like charges repel, opposite charges attract, and the two charges exert equal-and-opposite forces on each other (Newton's third law applies even if one charge is huge and the other tiny).
Coulomb's Law is the foundation of basically everything electrostatic in AP Physics 2. It shows up first in Topics 3.4 and 3.6 when you study charging by friction, conduction, and induction and need to predict which way charged objects move. Topic 3.9 puts it side by side with Newton's law of universal gravitation, since both are inverse-square laws between point objects, and Topic 7.1 frames the electromagnetic force as one of the fundamental forces of nature. Then in Unit 5 (Topics 5.1 and 5.4), Coulomb's Law becomes the parent of the electric field concept. The field of a point charge, E = kq/r², is literally Coulomb's Law with one charge divided out. If you understand this one equation deeply, you've pre-learned half of electrostatics.
Keep studying AP Physics 2 Unit 5
Electric Field (Unit 5)
The electric field of a point charge is Coulomb's Law per unit charge. Divide F = kq₁q₂/r² by one of the charges and you get E = kq/r². The field is just Coulomb's Law repackaged so you can describe the force a charge would feel before that charge even shows up.
Newton's Law of Universal Gravitation (Topics 3.9 and 7.1)
F = Gm₁m₂/r² and F = kq₁q₂/r² are the same mathematical shape. The big differences you need: gravity only attracts, electric force can attract or repel, and the electric force between fundamental particles is enormously stronger than their gravitational pull. Comparison questions love this pairing.
Electric Permittivity and Dielectric Constant (Topic 3.5)
Coulomb's constant hides permittivity inside it, k = 1/(4πε₀). Put the charges in a material with a higher permittivity (a dielectric) and the force between them shrinks. This is the same physics that makes capacitors store more charge when you slide a dielectric between the plates.
Electric Potential Energy (Unit 5)
Coulomb's Law is the force; electric potential energy is the energy stored in that interaction, U = kq₁q₂/r. Notice the r is not squared in the energy version. Mixing up r and r² between these two equations is one of the most common point-losers in Unit 5.
Multiple-choice questions usually test proportional reasoning rather than calculator crunching. A classic stem doubles one charge and triples the separation, then asks for the new force as a fraction of the old one (answer: 2/9 of the original). You'll also see ranking tasks where three charges sit on a line and you rank the net force on each, which requires adding Coulomb forces as vectors. On free-response questions, Coulomb's Law shows up inside bigger problems: finding where the net force on a charge is zero, comparing electric and gravitational forces between particles, or justifying why a charged object accelerates toward an induced charge. No released FRQ needs you to recite the law by name, but you're expected to pull F = kq₁q₂/r² off the equation sheet, apply it along the correct line, and explain attraction versus repulsion using the signs of the charges.
Coulomb's Law gives a force between TWO charges (F = kq₁q₂/r², units of newtons). The point-charge field equation describes what ONE charge does to the space around it (E = kq/r², units of N/C). They're related by F = qE, so the field equation is Coulomb's Law with the test charge factored out. If a question gives you two charges, use Coulomb's Law. If it asks what a single charge creates at a point in space, use the field equation.
Coulomb's Law, F = kq₁q₂/r², says the electric force grows with the product of the charges and falls off with the square of the distance between them.
Doubling the distance between two charges cuts the force to one fourth, and tripling it cuts the force to one ninth, because of the inverse-square relationship.
Like charges repel and opposite charges attract, and the two charges always exert equal and opposite forces on each other regardless of their sizes.
Coulomb's constant comes from permittivity, k = 1/(4πε₀), so the force between charges is weaker inside a dielectric material than in a vacuum.
Coulomb's Law and Newton's law of gravitation have the same inverse-square form, but the electric force can repel while gravity only attracts.
The electric field of a point charge, E = kq/r², is Coulomb's Law divided by one charge, which is how Unit 3 force ideas turn into Unit 5 field ideas.
It's the law giving the electric force between two point charges: F = kq₁q₂/r², with k ≈ 8.99 × 10⁹ N·m²/C². The force is proportional to the product of the charges and inversely proportional to the square of their separation.
No. Unlike gravity, the Coulomb force goes both ways. Opposite charges attract and like charges repel, with the same magnitude formula either way. The signs of the charges tell you the direction.
Coulomb's Law (F = kq₁q₂/r²) needs two charges and gives a force in newtons. The field equation (E = kq/r²) needs one charge and gives the field in N/C at a point in space. They connect through F = qE.
Both are inverse-square laws between point objects, which is why Topic 3.9 compares them directly. But the electric force depends on charge instead of mass, it can repel as well as attract, and between fundamental particles it's vastly stronger than gravity.
Yes, F = kq₁q₂/r² is provided, so you don't memorize it. The exam rewards knowing how to use it: proportional reasoning when charges or distances change, vector addition of forces from multiple charges, and explaining attraction versus repulsion from charge signs.