The Coulomb constant (k ≈ 8.99 × 10⁹ N·m²/C²) is the proportionality constant in Coulomb's Law, F = kq₁q₂/r², that sets how strong the electrostatic force between two point charges is. It can also be written as k = 1/(4πε₀), where ε₀ is the permittivity of free space.
The Coulomb constant, usually written as k (sometimes kₑ or the "electrostatic constant"), is the number that converts charges and distance into an actual force. Coulomb's Law says the electrostatic force between two point charges is F = kq₁q₂/r². The charges and the separation tell you the shape of the relationship, but k tells you the scale. Its value is about 8.99 × 10⁹ N·m²/C², which you can round to 9 × 10⁹ for quick estimates.
That huge value is the headline. Compare it to the gravitational constant G, which is about 6.67 × 10⁻¹¹. The electrostatic force between two charged particles dwarfs the gravitational force between them, and k is the reason why. One more thing worth knowing cold is that k is not its own independent constant. It's defined as k = 1/(4πε₀), where ε₀ is the permittivity of free space. The AP equation sheet writes Coulomb's Law both ways, so you should recognize them as the same equation in different clothes.
The Coulomb constant lives in Topic 3.7, Electric Forces and Free-Body Diagrams, in Unit 3 of AP Physics 2. Every time you calculate an electrostatic force, draw a free-body diagram with an electric force on it, or compare electric and gravitational forces on a charged particle, k is in the math. It's also your gateway to the rest of Unit 3, because the electric field equation E = kq/r² and the electric potential equation V = kq/r reuse the same constant. If you're comfortable with where k comes from and what it's worth numerically, three different Unit 3 equations suddenly look like one family.
Keep studying AP Physics 2 Unit 3
Electrostatic Force (Unit 3)
k is meaningless without Coulomb's Law. The electrostatic force F = kq₁q₂/r² is where the constant actually does its job, turning two charges and a distance into newtons you can put on a free-body diagram.
Permittivity of Free Space (Unit 3)
These two constants are flip sides of the same coin, since k = 1/(4πε₀). The equation sheet uses ε₀ for capacitance and field formulas and k for Coulomb's Law, but they encode the exact same physics about how strongly vacuum transmits electric force.
Inverse Square Law (Unit 3)
Coulomb's Law is an inverse square law, just like gravity. k sets the strength, while the 1/r² part sets the pattern. Double the distance and the force drops to a quarter, no matter what k is.
Gravitational Force (AP Physics 1 crossover)
F = Gm₁m₂/r² and F = kq₁q₂/r² are structural twins. The classic AP comparison is the constants themselves. k is about 10⁹ while G is about 10⁻¹¹, which is why the electric force between a proton and electron crushes their gravitational attraction by roughly 39 orders of magnitude.
You won't get a question that just asks "what is k." Instead, k is a tool you grab off the equation sheet (it's given to you, so don't memorize it past "about 9 × 10⁹"). Expect to use it in MCQs computing or comparing electrostatic forces, in ratio problems where k cancels out (what happens to F if both charges double and r is halved?), and in free-response work where you put a Coulomb force on a free-body diagram alongside gravity, tension, or normal forces, the core skill of Topic 3.7. Also watch for questions written with 1/(4πε₀) instead of k. They're testing whether you recognize Coulomb's Law in its other standard form. No released FRQ hinges on the constant by name, but nearly every electrostatics FRQ uses it implicitly.
Students mix these up because both show up in Coulomb's Law on the equation sheet. They're related by k = 1/(4πε₀), so they're not independent constants. The practical difference is where each appears. k is the friendly form used in force, field, and potential equations (F = kq₁q₂/r²), while ε₀ shows up in capacitance (C = κε₀A/d) and in the formal version of Coulomb's Law. Note that ε₀ sits in the denominator, so a bigger permittivity would mean a weaker force, the opposite direction from k.
The Coulomb constant k is approximately 8.99 × 10⁹ N·m²/C², and it sets the strength of the electrostatic force in Coulomb's Law, F = kq₁q₂/r².
k equals 1/(4πε₀), so Coulomb's Law written with k and written with the permittivity of free space are the same equation.
You don't memorize k for the AP exam; it's on the constants sheet, but knowing it's roughly 9 × 10⁹ helps you estimate and sanity-check answers.
Comparing k (about 10⁹) with the gravitational constant G (about 10⁻¹¹) explains why the electric force dominates gravity at the particle scale, a classic AP comparison.
The same k appears in the electric field (E = kq/r²) and electric potential (V = kq/r) equations, tying together force, field, and potential across Unit 3.
In ratio-style questions, k cancels out, so focus on how changing the charges or the distance scales the force.
It's the proportionality constant k in Coulomb's Law, F = kq₁q₂/r², with a value of about 8.99 × 10⁹ N·m²/C². It determines how strong the electrostatic force between two point charges is.
No. The value of k is printed on the AP Physics 2 constants sheet. It's still worth remembering it's roughly 9 × 10⁹ so you can estimate answers and catch calculator mistakes.
No, but they're directly related by k = 1/(4πε₀). ε₀ is about 8.85 × 10⁻¹², and plugging it into that formula gives you k ≈ 8.99 × 10⁹. The exam uses both forms of Coulomb's Law, so recognize them as equivalent.
Both play the same structural role in twin inverse square laws, but their sizes are wildly different. k is about 8.99 × 10⁹ while G is about 6.67 × 10⁻¹¹, which is why the electric force between charged particles overwhelms their gravitational attraction.
That's its definition in SI units. Writing Coulomb's Law with ε₀ matches the form used in field and capacitance equations, while k is just shorthand that makes the formula cleaner. Same physics, two notations.