Coulomb's constant (k ≈ 8.99 × 10⁹ N·m²/C²) is the proportionality constant in Coulomb's law, F = kq₁q₂/r², that converts the product of two charges divided by distance squared into an actual force in newtons. On the AP Physics 2 exam, it appears in Topic 3.8 (Describing Electric Force).
Coulomb's constant, written as k, is the number that makes Coulomb's law work. The law says the electrostatic force between two point charges is F = kq₁q₂/r². The charges and the distance tell you the shape of the relationship, but k tells you the strength. 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. It means even tiny charges (a coulomb is an enormous amount of charge) produce serious forces. Compare it to the gravitational constant G ≈ 6.67 × 10⁻¹¹, and you see why electric forces dominate at the atomic scale while gravity only matters when you pile up planet-sized masses. You'll also see k written as 1/(4πε₀), where ε₀ is the vacuum permittivity. Those are two notations for the same physics, and both forms show up on the reference tables.
Coulomb's constant lives in Topic 3.8, Describing Electric Force, in Unit 3 of AP Physics 2. Every quantitative electric force problem runs through it. You use k to calculate forces between point charges, and the same constant carries forward when you build electric field (E = kq/r²) and electric potential (V = kq/r) expressions later in the unit. So getting comfortable with k early pays off across the whole unit. Conceptually, it also anchors one of the exam's favorite comparison moves, putting Coulomb's law next to Newton's law of gravitation. Both are inverse-square laws with the same mathematical skeleton, and the constants k and G are what make their strengths wildly different.
Keep studying AP Physics 2 Unit 3
Inverse Square Law (Unit 3)
Coulomb's law is an inverse-square law, and k is its scaling factor. The 1/r² part tells you doubling the distance cuts the force to a quarter, while k tells you how big the force is in the first place. Exam questions often test the r² reasoning without making you touch k's actual value.
Electric Charge (Unit 3)
k is the bridge between charge and force. Charges measured in coulombs only become a force in newtons after you multiply by k. Since real charges are usually nanocoulombs or microcoulombs, the giant 10⁹ in k often cancels the tiny 10⁻⁹ in the charge, which is why answers come out in sensible newton ranges.
Force Field (Unit 3)
The same constant appears when you switch from force to field. E = kq/r² is just Coulomb's law with one charge removed, describing the field a single charge creates. If you know k's job in the force equation, you already know its job in the field equation.
Newton's Law of Gravitation (Unit 1 review / Unit 3 comparison)
F = Gm₁m₂/r² and F = kq₁q₂/r² are mathematical twins. The constants are where they split. k is about 10⁹ while G is about 10⁻¹¹, a difference of twenty orders of magnitude that explains why a balloon's static charge can beat the entire Earth's gravity in lifting your hair.
Coulomb's constant is given on the AP Physics 2 reference tables, so you never memorize its value, but you do need to know what to do with it. Multiple-choice questions usually test the structure of Coulomb's law rather than the arithmetic. Expect ratio reasoning like "the distance triples, what happens to the force?" where k cancels out entirely. When calculations do appear, the rounded value 9 × 10⁹ keeps the math clean, especially when charges are given in microcoulombs or nanocoulombs. On free-response questions, you might derive an expression for force or field in terms of k, q, and r, or compare electric and gravitational forces between two particles. In that comparison, the size gap between k and G is the whole point of the answer. Watch your units too. The N·m²/C² in k exists precisely so that coulombs squared over meters squared comes out as newtons.
Both constants describe the same physics, and the reference tables list Coulomb's law in both forms. k ≈ 8.99 × 10⁹ N·m²/C² is the version you use directly in F = kq₁q₂/r². ε₀ ≈ 8.85 × 10⁻¹² C²/(N·m²) is its inverse cousin, related by k = 1/(4πε₀), and it shows up on its own in capacitance formulas like C = κε₀A/d. The trap is grabbing the wrong one off the formula sheet, since both start with 8.8-ish but differ by about 21 orders of magnitude. If your electric force comes out around 10⁻²⁰ N for lab-scale charges, you probably used ε₀ where you needed k.
Coulomb's constant k ≈ 8.99 × 10⁹ N·m²/C² is the proportionality constant in Coulomb's law, F = kq₁q₂/r².
The value of k is given on the AP Physics 2 reference tables, so your job is using it correctly, not memorizing it.
The huge size of k (compared to G ≈ 6.67 × 10⁻¹¹) is why electric forces crush gravitational forces between charged particles.
k can also be written as 1/(4πε₀), so Coulomb's law in terms of ε₀ is the same equation in different clothes.
The same constant reappears in electric field (E = kq/r²) and electric potential (V = kq/r) formulas throughout Unit 3.
In ratio problems about changing charge or distance, k cancels out, so focus on the q and r² relationships.
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 converts charges (in coulombs) and distance (in meters) into a force in newtons, and it's central to Topic 3.8, Describing Electric Force.
No. The value of k is printed on the AP Physics 2 reference tables along with the equation itself. You should still know it's roughly 9 × 10⁹ so you can sanity-check answers and do quick estimates.
They're related by k = 1/(4πε₀). Coulomb's constant k ≈ 8.99 × 10⁹ N·m²/C² goes directly into F = kq₁q₂/r², while ε₀ ≈ 8.85 × 10⁻¹² C²/(N·m²) appears in formulas like capacitance. Same physics, inverse forms, and mixing them up wrecks your answer by about 21 orders of magnitude.
k ≈ 9 × 10⁹ versus G ≈ 6.67 × 10⁻¹¹, a gap of roughly 10²⁰. That gap reflects that the electric force is fundamentally far stronger than gravity, which is why two protons repel electrically about 10³⁶ times harder than they attract gravitationally. This comparison is a classic AP question setup.
No. The k in F = kq₁q₂/r² is Coulomb's constant, a fixed universal value of 8.99 × 10⁹ N·m²/C². The k in F = -kx is a spring constant that's different for every spring. Same letter, completely different quantities, so read the equation context carefully.
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