The Memory Trick
💡 F = kq₁q₂/r²
Coulomb's Law calculates the electric force between two point charges: F = kq₁q₂/r², where k = 8.99×10⁹ N·m²/C² is Coulomb's constant. Like charges (both positive or both negative) repel; unlike charges (one positive, one negative) attract. This is an inverse square law, structurally identical in form to Newton's Law of Universal Gravitation.
Why It Works
Notice the direct parallel to gravity: F = Gm₁m₂/r² for gravity vs. F = kq₁q₂/r² for electric force — both follow the same inverse-square mathematical structure, just with mass replaced by charge and G replaced by k. The key difference: electric force can be either attractive or repulsive (depending on charge signs), while gravity is always attractive.
Step by Step
Applying Coulomb's Law
1
Determine attraction or repulsion from the signs
Before calculating magnitude, check the signs of both charges: same sign means repulsion (force pushes them apart); opposite signs mean attraction (force pulls them together).
Two electrons (both negative) always repel each other; a proton and an electron (opposite signs) always attract.
2
It's an inverse SQUARE law — same caution as gravity
Distance is squared in the denominator, so doubling the distance between two charges reduces the force to just one-quarter of its original value, not one-half.
Tripling the separation between two charges reduces the force between them to 1/9 of its original value.
3
Much stronger than gravity at atomic scales
Coulomb's constant k is vastly larger relative to typical atomic-scale quantities than G is, which is why electric forces, not gravity, dominate the behavior of atoms, molecules, and chemical bonding.
The electric force between a proton and electron in a hydrogen atom is roughly 10³⁹ times stronger than the gravitational force between them — an almost incomprehensibly large ratio.
🏥 Worked Example
Two point charges of +3×10⁻⁶ C and −2×10⁻⁶ C are separated by 0.5 m. Calculate the force between them, and state whether it's attractive or repulsive.
1
Check the signs first: one charge is positive, one is negative — opposite signs mean the force is attractive.
2
Apply F = kq₁q₂/r²: F = (8.99×10⁹)(3×10⁻⁶)(2×10⁻⁶)/(0.5)².
3
Solve: F = (8.99×10⁹)(6×10⁻¹²)/0.25 = (0.05394)/0.25 ≈ 0.216 N — an attractive force pulling the two charges together, with a magnitude of about 0.216 N.
📌 Exam Application
Exams test correctly applying F = kq₁q₂/r², determining attraction vs. repulsion from charge signs before calculating magnitude, and correctly applying the inverse-square relationship when distance changes.
⚠️ Most Common Coulomb's Law Mistakes
The most common trap is forgetting to check charge signs before interpreting the force direction — Coulomb's Law gives you a magnitude, but whether that force is attractive or repulsive must be reasoned separately from the signs of the two charges involved.
✓ Quick Self-Test
1) Write Coulomb's Law. F = kq₁q₂/r². 2) What determines whether the force between two charges is attractive or repulsive? Whether the charges have the same sign (repulsive) or opposite signs (attractive). 3) If the distance between two charges triples, what happens to the force between them? It drops to 1/9 of its original value (inverse square law). 4) What structural similarity does Coulomb's Law share with Newton's Law of Universal Gravitation? Both are inverse-square laws with the same mathematical form, just with charge/k replacing mass/G. 5) Why does electric force dominate over gravity at atomic scales? Coulomb's constant k is vastly larger relative to atomic-scale quantities than G is, making electric force enormously stronger than gravity between subatomic particles.