AP® Physics C: Electricity and Magnetism · Unit 8 · Topic 8.1
Coulomb's Law
Coulomb's law says the electric force between two point charges is k times the product of their charges divided by the square of the distance between them, directed along the line joining them.
Coulomb's law is F = k q1 q2 / r2, with k = 8.99 x 109 N m2/C2. Like charges push apart, opposite charges pull together, and the force acts along the line connecting the two charges. The 1/r2 isn't an accident of chemistry or some fitted curve. It comes from geometry: whatever a charge sends out into space, electric influence, spreads over the surface of a sphere, and a sphere's surface area grows as 4 π r2. Double the distance and that same influence is spread over four times the area, so the force any single point feels drops by a factor of four. This is the same reason light from a bulb gets dimmer with distance by the same 1/r2 rule.
A common snag: students expect the bigger charge to win, like a bully shoving a smaller kid harder than it gets shoved back. But Coulomb's law multiplies both charges together into one shared product, and Newton's third law locks the two forces into an action-reaction pair. A +8 microC charge and a -2 microC charge pull on each other with identical magnitude, just in opposite directions, no matter how lopsided the charges look.
Coulomb's law is the seed for everything else in this unit. Stack up many point charges and you're superposing many Coulomb forces, which is how the electric field gets built as force per unit charge. When the charge distribution turns messy, continuous and spread over wires or spheres, Coulomb's law becomes painful to integrate directly, which is exactly the gap Gauss's law exists to fill for symmetric cases.
Key terms
- Point charge
- An idealized charge treated as having no size, so distance to it is unambiguous.
- Coulomb's constant (k)
- The proportionality constant 8.99 x 109 N m2/C2 that sets the strength of the electric force in vacuum.
- Inverse-square law
- A relationship where a quantity falls off as 1 over the square of distance, tied to influence spreading over a sphere's surface area.
- Superposition
- The net force or field from multiple charges is the vector sum of each charge's individual contribution.
Watch it explained
- How it worksWalk me through how the 1/r2 in Coulomb's law falls out of the geometry of space.
- Worked exampleFind the force between a 2 microcoulomb charge and a -5 microcoulomb charge 30 cm apart.
- Worked exampleFind where a third charge must sit on the line joining +4 nC and +9 nC so it feels nothing.
- Common mistakeWhy doesn't the bigger charge push harder on the smaller one than it gets pushed back?
- Going furtherWhat changes about Coulomb's law when the two charges sit in water instead of vacuum?
Check yourself
End of topic.