Charge & Coulomb’s Law
A short lesson with diagrams, a worked example, a problem to try, and a quick check. Then quiz yourself on 6 practice questions.
Like charges repel and unlike charges attract. The force follows Coulomb’s law, F = k|q1q2|/r²: double the distance and the force drops to a quarter. The two charges always push or pull on each other with equal and opposite forces.
1. Coulomb’s law
2. Moving charge around
Charge is conserved. Rubbing, touching or grounding only moves electrons; the total never changes.
Contact: two identical conductors that touch end up sharing the total charge equally.
Conductors let electrons move freely; insulators don’t.
Induction: hold a charged rod near a neutral conductor, ground it, remove the ground, then remove the rod. The conductor ends up with the opposite charge of the rod.
Polarization: a charged object attracts a neutral one by pulling its charges slightly apart, with the opposite charge closer.
3. Example, then try it
A +2.0 µC charge and a −3.0 µC charge are 0.30 m apart. Find the force between them.
F = (9.0 × 10⁹)(2.0 × 10⁻⁶)(3.0 × 10⁻⁶) ÷ (0.30)² = 0.054 ÷ 0.090 = 0.60 N.
Opposite signs, so it’s attractive.
Two identical metal spheres hold +8.0 µC and −2.0 µC, 0.30 m apart. Find the force. They are touched together, then put back 0.30 m apart. Find the new charges and force.
Before: F = (9.0 × 10⁹)(8.0 × 10⁻⁶)(2.0 × 10⁻⁶) ÷ 0.090 = 1.6 N, attractive.
Touching: the total is +8.0 − 2.0 = +6.0 µC, shared equally: +3.0 µC each.
After: F = (9.0 × 10⁹)(3.0 × 10⁻⁶)² ÷ 0.090 = 0.90 N, now repulsive.
Answer: 1.6 N attractive before; +3.0 µC each and 0.90 N repulsive after.
4. Common mistakes
Two point charges are moved to half their original distance apart. What happens to the force between them?
F ∝ 1/r². Halving r multiplies the force by 2² = 4.
Ready to practice?
6 questions on Charge & Coulomb’s Law, each with a hint and an explanation for every wrong answer.