Electric Charge & Coulomb’s Law

You’ll be able to

Describe electric charge as quantized and conserved, and distinguish conductors from insulators
Use Coulomb’s law to find the force between two point charges
Predict how the electric force changes as charge or separation changes

The two rules of charge

All electric phenomena start with charge, which comes in two kinds — positive and negative. Like charges repel; opposite charges attract. Charge obeys two deep rules. First it is quantized: every charge is a whole-number multiple of the elementary charge e = 1.6 × 10⁻¹⁹ C, carried by protons (+e) and electrons (−e). Second it is conserved: charge is never created or destroyed, only transferred. When you rub a balloon on your hair, electrons move from hair to balloon — the balloon gains exactly the negative charge the hair loses.

Conductors vs. insulators

Materials differ in how freely charge moves through them. In a conductor (most metals) some electrons are free to roam the whole material, so charge spreads out and flows easily. In an insulator (rubber, glass, plastic) electrons are locked to their atoms, so charge stays where you put it. This distinction explains charging methods: conduction (touching a charged object transfers charge) and induction (a nearby charge rearranges a conductor’s electrons without touching).

Coulomb’s law

F = k · |q₁ · q₂| / r²

k = 8.99 × 10⁹ N·m²·C⁻² (often rounded to 9.0 × 10⁹). r is the center-to-center distance. The force acts along the line joining the charges: repulsive for like charges, attractive for opposite.

An inverse-square law

Coulomb’s law has the same shape as Newton’s law of gravitation: the force weakens with the square of the distance. Push the charges twice as far apart and the force drops to one quarter, not one half. Because the two charges multiply in the numerator, doubling either charge doubles the force, and doubling both quadruples it. Keep the signs out of the magnitude calculation — use them only at the end to decide attraction versus repulsion.

Worked example

Two point charges, q₁ = +2.0 µC and q₂ = +3.0 µC, are separated by 0.30 m. Find the magnitude of the electric force between them.

1.List values in SI units: q₁ = 2.0 × 10⁻⁶ C, q₂ = 3.0 × 10⁻⁶ C, r = 0.30 m.
2.Apply Coulomb’s law: F = k q₁ q₂ / r² = (9.0 × 10⁹)(2.0 × 10⁻⁶)(3.0 × 10⁻⁶) / (0.30)².
3.Numerator: 9.0 × 10⁹ × 6.0 × 10⁻¹² = 5.4 × 10⁻².
4.Divide by r² = 0.090: 5.4 × 10⁻² / 0.090 = 0.60 N.

Answer: ≈ 0.60 N, directed as a repulsion (both charges are positive, so they push apart).

Watch out

Watch the units. Microcoulombs (µC) are 10⁻⁶ C and distances must be in meters, not centimeters. Forgetting to square r, or leaving r in cm, are the two most common Coulomb’s-law errors.

Checkpoint

Two point charges exert a force F on each other. If the distance between them is doubled and the charges are unchanged, what is the new force?

Checkpoint

A neutral metal sphere is touched by a positively charged rod, and some charge is shared. What best describes what happens?

On the exam

When only ratios change (charge or distance scaled up or down), you rarely need to plug into Coulomb’s law fully. Track the proportionality: F ∝ q₁q₂/r². Double one charge → ×2; triple the distance → ×1/9.

Answer the 2 checkpoints as you read.