Coulomb's law and the electric field.
The electric force between two charges is the gravitational force's stronger, more interesting cousin. Same 1/r² shape, much larger constant, and — crucially — it can attract or repel.
Coulomb's law
The magnitude of the electrostatic force between two point charges:
F = k · |q₁ q₂| / r²where k ≈ 8.99 × 10⁹ N·m²/C². The direction is along the line between the charges: attractive if they have opposite signs, repulsive if the same sign. Note the 1/r² — same shape as gravity, but the constant is about 10²⁰ times larger.
The electric field
A single charge modifies the space around it. Other charges placed in that space feel a force. The electric field E is force per unit positive test charge:
E = F / qtest = k · Q / r²Units: N/C (or equivalently V/m). E is a vector field — it has a value and direction at every point in space, even when no test charge is there.
Superposition
When multiple charges contribute, the total field at a point is the vector sum of each charge's contribution. The fields don't interfere or merge — they just add.
Etotal = E₁ + E₂ + E₃ + ⋯This is what makes field problems tractable: break them into single-charge contributions, compute each, then add vectors.
Worked example
Two charges, +3 μC and −1 μC, are 0.2 m apart. What is the magnitude of the force between them?
F = (8.99 × 10⁹) · (3 × 10⁻⁶)(1 × 10⁻⁶) / (0.2)² F = (8.99 × 10⁹) · (3 × 10⁻¹²) / 0.04 F ≈ 0.67 NAttractive — opposite signs pull together. Tiny charges, tiny distance, but a force you can feel. Compare with gravity: the electric force between these charges exceeds the gravitational force between the protons and electrons by a factor of about 10³⁹.
Flashcard · Unit 7
Coulomb's law — the magnitude of the electrostatic force.
Check your understanding
You double the distance between two point charges. By what factor does the force change?