Short on time? This page is the recap. For the explanations, Figures 1 and 2 and the worked examples, use the full study guide.
Recap
- Charge is a scalar, positive or negative. Proton +e, electron −e, neutron 0.
- Objects charge by gaining electrons (negative) or losing them (positive). Protons do not move.
- A point charge is an object whose size is negligible compared with the distances involved.
- Like charges repel; unlike charges attract. The forces in a pair are equal and opposite.
- Electric forces can attract or repel; gravity only attracts. Between particles the electric force is far larger, but large bodies are nearly neutral, so gravity dominates at large scales.
- Contact forces (normal force, friction, tension) are electric in origin, but are modelled as non-fundamental forces.
- Polarisation: a field shifts electrons relative to nuclei inside a material. Permittivity measures how much a material or medium polarises. Free space has ε₀.
- Conductors: charge carriers move easily. Insulators: they do not.
Key relationships
| Quantity | Relationship | Notes |
|---|---|---|
| Charge on an object | q = ne | n a whole number; e = 1.60 × 10⁻¹⁹ C |
| Coulomb force (size) | F = (1/(4πε₀)) |q₁q₂|/r² | 1/(4πε₀) = 8.99 × 10⁹ N·m²/C² |
| Coulomb force (vector) | F₁₂ = (1/(4πε₀)) (q₁q₂/r²) r̂₁₂ | r̂₁₂ points from 1 to 2 |
| Net force | F_net = F₁ + F₂ + … | vector sum, at most four charges in calculations |
| Electric vs gravity | F_e/F_g = (1/(4πε₀)) |q₁q₂|/(Gm₁m₂) | r cancels; proton–electron ≈ 2.3 × 10³⁹ |
| Permittivity of free space | ε₀ = 8.85 × 10⁻¹² C²/(N·m²) | appears in Coulomb’s law |
Assumptions behind the results
- The charges are point charges (or uniform spheres seen from outside).
- The charges are at rest (electrostatics).
- The charges are in empty space (or air, which behaves almost like empty space).
Mistakes to avoid
- F ∝ 1/r. It is 1/r²: double r, quarter F.
- Forgetting SI units. Convert nC, μC and cm before using the formula.
- Adding magnitudes. Add components of vectors.
- Signs in 2D. Use magnitudes for size; decide each direction by “like repel, unlike attract”.
- “The bigger charge pushes harder.” The pair forces are equal and opposite.
- “Gaining protons.” Only electrons move between objects.
Quick self-check
- How many electrons must be removed from a neutral object to give it +1.0 μC? (6.25 × 10¹²)
- The separation of two charges is halved. By what factor does the force change? (It becomes 4 times larger)
- Why does a charged rod attract a neutral piece of paper? (It polarises the paper; the nearer, opposite charges are attracted more than the farther, like charges are repelled)
Next: practice questions.