Short on time? This page is the recap. For explanations, Figures 1 and 2 and the worked examples, use the full study guide.
Recap
- Charge is a basic property of matter. It is positive or negative.
- Proton +e, electron −e, neutron 0. The elementary charge e is the smallest charge that exists on its own, so q = Ne with N a whole number.
- A neutral object has equal amounts of positive and negative charge, not zero charges.
- A point charge is a model: the object’s size is negligible compared with the distances involved.
- The electric force acts along the line joining two charges. Like charges repel; unlike charges attract. The two forces in a pair are equal and opposite.
- Several charges: find each pair force, then add as vectors.
- Electric forces can attract or repel; gravity only attracts. For particles, gravity is far weaker. Gravity dominates at large scales because large objects are nearly neutral.
- Contact forces (normal, friction, tension) are electric forces between atoms, modelled in bulk.
- Permittivity measures how strongly a material polarizes; polarization is an induced separation of charge inside a neutral material. Conductors let charge move easily; insulators do not.
Key relationships
| Relationship | Symbols and units | Use it to |
|---|---|---|
| q = Ne | e = 1.60 × 10⁻¹⁹ C; N a whole number | count extra or missing electrons |
| F = k|q₁q₂|/r² | k = 9.0 × 10⁹ N·m²/C²; q in C; r in m | find the size of the force between two point charges |
| k = 1/(4πε₀) | ε₀ = 8.85 × 10⁻¹² C²/(N·m²) | switch between the two forms of Coulomb’s law |
| F ∝ |q₁q₂|/r² | factors multiply | predict new forces without k |
| F_net = ΣF (vectors) | components with signs from a diagram | combine up to four charges |
Assumptions behind the numbers
- Charged objects are treated as point charges: small compared with their separation.
- Charges are at rest (electrostatics).
- Only the charges named in the question act; everything else is far away or neutral.
Mistakes to avoid
- 1/r, not 1/r². Doubling r quarters F.
- Using the sign of the answer as the direction. Use |q₁q₂|, then decide direction from a diagram.
- “Bigger charge, bigger force on it.” Pair forces are always equal in size.
- Adding magnitudes of forces at an angle. Use components.
- Charges that are not multiples of e. 2.4 × 10⁻¹⁹ C (1.5e) is impossible.
- Forgetting unit prefixes. μC = 10⁻⁶ C, nC = 10⁻⁹ C; r in metres.
Quick self-check
- The distance between two point charges is halved. By what factor does the force change? (×4)
- A bead has charge +8.0 × 10⁻¹⁹ C. How many electrons is it missing? (5)
- One charge is tripled and the separation is tripled. What happens to the force? (It becomes 3/9 = 1/3 as large.)
- Why does the Moon orbit Earth because of gravity and not electric force? (Both are almost exactly neutral, so the electric force between them is close to zero; gravity never cancels.)
Next: practice questions.