Short on time? This page is the recap. For the explanations, Figure 1 and the worked examples, use the full study guide.
Recap
- Conservation of charge: the net charge of a system is constant unless charge moves between the system and its surroundings. Charge is moved, never made.
- In solids, electrons move. Negative = gained electrons; positive = lost electrons.
- Friction: electrons move from one material to the other. Equal and opposite charges result.
- Contact: charge flows between touching objects. Both end with the same sign.
- Polarization (induced charge separation): a nearby charge rearranges charge inside an object, even a neutral one. Conductors: free electrons move across the object. Insulators: each molecule’s electron cloud shifts a little.
- Grounding: connecting an object to a huge, nearly neutral system such as Earth, which can supply or absorb electrons.
- Induction: polarize, ground, remove the ground, then remove the rod. The object ends with the opposite sign to the rod.
Key relationships
| Idea | Relationship |
|---|---|
| Charge is quantized | q = Ne, with e = 1.60 × 10⁻¹⁹ C |
| Electrons moved | N = |Δq| / e |
| Conservation (closed system) | Σq before = Σq after |
| Two identical conductors touching | q_each = (q₁ + q₂) / 2 |
| Neutral object near a charge | Net force is attractive (opposite charge is closer; F ∝ 1/r²) |
Assumptions
- Stands, threads and air are insulating, so no charge leaks away unless a path is stated.
- “Identical” spheres are identical conductors; unequal sizes share unequally (Topic 10.2).
- Earth acts as an unlimited source or sink of electrons.
Mistakes to avoid
- Saying protons moved. Say the object lost electrons.
- Forgetting the partner. If the rod gains −q, the cloth gains +q.
- Halving each charge separately. Add the charges first, then share.
- Removing the rod before the ground. The electrons flow back and the sphere ends neutral.
- Using attraction as proof of charge. Neutral objects are attracted too; use repulsion.
Quick self-check
- A rod gains −3.2 nC by rubbing. How many electrons did it gain, and what is the cloth’s charge? (2.0 × 10¹⁰ electrons; +3.2 nC)
- Identical metal spheres with +5.0 nC and +1.0 nC touch. Final charges? (+3.0 nC each)
- A positive rod is used to charge a sphere by induction. Final sign? (Negative: electrons come up from Earth)
Next: practice questions.