Short on time? This page is the recap. For explanations, Figures 1 and 2 and the worked examples, use the full study guide.
Recap
- Conservation of charge: a system’s net charge is constant unless charge moves in or out. Any change is matched by an opposite change in the surroundings.
- In solids, charging means moving electrons. Negative = gained electrons; positive = lost electrons.
- Friction (rubbing): electrons move from one material to the other; the two end with equal and opposite charges.
- Contact: touching conductors share charge; the total is unchanged. Identical spheres end with equal shares.
- Induced charge separation: a nearby charge pushes free electrons across a conductor. The near side takes the opposite sign; net charge is unchanged. It happens in neutral objects too.
- Polarization in insulators: electrons shift within each molecule; the near surface takes the opposite sign.
- A charged object attracts a neutral one, because the opposite charge is nearer (1/r²). Only repulsion proves like charges.
- Grounding: connecting to Earth, a huge, nearly neutral system that can give or take electrons.
Key relationships and procedures
| Idea | Rule | Use it to |
|---|---|---|
| q = Ne | e = 1.60 × 10⁻¹⁹ C | count electrons moved |
| Σq before = Σq after | for an isolated system | check any charging problem |
| q_each = (q₁ + q₂)/2 | identical conductors after contact | find charges after touching |
| Induction | rod near → ground → break ground → remove rod | give a sphere the opposite charge to the rod |
Assumptions behind the answers
- Conductors are on insulating stands, so charge leaves only through deliberate contact or grounding.
- Equal sharing applies only to identical conductors.
- Earth’s own change in charge is negligible.
Mistakes to avoid
- “Protons moved.” Electrons moved.
- Halving each charge separately on contact. Add the charges first, with signs, then share.
- “Attraction proves it is charged.” Neutral objects are attracted too.
- Wrong order in induction. Remove the ground before the rod, or the sphere ends neutral.
- “The rod lost charge in induction.” It never touched the sphere.
- “Insulators cannot be charged.” They can; the charge just does not spread.
Quick self-check
- Identical metal spheres with +6 nC and −2 nC touch and separate. What is the charge on each? (+2 nC)
- An object gains 1.0 × 10¹⁰ electrons. What is its charge? (−1.6 × 10⁻⁹ C)
- A positive rod is used to charge a sphere by induction. What sign does the sphere end with? (Negative: electrons flow up from the ground.)
Next: practice questions.