State that positive charges repel other positive charges, negative charges repel other negative charges, but positive charges attract negative charges
4.2.1 Electric Charge
Learning Objective
State and explain the behaviour of electric charges: like charges repel, unlike charges attract. Relate this behaviour to Coulomb’s law, to the production and detection of charge, and to the concept of an electric field.
1. Fundamental Concepts
- Electric charge – a basic property of matter that determines the electrostatic force it experiences.
- SI unit: coulomb (C). 1 C = 1 A · s (the charge transferred by a current of 1 A in 1 s).
- Two types of charge exist:
- Positive (+)
- Negative (‑)
- Conservation of charge – the total charge of an isolated system remains constant.
- In the Cambridge syllabus, it is required to state that charging by friction transfers only electrons (the negative charge carriers).
2. Behaviour of Charges
- Like charges repel: two positives or two negatives push each other apart.
- Unlike charges attract: a positive charge pulls a negative charge toward it (and vice‑versa).
3. Quantitative Description – Coulomb’s Law
The magnitude of the electrostatic force between two point charges is
\(F = k\,\dfrac{|q1 q2|}{r^{2}}\)
- \(F\) – force (N)
- \(k = 9.0 \times 10^{9}\ \text{N m}^2\text{C}^{-2}\) (Coulomb constant)
- \(q1, q2\) – magnitudes of the charges (C)
- \(r\) – centre‑to‑centre separation (m)
- The sign of the product \(q1 q2\) determines the direction of the force:
- Positive product → repulsive force
- Negative product → attractive force
4. Production of Charge – Triboelectric (Friction) Charging
- When two different materials are rubbed together, electrons are transferred from the material with lower electron affinity to the one with higher affinity.
- Only electrons move; the nuclei remain fixed, so the material losing electrons becomes positively charged and the material gaining electrons becomes negatively charged.
- Typical classroom example:
- Rub a glass rod with silk → electrons flow from glass to silk, leaving the glass positively charged and the silk negatively charged.
- Rub a rubber balloon on hair → electrons transfer from hair to balloon, giving the balloon a negative charge.
- Simple lab activity (5 min): rub two different plastics (e.g., PVC and acrylic) together, bring each near a gold‑leaf electroscope and record whether the leaves diverge or converge.
5. Detecting and Demonstrating Charge
- Gold‑leaf electroscope: a charged object brought near the metal knob causes the leaves to diverge (repulsion) if the object has the same sign, or to converge (attraction) if the object has the opposite sign.
- Pith‑ball experiment: a lightweight, charged pith ball is attracted to an oppositely charged rod and repelled by a similarly charged one.
- Both set‑ups illustrate the fundamental rule “like charges repel, unlike charges attract”.
6. Measuring Charge
- Charge can be measured indirectly by measuring the current that flows when the charge is transferred and integrating over time:
\[
Q = \int I\,dt
\]
- In the laboratory a charge collector (e.g., a metal can of known capacitance) connected to a galvanometer or ammeter is commonly used.
7. Conductors vs. Insulators (Simple Electron Model)
- Atoms consist of a nucleus (protons + neutrons) surrounded by electrons.
- Conductors (metals): some electrons are free to move through the lattice; this mobility allows charge to flow easily.
- Insulators (rubber, glass, plastic): electrons are tightly bound to their atoms, so charge does not move freely.
- Consequences:
- A charged metal sphere distributes excess charge uniformly over its surface.
- A charged glass rod retains the charge where it was deposited because the electrons cannot migrate.
8. Electric Field
- An electric field (E) is a region of space around a charge in which another charge would experience a force.
- Direction of the field:
- Away from a positive charge.
- Toward a negative charge.
- Magnitude: \(E = \dfrac{F}{q}\) (N C\(^{-1}\)).
9. Field‑Line Patterns
| Configuration | Field‑line pattern |
|---|---|
| Isolated point charge (or uniformly charged sphere) | Radial lines emanating outward (positive) or inward (negative) |
| Two opposite charges (electric dipole) | Lines start on the positive charge and end on the negative charge, curving between them |
| Parallel‑plate capacitor (equal and opposite charges) | Uniform, parallel lines between the plates; negligible outside |
10. Safety and Practical Considerations
- Never touch objects that have been charged by friction – they can give a mild shock.
- Keep charged objects away from sensitive electronic equipment and flammable materials.
- When using an electroscope, avoid accidental grounding; use an insulated stand.
- Store charged rods or balloons in a non‑conductive container to prevent unintended discharge.
11. Summary Table – Interaction of Charges
| Charges Involved | Force Direction |
|---|---|
| Positive – Positive | Repulsion |
| Negative – Negative | Repulsion |
| Positive – Negative | Attraction |
12. Illustrative Examples
- Two positively charged metal spheres are released from rest at a separation of 10 cm. They move apart because the repulsive Coulomb force exceeds any other force.
- A negatively charged silk cloth is brought near a positively charged glass rod; the rod attracts the cloth and the leaves of a gold‑leaf electroscope collapse.
- Two rubber balloons rubbed on hair acquire the same negative charge and repel each other when brought close together.
- In a parallel‑plate capacitor the uniform field between the plates can be used to calculate the force on a test charge placed midway between them ( \(F = qE\) ).
13. Common Misconceptions
- Opposite ≠ direction of force. “Opposite” refers to the type of charge, not to the direction in which a charge moves.
- Neutral objects are not “uncharged”; they contain equal numbers of positive and negative charges, giving a net charge of zero.
- Charge quantity depends on the excess or deficit of electrons, not on the size of the object.
- Charging by friction does not involve transfer of protons – only electrons move.
14. Check Your Understanding
- What happens when a positively charged rod is brought near a negatively charged rod? Use the interaction table to justify your answer.
- Two identical charges are separated by a distance \(r\). If the distance is halved, by what factor does the magnitude of the electrostatic force change? Show the calculation using Coulomb’s law.
- Explain why a metal sphere can be charged by touching it with a charged rod, whereas a glass rod cannot easily transfer charge to a rubber sheet.
- Sketch the electric field lines for (a) a positively charged sphere and (b) a parallel‑plate capacitor.
- State which particle is transferred in a friction‑charging experiment and why this leads to one object becoming positive and the other negative.