Overview
This lecture introduces the concept of electric charge, the properties of conductors and insulators, and details Coulomb's Law with worked examples.
Electric Charge
- Matter has a property called electric charge, measured in Coulombs (C).
- Electric charge comes in two types: positive and negative.
- Separating these charges leads to observable electric forces.
- Elementary charge (e) is quantized: e = 1.602 × 10⁻¹⁹ C.
- Protons carry +e, electrons carry –e, and neutrons have no charge.
- Electric charge is conserved in an isolated system.
Behavior of Electric Charges
- Like charges repel; opposite charges attract.
- Conductors allow free movement of excess charge.
- Insulators do not allow free movement of excess charge.
Coulomb's Law
- The force (F) between two point charges is F = k|q₁q₂|/r², where k = 8.99 × 10⁹ Nm²/C².
- The force is along the line joining the charges: repulsive for like, attractive for unlike charges.
- The force decreases with the square of the distance (inverse-square law).
- For multiple charges, net force is the vector sum of individual forces.
- 1 Coulomb is a large amount of charge; practical charges are often μC or nC.
Worked Examples
- To get 1.0 C, you need 6.2 × 10¹⁸ electrons (about 1.04 × 10⁻⁵ moles).
- Adding 6.0 × 10¹³ electrons (–9.6 μC) to a +8.0 μC sphere gives a net charge of –1.6 μC.
- Two charges (4.5 × 10⁻⁹ C and –2.8 × 10⁻⁹ C) separated by 3.2 m exert a force of 1.1 × 10⁻⁸ N.
- An alpha particle (+2e) and gold nucleus (+79e) at 2.0 × 10⁻¹⁴ m apart feel a force of 91 N.
- Two spheres, one with 12 nC and one with –18 nC at 0.30 m: force is 2.16 × 10⁻⁵ N (before connecting), and 8.99 × 10⁻⁷ N (after connecting and reaching equilibrium with 3 nC each).
- For three charges at different positions, use vector addition to find net force magnitude and direction (e.g., 1.38 × 10⁻⁵ N at 103° from +x axis).
- For two 0.20 g spheres at 5° angle with 30 cm strings, the charge per sphere is 7.2 nC.
Key Terms & Definitions
- Electric Charge — Fundamental property of matter, measured in Coulombs (C).
- Coulomb (C) — SI unit of electric charge.
- Quantization of Charge — Charge occurs in discrete multiples of elementary charge e.
- Conductor — Material allowing free movement of electric charge.
- Insulator — Material that restricts movement of electric charge.
- Coulomb’s Law — Equation for electrostatic force: F = k|q₁q₂|/r².
- Elementary Charge (e) — Magnitude of charge on a proton or electron, 1.602 × 10⁻¹⁹ C.
Action Items / Next Steps
- Practice problems applying Coulomb’s Law to various charge configurations.
- Review distinguishing features of conductors vs. insulators.
- Prepare for further discussion of electric fields and forces.