Electric Charge & Coulomb's Law

Jun 10, 2025

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.