Faraday and the Concept of Electric Fields

Introduction

• Hat Trick: Reference to scoring three goals in ice hockey. In this context, delivering three major scientific concepts:
  1. What an electric field is
  2. Solving Newton's field theory problem
  3. Introducing Gauss's law

Michael Faraday: Background

• Early Life: Modest beginnings, limited formal education
• Career Progression:
  • Apprenticed as a bookbinder
  • Attended scientific lectures at Royal Institution, London
  • Worked menial jobs at the Royal Institution
  • Became the most famous scientist in Europe despite poor mathematical skills
• Key Idea: Lines of constant electric force radiating in space

Scientific Context

• Coulomb’s Law (1789): Electric force is inversely proportional to the square of the distance between charges
• Newton’s Law of Universal Gravitation:
  • Attraction between masses is also inversely proportional to the square of the distance
  • Action at a distance problem: explaining how bodies apply forces over vast distances

Inverse Square Law

• Explanation:
  • Light intensity from Sun decreases with distance
  • Concept of “flux”: Total flow of light passing through any spherical surface around the Sun is constant

Faraday’s Breakthrough

• Electric and Magnetic Forces: Recognized as real forces in space
• Field Concept:
  • Pattern of forces from electric charges exist in space, even without a test charge
  • Idea of electric field: Force on a test charge at each point in space
• Visualizing Field:
  • Lines or tubes of force radiate from charges; never cross/tangle
  • Strength indicated by the density of the lines

Gauss’s Law

• Carl Friedrich Gauss: Used mathematics to formalize Faraday’s ideas
• Law Statement: Total electric flux through a closed surface is proportional to the net charge within
• Applications: Fits for electric, gravitational, and magnetic fields

Practical Implications

• Conductors:
  • Electric field inside a conductor becomes zero in electrostatic equilibrium
  • “Faraday Cage”: Metal box that blocks external electric fields
  • Examples include gold leaf electroscope demonstration, bridges, and tunnels

Maxwell’s Contribution

• James Clerk Maxwell: Mathematically formalized Faraday's ideas
• Modern View: Electric field theory doesn’t involve Faraday's lines of force but is built upon the concept

Reality of Scientific Concepts

• Quarks Analogy: Similar to Faraday’s lines of force, quarks (components of protons and neutrons) may be mental scaffolding
• Final Edifice: Scaffolding isn’t needed once the final theory is established but was crucial for development