Chapter 31:  Faraday's Law

 

Learning Goals

  1. Understand Faraday's law of induction.
  2. Understand motional emf's both microscopically and macroscopically.
  3. Understand Lenz's law.
  4. Understand induced electric fields.

 

Faraday’s Law of Induction

Faraday’s law describes induced electric field caused by a changing magnetic flux:

Where e is the induced electromotive force (emf) induced in the circuit C. The minus sign in this equation comes from Lenz’s Law which states that the emf is always induced so as to oppose the change in magnetic flux.

Faraday’s Law is a Maxwell Equation.

 

Maxwell’s Equations

This is a good time to summarize all four of Maxwell’s Equations, since we have now discussed them all.
  1. Gauss's Law for Electric Fields

     

  2. Gauss's Law for Magnetic Fields - no magnetic monopoles.

     

  3. Faraday's Law - a changing magnetic field produces an electric field.

     

  4. Generalized Ampere's Law - a changing electric field produces a magnetic field.

These four equations along with the Lorentz Force Equation:

can be used to solve any problem in classical electromagnetism!