PhysicsLAB Resource Lesson
Maxwell's Equations

Maxwell's Equations are to electromagnetism as Newton's Laws are to mechanics. They form a basic set of equations that can be used to solve virtually any problem in classical electromagnetism.
 
  • Gauss' Law for electric fields
 
 
  • Gauss' Law for magnetic fields
 
 
  • Faraday's Law
 
 
 
 
Faraday's Law states that a changing magnetic field through a closed curve will induce an electric field that is proportional to the magnetic field's rate of change. Maxwell's modification of Ampere's Law states that a changing electric field  through a closed surface will induce a magnetic field that is proportional to the electric field's rate of change. This amazing set of symmetric dependencies indicates that an electromagnetic wave, once initiated, would be self-propagating.
 

image courtesy of MIT's OpenCourseWare
 
 
Although the actual derivation is beyond the scope and mathematics of this introductory course, when Maxwell combined these equations he discovered a wave equation for the electric and magnetic field vectors. In 1886, Maxwell postulated that his waves could be generated by accelerating electric charges and that they would travel at a speed equal to the speed of light. This extraordinary result would prove to be the unifying link between electricity and light.
 
 
where
 
 
In 1887, Heinrich Hertz actually produced the first radio waves in his laboratory at the Karlsruhe Polytechnic in Germany. Today broadcasting rights for bands of the electromagnetic spectrum are licensed in the United States by the Federal Communications Commission (FCC).




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