Resource Lesson
Maxwell's Equations
Printer Friendly Version
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
Ampere's Law
(modified with
Maxwell's displacement current
)
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 selfpropagating.
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
the
permittivity of free space
used in
Coulomb's Law
and
Gauss' Law

the
permeability of free space
used in
Ampere's Law
and the
BiotSavart Law

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).
Related Documents
Lab:
Labs 
Forces Between Ceramic Magnets
Labs 
Magnetic Field in a Solenoid
Labs 
Mass of an Electron
Labs 
RC Time Constants
Labs 
Telegraph Project
Resource Lesson:
RL 
A Comparison of RC and RL Circuits
RL 
A Guide to BiotSavart Law
RL 
A Special Case of Induction
RL 
Ampere's Law
RL 
Dielectrics: Beyond the Fundamentals
RL 
Eddy Currents plus a Lab Simulation
RL 
Electric Field Strength vs Electric Potential
RL 
Electricity and Magnetism Background
RL 
Famous Experiments: Cathode Rays
RL 
Generators, Motors, Transformers
RL 
Induced Electric Fields
RL 
Induced EMF
RL 
Inductors
RL 
Introduction to Magnetism
RL 
LC Circuit
RL 
Magnetic Field Along the Axis of a Current Loop
RL 
Magnetic Forces on Particles (Part II)
RL 
Magnetism: CurrentCarrying Wires
RL 
Meters: CurrentCarrying Coils
RL 
Motional EMF
RL 
RL Circuits
RL 
Spherical, Parallel Plate, and Cylindrical Capacitors
RL 
Torque on a CurrentCarrying Loop
Review:
REV 
Drill: Induction
Worksheet:
APP 
Maggie
APP 
The Tree House
CP 
Induction
CP 
Magnetism
CP 
Power Transmission
CP 
Transformers
NT 
Bar Magnets
NT 
Induction Coils
NT 
Magnetic Forces
NT 
Meters and Motors
WS 
Induced emf
WS 
Magnetic Forces on CurrentCarrying Wires
WS 
Magnetic Forces on Moving Charges
WS 
Practice with Ampere's Law
WS 
Practice with Induced Currents (Changing Areas)
WS 
Practice with Induced Currents (Constant Area)
TB 
36A: Magnets, Magnetic Fields, Particles
TB 
36B: Current Carrying Wires
TB 
Electric Field Strength vs Electric Potential
TB 
Exercises on Current Carrying Wires
PhysicsLAB
Copyright © 19972022
Catharine H. Colwell
All rights reserved.
Application Programmer
Mark Acton