Animation shows an electromagnetic wave traveling in the positive z direction. Electric field vectors (x axis) are shown in red color and the magnetic field vectors (y axis) are in blue color.Direction of propagation of the wave is the direction of E×B which is z direction in this case.
Double clicking at any point in the animation area shifts the origin to that point. Dragging changes the orientation of the axes.
Poetry from a previous edition of Halliday and Resnick (A must read)
All equations of physics that serve, as Maxwell's do, to correlate experiments in a vast area and to predict new results have a certain beauty about them that can be appreciated, by those who understand them, on a purely aesthetic level. This is true for Newton's laws of motion, for the laws of thermodynamics, for the theory of relativity and for the theories of quantum physics.
As for Maxwell's equations, the physicist Ludwig Boltzmann (quoting a line from Goethe) wrote: "Was it a God who wrote these lines ...?" In more recent times J.R. Pierce, in a book chapter entitled "Maxwell's Wonderful Equations," wrote: "To anyone who is motivated by anything beyond the most narrowly practical it is worthwhile to understand Maxwell's equations simply for the good of his soul." The scope of these equations has been well summarized by the remark that Maxwell's equations account for the facts that a compass needle points north, That light bends when it enters water, and that your car starts when you turn the ignition key. These equations are the basis for the operation of all such electromagnetic and optical devices as electric motors, telescopes, cyclotrons, eyeglasses, television transmitters and receivers, telephones, electromagnets, radar, and microwave ovens.
James Clerk Maxwell, who was born in the same year that Faraday discovered the law of induction, died at age 48 in 1879, the year in which Einstein was born. (One is reminded that Newton was born in the year in which Galileo, his illustrious predecessor, died.) Maxwell spent much of his short but highly productive life providing a theoretical basis for the experimental discoveries of Faraday. It is fair to say that Einstein was led to his theory of relativity by means of his close scrutiny of Maxwell's equations. Einstein, a great admirer of Maxwell, once wrote of him, "Imagine his feeling when the differential equations he had formulated proved to him that electromagnetic fields spread in the form of polarized waves and with the speed of light!"