we can scarcely avoid the inference that light consists in the transverse undulations of the same medium whichis the cause of electric and magnetic phenomena. This was surely one of the crowning moments in the history of physics. Imagine his excitement in 1854(?) when he calculated the characteristicspeed of the waves with the best known values of Mu and Epsilon for a vacuum and discovered that it was quite close to the observed value of the speed of light. Of course, Clerk Maxwell's equations imply that the electric and magnetic fields in a wave are coupled if we assume a traveling wave, the fields E and B turn out to oscillate exactly out of phase.Īfter deducing the possibility of these electromagnetic waves, Clerk Maxwell was interested in studying the properties of these waves to see whether they could be experimentally verified. A very similar analysis shows that each component of E satisfies the same wave equation. Where the Laplacian of a vector v = (v 1, v 2,v 3) is defined by its action on each component:īecause of the absence of magnetic monopoles, the vector identity as applied to B becomesĬlerk Maxwell recognized that this equation was the wave equation in three dimensions,for each component of the magnetic field B. There happens to be a vector identity for the curl of a curl: Let us calculate the second time derivative of B: In free space, rho = 0 and J = 0, while the value of Mu Epsilon turns out to equal 1/c 2, where c is the speed of light. Here, H is the magnetic force and B = Mu H is the magnetic induction E is the electric intensity and D = Epsilon E is the electric induction J is the current density and rho is the charge density. ( Gauss's law for magnetism, in the absence of monopoles) All rights reserved.Ĭlerk Maxwell codified the laws of electricity and magnetism in fourpartial differential equations, which in in rationalized mks units read:
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