By Jerry Marion (Eds.)
The revision of this hugely acclaimed textual content is designed to be used in complex physics courses--intermediate point juniors or first yr graduates. uncomplicated wisdom of vector calculus and Fourier research is believed. during this version, a truly obtainable macroscopic view of classical electromagnetics is gifted with emphasis on integrating electromagnetic conception with actual optics. The presentation follows the historic improvement of physics, culminating within the ultimate bankruptcy, which makes use of four-vector relativity to completely combine electrical energy with magnetism
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Extra info for Classical Electromagnetic Radiation
However, it is possible to define the * After the English theorist , P. A. M. Dira c (1902) who introduce d the functio n int o quantu m theory . Dira c was the 1933 Nobel Laureat e in physics . 11 POIN T CHARGE S AND TH E DELT A FUNCTIO N 27 delta function as the limit of an ordinary function* so that it remains integrable and approaches infinity in the limit. 77) = 0, r Ö r Therefore, the equivalents of Eqs. 81) we may write the integral of Eq. 84) •'al l spac e Combining Eqs. 83), we have ß J a i l spac e ø(-\Üí ^' Since V ( l / r ) vanishes for r > 0 and has an integral over all space of — 4ð, 2 * Ther e ar e man y method s of definition ; see, for example , Proble m 1-30.
1b) The Laplacian operator occurs in many different types of physical problems,* probably the most important of which is that of wave propagation. Although we are interested in this book primarily in electromagnetic wave phenomena rather than in electrostatics, some of the mathematical functions which arise in the solution of wave equations are the same as those that result from the solution of Laplace's equation. It is somewhat easier to introduce these harmonic functions (Legendre functions, spherical harmonics, and Bessel functions) in connection with electrostatic problems.
Show that the electric dipole m o m e n t of a system of charges is independent of the choice of origin if the system has zero net charge. 2-4. Show that the force on an electric dipole is F = (p · grad)E. Then consider the interaction of a charge q and a dipole ñ that are a distance r apart, with the dipole oriented perpendicular to the line between them. Calculate the (vector) force (a) on q due t o p, and (b) on ñ due to q. If your results violate Newton's third law, try again. 2-5. Show that a simple finite dipole (charges ± q located at æ = ± 1/2) has zero quadrupole m o m e n t with respect to its center as the origin.