Classical Electromagnetic Radiation by Jerry Marion (Eds.)

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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. easy wisdom of vector calculus and Fourier research is thought. during this variation, a truly available macroscopic view of classical electromagnetics is gifted with emphasis on integrating electromagnetic thought with actual optics. The presentation follows the old 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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50) becomes s Ê = — cn ÷ Ì where Ê ' is the Amperian surface current density, analogous to that of Eq. 72). 1-23. Within a dielectric sphere of radius a the polarization vector Ñ is radial outward and its magnitude is proportional to the distance from the center of the sphere: Ñ = P r. Find p\ D, and Å as functions of r. 0 * l - 2 4 . Show that the electric field inside a uniformly polarized sphere is constant and is given by Å = — (4ð/3)Ñ. Use this result to show that the electric field E which exists in a spherical cavity cut in a uniformly polarized dielectric medium is related to the field Å in the medium by s 1-25.

0 1-21. Show that the torque on an electric dipole placed in a uniform electric field is given by x = ñ ÷ Å and that the torque on a magnetic dipole placed in a uniform field is given by x = m ÷ Â. Show also that there is n o net force on the dipole in either case. e m 1-22. Show that at the macroscopic boundary of a dielectric (where Ñ goes discontinuously to zero), Eq. 17) becomes P' = s n-F where p' is the surface density of polarization charge, analogous to that of Eq. 65), and ç is the normal vector out of the dielectric.

17) becomes P' = s n-F where p' is the surface density of polarization charge, analogous to that of Eq. 65), and ç is the normal vector out of the dielectric. Similarly, show that at the boundary of a magnetic material, Eq. 50) becomes s Ê = — cn ÷ Ì where Ê ' is the Amperian surface current density, analogous to that of Eq. 72). 1-23. Within a dielectric sphere of radius a the polarization vector Ñ is radial outward and its magnitude is proportional to the distance from the center of the sphere: Ñ = P r.

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