Download e-book for iPad: Classical Electromagnetic Radiation by Jerry Marion (Eds.)

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 12 months graduates. uncomplicated wisdom of vector calculus and Fourier research is believed. during this version, a really available macroscopic view of classical electromagnetics is gifted with emphasis on integrating electromagnetic thought with actual optics. The presentation follows the ancient improvement of physics, culminating within the ultimate bankruptcy, which makes use of four-vector relativity to totally combine electrical energy with magnetism

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We let ç be the unit normal to the surface S. The pillbox is of volume V = S At and is assumed to contain a certain amount of free charge (not polarization charge) whose density is p. 63a) The left-hand side may be integrated by noting that since the normal component of D is involved there is n o contribution from the sides of the pillbox. The right-hand side may be integrated if the volume Ê is sufficiently small so that ñ is essentially constant. Thus, ( D . 64) Since free charge may exist on the interface, the product ñ · Äß must remain finite as Äß approaches zero.

29) Although this expression may be used directly for the calculation of quadrupole potentials, it is frequently more convenient to m a k e a modification which transforms the expression into a form that is familiar from a study of the inertia tensor in rigid-body dynamics. We may proceed in the following manner. 30a) Since this is a null quantity, any constant times this quantity may be added to Ö without altering the value. 31) We may write this expression as 1\ _ dxf dxj \ r ! , Q = Q so that { Q } can contain at most six independent elements.

Find the expression for the corresponding electric field vector and sketch some of the field lines for the plane è = ð/2. 2-10. A charge q is distributed uniformly along the line from æ = — h to æ = h. Calculate the first three multipole m o m e n t s of this charge distribution. 2-11. Calculate the dipole and quadrupole m o m e n t s of a uniformly charged ring of radius a which has total charge + q. Add a charge — q at the center of the ring and recompute the moments. 2-12. The linear charge density on a ring of radius a is given by PI q = - (cos ö — sin 2ö) a Find the monopole, dipole, and quadrupole m o m e n t s of the system and calculate the potential at an arbitrary point in space, accurate to terms in 1/r .

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