Unformatted text preview: Physics 835: Problem Set 7.
Due Wednesday, March 2 by 5PM. 1. Prove the following properties of vector spherical harmonics and the operators L: (a). Jackson (9.20). (This proof was sketched in class.) (b). L L = iL. (c). Show that the operator multiplying Y`m on the lefthand side of eq. (9.99) can be written as L L, where L is de ned in eq. (9.101). x 2. A radiating source consists of an electric dipole p = p exp(?i!t)^ and m = m exp(?i!t)^. Both electric and magnetic dipoles are small comy pared to the wavelength and both are located at the origin. Find the angular distribution of the timeaveraged radiated power per unit solid angle. 3. For the spherical cavity discussed in class, nd the frequency of the lowest TE mode, in terms of the radius R of the cavity, and nd the corresponding electric and magnetic elds. 1 ...
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 Winter '05
 STROUD
 Physics, Fundamental physics concepts, electric dipole moment, vector spherical harmonics

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