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p835eps7 - Physics 835 Problem Set 7 Due Wednesday March 2...

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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 left-hand 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 time-averaged 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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