506 Physics Practice Midterm
Winter 2006
The midterm will be a 120 minute open book, open notes exam. Do all three problems. 1. A resonant cavity is in the shape of a rectangular box with sides of lengths a, b and c. a) Assuming innite conductivity for the walls, determine the modes of the cavity and their respective resonant frequencies. b) Calculate Q for each of the modes in part a), assuming the walls have large but nite conductivity . 2. A current I = I0 eit is owing in a circular antenna with radius a centered on the origin and lying in the x-y plane. a) Compute the exact multipole radiation coecients aE (l, m) and (l, aM m). b) What is the dominant radiation mode (electric dipole, magnetic dipole, electric quadrupole, etc.) in the limit ka 1? Compute the total radiated power for this mode (in the limit ka 1). 3. a) Using the Born approximation, compute the unpolarized dierential cross section for the scattering of electromagnetic radiation o of a uniform dielectric sphere of relative di...