# HW02 - each with a round cross-section but its own diameter...

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C:\User\Teaching\505-506\F10\HW02.doc PHY 505 Classical Electrodynamics I Fall 2010 Homework 2 (due Friday Sep. 24) Problem 2.1 (to be graded of 10 points). Use the Gauss law to calculate the mutual capacitance of the following 2-electrode systems, with the same cross- section (see Fig. on the right): (i) a conducting sphere inside a concentric spherical cavity in another conductor, and (ii) a conducting cylinder inside a coaxial cavity in another conductor. (In this case, we speak about capacitance per unit length.) Compare the results with those obtained in class using the Laplace equation solution. Problem 2.2 (10 points). Following the class discussion of two weakly coupled conducting spheres, find an approximate expression for the mutual capacitance (per unit length) between two thin, parallel wires,
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Unformatted text preview: each with a round cross-section, but its own diameter. Both diameters, D 1 and D 2 , are much smaller than the distance d between the wires. Compare the result with that for two spheres, and interpret the difference. Problem 2.3 (20 points). Using the results for a single thin, round, conducting disk, obtained in class, consider a system of two such disks at a small distance d << R from each other - see Fig. on the right. In particular, calculate: (i) the reciprocal capacitance matrix of the system, (ii) the mutual capacitance between the disks, (iii) the partial capacitance, and (iv) the effective capacitance of one disk, (all in the first non-vanishing approximations in d / R << 1). Compare the results (ii)-(iv) and interpret their similarities and differences. a b a d R...
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