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4. Assume that space between the inner and outer conductors of a long coaxial cylindricai structure is filled with an electron cloud having a charge density of a = A/p³ for a< p

4. Assume that space between the inner and outer conductors of a long coaxial cylindricai structure is filled with an electron cloud having a charge density of a = A/p³ for a< p

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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4. Assume that space between the inner and outer conductors of a long coaxial cylindricat structure is filled with an electron cloud having a charge density of p = A/p3 for a < p<b, where a and b are, respectively, the radii of the inner and outer conductors. The inner conductor is maintained at a potential Vo, and the outer conductor is grounded, i.e., V(p= a) = Vo and V(o= b) = 0. Determine the potential distribution in the region a< p< b by solving Poisson's equation V²V = -p/ɛ. This is cylindrical coordinates and V is a function of p only. (a) Find ƏV/ôp (b) Find V (c) Find the constants Ci and C2 and simplify as much as possible.
Transcribed Image Text:4. Assume that space between the inner and outer conductors of a long coaxial cylindricat structure is filled with an electron cloud having a charge density of p = A/p3 for a < p<b, where a and b are, respectively, the radii of the inner and outer conductors. The inner conductor is maintained at a potential Vo, and the outer conductor is grounded, i.e., V(p= a) = Vo and V(o= b) = 0. Determine the potential distribution in the region a< p< b by solving Poisson's equation V²V = -p/ɛ. This is cylindrical coordinates and V is a function of p only. (a) Find ƏV/ôp (b) Find V (c) Find the constants Ci and C2 and simplify as much as possible.
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