1. Two halves of a hollow metallic cylinder of radius a, separated by an infinitesimal gap, are kept at potential V and -V: -V (a, 4) = 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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1. Two halves of a hollow metallic cylinder of radius a, separated by an infinitesimal gap,
are kept at potential V and -V:
S-v
Ф(а, 9) %3
0 < 9 < T
(a) Find a Fourier series expansion of the potential (a, p) in the interval -7 <p < n.
(b) Use this Fourier series to show
(6) 를 =D 1-3+1--.
(ii) 끓3D 1+ + +
T%3D0 2r+1
...-
Lr=0- (2r+1)²
Transcribed Image Text:1. Two halves of a hollow metallic cylinder of radius a, separated by an infinitesimal gap, are kept at potential V and -V: S-v Ф(а, 9) %3 0 < 9 < T (a) Find a Fourier series expansion of the potential (a, p) in the interval -7 <p < n. (b) Use this Fourier series to show (6) 를 =D 1-3+1--. (ii) 끓3D 1+ + + T%3D0 2r+1 ...- Lr=0- (2r+1)²
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