y Figure 2.12 Intersection of two conducting planes defining a corner in two dimensions with opening angle B.

Classical Dynamics of Particles and Systems
5th Edition
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Stephen T. Thornton, Jerry B. Marion
Chapter6: Some Methods In The Calculus Of Variations
Section: Chapter Questions
Problem 6.11P
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Figure 2.12 Intersection of two conducting planes defining a corner in two dimensions
with opening angle B.
B.
Transcribed Image Text:Figure 2.12 Intersection of two conducting planes defining a corner in two dimensions with opening angle B. B.
Two conducting planes at zero potential meet along the z axis, making an angle B
between them, as in Fig. 2.12. A unit line charge parallel to the z axis is located
between the planes at position (p', ').
(a) Show that (4 rE,) times the potential in the space between the planes, that is,
the Dirichlet Green function G(p, d; p', 4'), is given by the infinite series
1
G(p, ¢: p', d') = 4 E pp"
mm sin(m TolB) sin(m To'IB)
Transcribed Image Text:Two conducting planes at zero potential meet along the z axis, making an angle B between them, as in Fig. 2.12. A unit line charge parallel to the z axis is located between the planes at position (p', '). (a) Show that (4 rE,) times the potential in the space between the planes, that is, the Dirichlet Green function G(p, d; p', 4'), is given by the infinite series 1 G(p, ¢: p', d') = 4 E pp" mm sin(m TolB) sin(m To'IB)
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