Given a function G(r) with spherical symmetry show the following Sspherical surface radius "R" G(r)da 4 n r2.G(r) 15. Sophericatl surface radius "R" G(r)dV = 4 n G(r) r?dr 16. Any function when expressed in cylindrical coordinates that is only a function of the radial distance from the center axis is said to have cylindrical symmetry

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.5: Polar Coordinates
Problem 98E
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Given a function G(r) with spherical symmetry show the following
spherical
surface_radius "R"
G(r)da = 4 r2 G(r)
15.
= 4• •r?
spherical
R
G(r)dV = 4 n.
S G(r) r?dr
2
16.
surface radius "R"
Any function when expressed in cylindrical coordinates that is only a function of the radial distance from the center axis is said to have cylindrical symmetry
Transcribed Image Text:Given a function G(r) with spherical symmetry show the following spherical surface_radius "R" G(r)da = 4 r2 G(r) 15. = 4• •r? spherical R G(r)dV = 4 n. S G(r) r?dr 2 16. surface radius "R" Any function when expressed in cylindrical coordinates that is only a function of the radial distance from the center axis is said to have cylindrical symmetry
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