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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

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

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.6: Parametric Equations
Problem 5ECP: Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle...
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Question
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
Expert Solution
Step 1

 Use the formulas,

        ∫Surface_radius_"R"Spherical Gr da=∮ Gr r2 sinθ dθ dϕ     ...i      

And ∫Surface_radius_"R"Spherical Gr dV=∮ Gr r2 sinθ dr dθ dϕ     ...ii  

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