part 3 of 3 In cases where we have radial symmetry about the origin (usually called spherical sym- metry), it is most useful to use spherical co- ordinates (r, 0, 0). In the spherical coordinate system, a point is defined by: its radial dis- tance from the origin r; the azimuthal angle o, defined as the angle between the +x-axis and the projection on the xy-plane of the line drawn from the origin to the point; the po- lar angle 9, defined as the angle between the +z axis and the line drawn from the origin to the point. Note that for the polar angle, 0 ≤ 0 ≤ T. (r.0.6) y Question: You are given a solid sphere of radius R centered at the origin. What are the Cartesian coordinates of an arbitrary point within the sphere in terms of spherical quan- tities. You will need to use the figure to determine the x,y, and z coordinates in terms of their spherical counterparts. 1. (r cos cos , r cos sino, r sin 0) 2. (r sin sin ó, r sin cos , r cos) 3. (r sin cos , r sin sinó, r cos 0) 4. (R sin cos , R sin 0 sino, R cos 0) 5. (r sin cos , r sin ó sin0, r cos 6) 6. (x, y, z)

part 3 of 3 In cases where we have radial symmetry about the origin (usually called spherical sym- metry), it is most useful to use spherical co- ordinates (r, 0, 0). In the spherical coordinate system, a point is defined by: its radial dis- tance from the origin r; the azimuthal angle o, defined as the angle between the +x-axis and the projection on the xy-plane of the line drawn from the origin to the point; the po- lar angle 9, defined as the angle between the +z axis and the line drawn from the origin to the point. Note that for the polar angle, 0 ≤ 0 ≤ T. (r.0.6) y Question: You are given a solid sphere of radius R centered at the origin. What are the Cartesian coordinates of an arbitrary point within the sphere in terms of spherical quan- tities. You will need to use the figure to determine the x,y, and z coordinates in terms of their spherical counterparts. 1. (r cos cos , r cos sino, r sin 0) 2. (r sin sin ó, r sin cos , r cos) 3. (r sin cos , r sin sinó, r cos 0) 4. (R sin cos , R sin 0 sino, R cos 0) 5. (r sin cos , r sin ó sin0, r cos 6) 6. (x, y, z)

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Scalars and Vectors

Scalars and Vectors are the classification of physical quantities that are used to denote various terms in physics.

Question

part 3 of 3
In cases where we have radial symmetry
about the origin (usually called spherical sym-
metry), it is most useful to use spherical co-
ordinates (r, 0, 0). In the spherical coordinate
system, a point is defined by: its radial dis-
tance from the origin r; the azimuthal angle
o, defined as the angle between the +x-axis
and the projection on the xy-plane of the line
drawn from the origin to the point; the po-
lar angle 0, defined as the angle between the
+z axis and the line drawn from the origin
to the point. Note that for the polar angle,
0 ≤ 0 ≤ T.
(r.0,6)
y
Question: You are given a solid sphere of
radius R centered at the origin. What are the
Cartesian coordinates of an arbitrary point
within the sphere in terms of spherical quan-
tities. You will need to use the figure to
determine the x,y, and z coordinates in terms
of their spherical counterparts.
1.
(r cos cos , r cos sino, r sin )
2.
(r sin sin, r sin cos , r cos 0)
3.
(r sin cos , r sin sinó, r cos 0)
4.
(R sin cos o, R sin sin o, R cos 0)
5.
(r sin cos , r sin o sin 0, r cos 6)
6. (x, y, z)

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