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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)

University Physics Volume 1
University Physics Volume 1
18th Edition
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:William Moebs, Samuel J. Ling, Jeff Sanny
Chapter2: Vectors
Section: Chapter Questions
Problem 59P: At one point in space, the direction of the electric field vector Is given In the Cartesian system...
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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)
Transcribed Image Text: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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