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In Cartesian coordinates, a vector field takes the form F = 2rzi+2yzj + (x² + y²) k throughout the whole of three-dimensional space. (a) Find the divergence and curl of F in Cartesian coordinates. (b) Use Procedure 1 of Unit 9 to express F in cylindrical coordinates (r, o, z). (c) Use your answer to part (b) to calculate the divergence and curl of F in cylindrical coordinates. Comment on the agreement with part (a)..

In Cartesian coordinates, a vector field takes the form F = 2rzi+2yzj + (x² + y²) k throughout the whole of three-dimensional space. (a) Find the divergence and curl of F in Cartesian coordinates. (b) Use Procedure 1 of Unit 9 to express F in cylindrical coordinates (r, o, z). (c) Use your answer to part (b) to calculate the divergence and curl of F in cylindrical coordinates. Comment on the agreement with part (a)..

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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In Cartesian coordinates, a vector field takes the form F = 2xzi+2yzj + (x² + y²) k throughout the whole of three-dimensional space. (a) Find the divergence and curl of F in Cartesian coordinates. (b) Use Procedure 1 of Unit 9 to express F in cylindrical coordinates (r, o, z). (c) Use your answer to part (b) to calculate the divergence and curl of F in cylindrical coordinates. Comment on the agreement with part (a).
Transcribed Image Text:In Cartesian coordinates, a vector field takes the form F = 2xzi+2yzj + (x² + y²) k throughout the whole of three-dimensional space. (a) Find the divergence and curl of F in Cartesian coordinates. (b) Use Procedure 1 of Unit 9 to express F in cylindrical coordinates (r, o, z). (c) Use your answer to part (b) to calculate the divergence and curl of F in cylindrical coordinates. Comment on the agreement with part (a).
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