Consider the family of rotating vector fields -Y (x² + y²)n/2 V(x, y, z) = î+ x (x² + y²)n/2Ĵ+0k, nez as shown over the page. (i) Compute the curl of V; i.e. Vx V. Simplify your answer as much as possible. (ii) Convert the Cartesian forms of V and V × V into cylindrical forms. Simplify your answers as much as possible. (iii) State the domains for V and Vx V - it will change with n.
Consider the family of rotating vector fields -Y (x² + y²)n/2 V(x, y, z) = î+ x (x² + y²)n/2Ĵ+0k, nez as shown over the page. (i) Compute the curl of V; i.e. Vx V. Simplify your answer as much as possible. (ii) Convert the Cartesian forms of V and V × V into cylindrical forms. Simplify your answers as much as possible. (iii) State the domains for V and Vx V - it will change with n.
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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Transcribed Image Text:Consider the family of rotating vector fields
-Y
(x² + y²)n/2
V(x, y, z) =
î+
x
(x² + y²)n/2Ĵ+0k, nez
as shown over the page.
(i) Compute the curl of V; i.e. Vx V. Simplify your answer as much as possible.
(ii) Convert the Cartesian forms of V and V × V into cylindrical forms. Simplify your answers as
much as possible.
(iii) State the domains for V and Vx V - it will change with n.
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