Consider the family of rotating vector fields V(x, y, z) (x² + y²)n/2 2 + I (x² + y²)n/2 ĵ+0k, n€Z 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 x V into cylindrical forms. Simplify your answers as much as possible.
Consider the family of rotating vector fields V(x, y, z) (x² + y²)n/2 2 + I (x² + y²)n/2 ĵ+0k, n€Z 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 x V into cylindrical forms. Simplify your answers as much as possible.
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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Help please.
Thanks
Transcribed Image Text:-1
-1
n=-2
0
n=1
1
1
-1
-1
n=-1
0
n = 2
-1
n=0
0
n=3
0
1
1
Transcribed Image Text:Consider the family of rotating vector fields
V(x, y, z)
(x² + y²)n/2
2 +
I
(x² + y²)n/2
ĵ+0k, n€Z
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 x V into cylindrical forms. Simplify your answers as
much as possible.
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hi, are you sure about the partial derivative above ? in part 1 i do not seem to get to the same answer i know partial derivative w.r.t x is (x2+y2-nx2 )/(x2+y2)(2+n)/2 and the partial derivative w.r.t y is (-y2+x2-nx2 )/(x2+y2)(2+n)/2
when I add them up, does not give me the same answer as yours.
Thanks
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