The curve C, is an arc of the unit circle centered at the origin. Show that: (a) The scalar curl of F is zero. (b) Sc, F - dĩ = Sc, F - dř. (c) So F - dř = 0, the angle at the origin subtended by the oriented curve C1. %3D
The curve C, is an arc of the unit circle centered at the origin. Show that: (a) The scalar curl of F is zero. (b) Sc, F - dĩ = Sc, F - dř. (c) So F - dř = 0, the angle at the origin subtended by the oriented curve C1. %3D
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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Question
![6. Let
F(1,y) = -y, z]
1² + y2
and let C1, C2 be oriented curves as below.
B
C1
C2
A
The curve C, is an are of the unit circle centered at the origin. Show that:
(a) The scalar curl of F is zero.
(b) ſc, F - dĩ = fc F · dĩ.
(c) Sa F - dĩ = 0, the angle at the origin subtended by the oriented curve C1.
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F690bc708-737a-4036-8bde-cd8ee17ec8dd%2Ff917e6be-98cc-4a62-80d5-5c245d11ab6b%2F46ea5fi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:6. Let
F(1,y) = -y, z]
1² + y2
and let C1, C2 be oriented curves as below.
B
C1
C2
A
The curve C, is an are of the unit circle centered at the origin. Show that:
(a) The scalar curl of F is zero.
(b) ſc, F - dĩ = fc F · dĩ.
(c) Sa F - dĩ = 0, the angle at the origin subtended by the oriented curve C1.
%3D
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