Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Consider the semicircle r(t) = a cos(t)i + asin(1)j with 0 ≤ ≤ and a > 0. For a given vector field F, the flux across r(t) is is [(F.N) ds. Σ dt. (a) ds = a (b) N= If our vector field is F₁ = 7xi - 4yj, then we have the flux being (c) F₁ (r(t)) <7'a*cos(t), -4'a'sin(t)> (F₁-N) ds = (d) As such, Σ (e) F₂(r(t)) = <3'a'cos(t), 7(a*cos(t)-a*sin(t))> (1) As such, (F₂N) ds -2pia^2 Σ Now, if our vector field is F₂ = 3xi +7(x - y)j, then we have the flux being (F₂-N)ds. Σ [(F₁-N)ds. Σ W

Consider the semicircle r(t) = a cos(t)i + asin(1)j with 0 ≤ ≤ and a > 0. For a given vector field F, the flux across r(t) is is [(F.N) ds. Σ dt. (a) ds = a (b) N= If our vector field is F₁ = 7xi - 4yj, then we have the flux being (c) F₁ (r(t)) <7'a*cos(t), -4'a'sin(t)> (F₁-N) ds = (d) As such, Σ (e) F₂(r(t)) = <3'a'cos(t), 7(a*cos(t)-a*sin(t))> (1) As such, (F₂N) ds -2pia^2 Σ Now, if our vector field is F₂ = 3xi +7(x - y)j, then we have the flux being (F₂-N)ds. Σ [(F₁-N)ds. Σ W

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
See similar textbooks
icon
Related questions
Question
Consider the semicircle r(t) = a cos(t)i + a sin(1)j with 0 ≤ ≤ and a > 0. For a given vector field F, the flux across r(t) is is (a) ds = a (b) N= <cos(t), sin(t)> If our vector field is F₁ = 7xi-4yj, then we have the flux being (d) As such, Σ dt. (F₁-N) ds = (c) F₁ (r(t)) <7'a*cos(t), -4*a* sin(t)> · SCF₁-1 Now, if our vector field is F₂ = 3xi +7(x - y)j, then we have the flux being (F₂-N)ds. (e) F₂ (r(t)) = <3*a*cos(t), 7(a*cos(t)-a*sin(t))> Σ (1) As such, (F₂N) ds -2pia^2 Σ Σ [(F₁-N)ds. Σ W -N) ds.
Transcribed Image Text:Consider the semicircle r(t) = a cos(t)i + a sin(1)j with 0 ≤ ≤ and a > 0. For a given vector field F, the flux across r(t) is is (a) ds = a (b) N= <cos(t), sin(t)> If our vector field is F₁ = 7xi-4yj, then we have the flux being (d) As such, Σ dt. (F₁-N) ds = (c) F₁ (r(t)) <7'a*cos(t), -4*a* sin(t)> · SCF₁-1 Now, if our vector field is F₂ = 3xi +7(x - y)j, then we have the flux being (F₂-N)ds. (e) F₂ (r(t)) = <3*a*cos(t), 7(a*cos(t)-a*sin(t))> Σ (1) As such, (F₂N) ds -2pia^2 Σ Σ [(F₁-N)ds. Σ W -N) ds.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS