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Find the circulation and flux of the field F = 4x²i + 4y²j around and across the closed semicircular path that consists of the semicircular arch r, (t) = (a cost)i + (a sin t)j, Osts, followed by the line segment r₂(t)=ti, -astsa. The circulation is 0 (Type an exact answer, using * as needed.) The flux is. (Type an exact answer, using as needed.)

Find the circulation and flux of the field F = 4x²i + 4y²j around and across the closed semicircular path that consists of the semicircular arch r, (t) = (a cost)i + (a sin t)j, Osts, followed by the line segment r₂(t)=ti, -astsa. The circulation is 0 (Type an exact answer, using * as needed.) The flux is. (Type an exact answer, using as needed.)

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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Find the circulation and flux of the field F = 4x²i+ 4y²j around and across the closed semicircular path that consists of the semicircular arch r₁ (t) = (a cost)i + (a sin t)j, 0≤ts, followed by the line segment r₂(t)=ti, -astsa. The circulation is 0 (Type an exact answer, using it as needed.) The flux is (Type an exact answer, using as needed.)
Transcribed Image Text:Find the circulation and flux of the field F = 4x²i+ 4y²j around and across the closed semicircular path that consists of the semicircular arch r₁ (t) = (a cost)i + (a sin t)j, 0≤ts, followed by the line segment r₂(t)=ti, -astsa. The circulation is 0 (Type an exact answer, using it as needed.) The flux is (Type an exact answer, using as needed.)
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