Use the surface integral in Stokes Theorem to calculate the circulation of the field F around the
Question:
Use the surface integral in Stokes’ Theorem to calculate the circulation of the field F around the curve C in the indicated direction.
F = x2y3i + j + zk
C: The intersection of the cylinder x2 + y2 = 4 and the hemisphere x2 + y2 + z2 = 16, z ≥ 0, counterclockwise when viewed from above
Transcribed Image Text:
THEOREM 6-Stokes' Theorem Let S be a piecewise smooth oriented surface having a piecewise smooth boundary curve C. Let F = Mi + Nj + Pk be a vector field whose components have continuous first partial derivatives on an open region containing S. Then the circulation of F around C in the direction counterclockwise with respect to the surface's unit normal vector n equals the integral of the curl vector field VX F over S: fF.dr = [[ S Counterclockwise circulation VXF ndo Curl integral (4)
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 62% (8 reviews)
To calculate the circulation of the vector field F x2y3i j zk around the curve C we can apply Stokes theorem Stokes theorem states that the circulation of a vector field around a closed curve is equal ...View the full answer
Answered By
Rodrigo Louie Rey
I started tutoring in college and have been doing it for about eight years now. I enjoy it because I love to help others learn and expand their understanding of the world. I thoroughly enjoy the "ah-ha" moments that my students have. Interests I enjoy hiking, kayaking, and spending time with my family and friends. Ideal Study Location I prefer to tutor in a quiet place so that my students can focus on what they are learning.
5.00+
1+ Reviews
10+ Question Solved
Related Book For
Thomas Calculus Early Transcendentals
ISBN: 9780321884077
13th Edition
Authors: Joel R Hass, Christopher E Heil, Maurice D Weir
Question Posted:
Students also viewed these Mathematics questions
-
Respecting the human rights of the population, can a higher level of human development be achieved? But. Explain. Why?
-
1.A baseball is batted at an angle into the air. Once airborne, and ignoring air drag, what is the ball's acceleration vertically? Horizontally? 2. At what part of its trajectory does the baseball...
-
X Finding Values of an Inverse Function Assume that f is a one-to-one function. -25. (a) If f(2)= 7, find f(7). (b) If f(3) = -1, find f(-1). 26. (a) If f(5) = 18, find f(18). (b) If f(4) = 2, find...
-
Draw Lewis structures for the AsCl4+ and AsCl6- ions. What type of reaction (acidbase, oxidationreduction, or the like) is the following? 2AsCl5(g) AsCl4AsCl6(s)
-
Valpaige Company is an industrial machinery and equipment manufacturer with several production departments. The company employs automated and heavy equipment in its production departments....
-
Six stations, A through F, communicate using the MACA protocol. Is it possible for two transmissions to take place simultaneously? Explain your answer.
-
Discuss the uses and limitations of the statement of financial position for decision-making purposes.
-
A tennis enthusiast wants to estimate the mean length of mens singles matches held during the Wimbledon tennis tournament. From the Wimbledon history archives, he randomly selects 40 matches played...
-
Let y = tan(3x+6). Find the differential dy when x = 5 and dx = 0.1 Find the differential dy when x = 5 and da = 0.2
-
Regents Corporation is a recently acquired U.S. manufacturing subsidiary located on the outskirts of London. Its products are marketed principally in the United Kingdom with sales invoiced in pounds...
-
Use the surface integral in Stokes Theorem to calculate the flux of the curl of the field F across the surface S in the direction of the outward unit normal n. F = xyi + 2yzj + 3zk S: r(r, 0) 0r 1,...
-
Which fields are conservative, and which are not? F = -yi + xj
-
Let \(\mathbf{F}(x, y)=\left\langle x^{2} y, x y^{2}ightangle\) be the velocity vector field for a fluid in the plane. Find all points where the angular velocity of a small paddle wheel inserted into...
-
1. Suppose you are about to sit down to a meal. You know how much you value different foods, either because of its value to your health or because it gives you pleasure. You also know how many...
-
You work as the Head of Human Resources (HR) for a large manufacturing company headquartered in California. The company is facing challenges in sales revenues and, as a result, they are working to...
-
Bridgeport Company changed depreciation methods in 2025 from double-declining-balance to straight-line. Depreciation prior to 2025 under double-declining-balance was $95,800, whereas straight-line...
-
After doing so, please compose a brief reflection addressing the following prompts: What are the differences between copyright infringement and plagarism? How can plagarism and copyright...
-
Identify which philosopher made the statements that follow: Hobbes, Aristotle, Plato, Austin, Cicero, Aquinas, Bentham, Saint Augustine 1) "No positive law is legally unjust." 2) "The first precept...
-
A cylindrical tank with radius 5 m is being filled with water at a rate of 3 m3/ min. How fast is the height of the water increasing?
-
An interest bearing promissory note for 90 days at 5.6% p.a. has a face value of $120,000. If the note is discounted 20 days after the issue date at a rate of 6.8% p.a., calculate the amount of...
-
In Problems 39 62, find the exact value, if any, of each composite function. If there is no value, say it is not defined. Do not use a calculator. $11 in-(sin (sin 2) 8
-
In Problems 21100, establish each identity. 1 sin 0 1 - cose = - cos
-
In Problems 21100, establish each identity. 1 + tan v 1 tan v cotv + 1 cot v - 1
-
6. Let G be a CFG with the following rules: SaSble Let Li = {ab" In 20}. Prove that L CL(G).
-
Shamrock, Inc.reports the following liabilities (in thousands) on its December 31, 2022, balance sheet and notes to the financial statements. Accounts payable $4,701 Mortgage payable $7,006 Unearned...
-
Contrast the Universal and Contingency Models of strategy development. Explain the key differences between these two approaches, highlighting their respective strengths and weaknesses. Additionally,...
Study smarter with the SolutionInn App