Concept explainers
Radial fields and zero circulation Consider the radial
a. Evaluate a line
b. For what values of p does Stokes’ Theorem apply? For those values of p, use the surface integral in Stokes’ Theorem to show that the field has zero circulation on C.
Want to see the full answer?
Check out a sample textbook solutionChapter 17 Solutions
Calculus, Early Transcendentals, Single Variable Loose-Leaf Edition Plus MyLab Math with Pearson eText - 18-Week Access Card Package
Additional Math Textbook Solutions
Thomas' Calculus: Early Transcendentals (14th Edition)
University Calculus: Early Transcendentals (3rd Edition)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
- 5) By using Stokes' Theorem, find the work performed by the vector field a particle that traverses the rectangle C in the plane E=x² + 4xy³i+y²xk,on z = y shown below. Ans: -90arrow_forwardStokes's Theorem / The Curl Theorem 2. Consider the vector field F(x, y, 2) = (yz?,x,x + y) and the closed curve C: r(t) = (cos t, sin t,0) 0sts 27 Note that C is the unit circle in the xy-plane traced out counterclockwise (as viewed from above). Also let D be the unit disc in the xy-plane and let E be the 45-degree cone whose tip is at the point (-1,0,0) and whose boundary is the curve C. That is, D= { (x,y,2) | x² + y²<1 and z = 0 } E = { (x,y.2)| z = J + y? – 1 and – 1szs0} a) Graph C,D, and E so that we can see what's going on. Note that D would be input as just z = 0, cut off by C as its boundary. You should note that E lines up with C as its boundary also. b) Find V x F, the curl of F. You will use this below. Now our goal is to verify the Curl Theorem, and again, we'll do it twice. The Curl Theorem claims that fF- dr = |v x F) - as = v×F) - as c) First evaluate the leftmost expression directly, the line integral of F along the closed curve C. d) Next evaluate the middle…arrow_forwardM2arrow_forward
- Use Stokes' Theorem to find the circulation of F = 5yi + 3zj + 6xk around a circle C of radius 7 centered at (5, 2, 7) in the plane z = 7, oriented counterclockwise when viewed from above. Circulation = [² с F. dr =arrow_forwardPlease provide Handwritten answer with explanationarrow_forwardanawer all the questionarrow_forward
- Use stokes theorem to evaluate the integralarrow_forwardThe magnetic field B due to a small current loop (which we place at the origin) is called a magnetic dipole (Figure). Let p=(2²+² +2²)¹/2 For p large, B-curl(A), where A= Let C be a horizontal circle of radius R3 with center (0, 0, 7). Use Stokes Theorem to calculate the flux of B through C R Current loop FIGURE y help (tractions) Activate Windowsarrow_forwardc) Verify Stokes's Theorem for F = (x²+y²)i-2xyj takes around the rectangle bounded by the lines x=2, x=-2, y=0 and y=4arrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning