12) Use Stokes' Theorem to calculate the circulation of the field Ể = x?i – xyj...
12) Use Stokes' Theorem to calculate the circulation of the field } = x?i – xyj + yk around the curve C in the indicated direction. C is the counterclockwise path around the perimeter of the rectangle in the x-y plane formed from the x-axis, y-axis , x = 2 and y = 3.
Use Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated direction. 11) F-3yi + yj + zk: C: the counterclockwise path around the boundary of the = 1
Use the surface integral in Stokes' Theorem to calculate the circulation of the field F=x^2i+5xj+z^2k around the curve C: the ellipse 16x^2 + y^2 = 1 in the xy-plane, counterclockwise when viewed from above.
13) Use Stokes' Theorem to calculate the circulation of the field } = -9y3i+ 9x3j + 8z?k around the curve C in the indicated direction. C is the portion of the paraboloid x² + y2 = z by the cylinder x2 + y2 = 4.
Use Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated direction 27) F 3xi2xj + 7zk; C: the cap cut from the upper hemisphere x2 + y2 + z2 = 16 (z z 0) by the cylinder x2+ y2 =4 27) Use Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated direction 27) F 3xi2xj + 7zk; C: the cap cut from the upper...
4. (18 points) Verify Stokes' Theorem in finding the counterclockwise circulation of the vector field, F - (r-i + (42)j + (r) k around the curve, C, where C is the triangular path determined by the points (6,0,0),(0,-4,0),and (0,0,10) . (i.e. calculate the circulation % F.iF directly, and then by using Stokes' Theorem and doing a surface integral.) Which way was easier? (Hint: You will need to find the equation of the plane that goes through these three points.) 4....
E 15.7.5 Question Help Use the surface integral in Stokes Theorem to calculate the circulation of the field F-(72)i+ (x+y)+(x+y)k around the curve C: The square bounded by the lines x 41 and y" t1 in the xy.plane, counterclockwise when viewed from above + d = С
Suppose \(\vec{F}=(5 x-3 y) \vec{i}+(x+4 y) \vec{j}\). Use Stokes' Theorem to make the following circulation calculations.(a) Find the circulation of \(\vec{F}\) around the circle \(C\) of radius 10 centered at the origin in the xy-plane, oriented clockwise as viewed from the positive z-axis. Circulation \(=\int_{C} \vec{F} \cdot d \vec{r}=\)(b) Find the circulation of \(\vec{F}\) around the circle \(C\) of radius 10 centered at the origin in the yz-plane, oriented clockwise as viewed from the positive \(x\)-axis. Circulation \(=\int_{C} \vec{F} \cdot...
Use Stokes' theorem to find the circulation of the vector field F around any smooth, simple closed curve C, where: (Sy 7sin() 5) Use Stokes' theorem to find the circulation of the vector field F around any smooth, simple closed curve C, where: (Sy 7sin() 5)
Use Stokes’ Theorem to calculate the work done by the force F⃗ = ⟨2y, xz, x + y⟩ on a particle moving counterclockwise around the curve of intersection of the plane z − y = 2 and the cylinder x2 + y2 = 1