E 15.7.5 Question Help Use the surface integral in Stokes Theorem to calculate the circulation of...
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.
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....
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.
12) Use Stokes' Theorem to calculate the circulation of the field Ể = 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
1 Help Entering Answers 1 point) Use Stokes' Theorem to evaluateF.dr where F(x,y,z) 6yzi 3xzj +3e k and C is the circy4,z 5 oriented counterclockwise as viewed from above Since the circle is oriented counterclockwise as viewed from above the surface we attach to the circle is oriented upwards The easiest surface to attach to this curve is the disk x2 + y2 < 4, z-5. Using this surface in Stokes' Theorem evaluate the following. F-dr = where sqrt(4-xA2) sqrt(4-x^2)...
using stokes theorem, set up integral that will calculate the circulationof the vector field Use Stokes' Theorem to find the integral which will calculate the circulation of the field F(x, y, z) = yzi + xzj + xyk where C is the intersection of the cylinder x + z2 = 9 and the planes z = 0, y = 0 and y = 1. Do not evaluate this integral.
Evaluate the line integral - dr by evaluating the surface integral in Stokes Theorem with an appropriate choice of metal Close counterdeckwite orientation when viewed from above С F-6²-82-x².7² -2²) C is the boundary of the square Ix 13. lys 13 in the plane 2 #0 Rewrite the given in integral as a | as a surface integral fro-SSO ds C 5 Evaluate the integral $r..-Type an exact answer
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.
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...