Use Stokes' Theorem to calculate the circulation of the field F around the curve C in...
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...
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 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 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.
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
Please explain (1 pt) Use Stokes' Theorem to find the circulation of F = (xy, yz, xz) around the boundary of the surface S given by z 0 x 4 and -2 < y < 2, oriented upward. Sketch both S and its boundary C 16 - x2 for Fdr = Circulation = (1 pt) Use Stokes' Theorem to find the circulation of F = (xy, yz, xz) around the boundary of the surface S given by z 0 x...
Use Stokes' Theorem to evaluate the line integral $cF.dr, where F(x, y, z) = xyzi + yj + zk, Sis the surface 3x + 4y + 2z = 12 in the first octant, and is the boundary of S with counterclockwise orientation (from above).