Use Stokes' Theorem to make the following circulation calculations.
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 \(=\int_{C} \vec{F} \cdot d \vec{r}=\)
Homework Answers
6. Estimates from geometric definitiions: (a) Suppose divF2z. Estimate the ux of F through a sphere of radius 0.01 centered at (b) Suppose curlF-(z + 4)it (2-ทั+ (:-3)E, estimate circulation of F...
6. Estimates from geometric definitiions: (a) Suppose divF2z. Estimate the ux of F through a sphere of radius 0.01 centered at (b) Suppose curlF-(z + 4)it (2-ทั+ (:-3)E, estimate circulation of F around a circle C of radius 0.1, centered at the origin, if C is on the ry- yz-, and rz-plane respectively oriented counter-clockwise when viewed from the positive z, positive a, and positive y-axis respectively 7. Three small squares Ci,C2, Cs each with sides 0.1, centered at the...
Please explain (1 pt) Use Stokes' Theorem to find the circulation of F = (xy, yz, xz) around the boundary of the sur...
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...
1. About circulation, circulation density and curl: Given curl( F) = z27-2mit cos(12 + y2) (a) Fi...
1. About circulation, circulation density and curl: Given curl( F) = z27-2mit cos(12 + y2) (a) Find the circulation density circnF (P) where P= (1,1,1) around the normal i-2- k. (b) Estimate the circulation for F around C, a circle of radius 0.01 centered at P- (1,1, 1), on the z-1 plane, oriented clockwise when viewed from the origin. (c) Find the maximum circulation density for F at P- (1,1, 1).
1. About circulation, circulation density and curl: Given curl(...
Find for the given F and C
Find \(\int_{C} \vec{F} \cdot d r\) for the given \(\vec{F}\) and \(C\).\(\cdot \vec{F}=-y \vec{i}+x \vec{j}+7 \vec{k}\) and \(C\) is the helix \(x=\cos t, y=\sin t r \quad z=t\), for \(0 \leq t \leq 2 \pi .\)$$ \int_{C} \vec{F} \cdot d \vec{r}= $$Find \(\int_{C} \overrightarrow{\mathrm{F}} \cdot d \overrightarrow{\mathrm{r}}\) for \(\overrightarrow{\mathrm{F}}=e^{y} \overrightarrow{\mathrm{i}}+\ln \left(x^{2}+1\right) \overrightarrow{\mathrm{j}}+\overrightarrow{\mathrm{k}}\) and \(C\), the circle of radius 4 centered at the origin in the \(y z\)-plane as shown below.$$ \int_{C} \vec{F} \cdot d \vec{r}= $$
(1 point) Evaluate the circulation of yi zj+6yk around a square of side 7. centered at the origin, lying in the yz-plane, and oriented counterclockwise when viewed from the positive x-axis Circulatio...
(1 point) Evaluate the circulation of yi zj+6yk around a square of side 7. centered at the origin, lying in the yz-plane, and oriented counterclockwise when viewed from the positive x-axis CirculationF dr-
(1 point) Evaluate the circulation of yi zj+6yk around a square of side 7. centered at the origin, lying in the yz-plane, and oriented counterclockwise when viewed from the positive x-axis CirculationF dr-
Use the surface integral in Stokes' Theorem to calculate the circulation of the field F=x^2i+5xj+z^2k around...
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.
8) Find the circulation of F =(6x+5 y,4y+3z, 2x+1z) around a square of side 7, centered at (1,2,1), lying in the pla...
8) Find the circulation of F =(6x+5 y,4y+3z, 2x+1z) around a square of side 7, centered at (1,2,1), lying in the plane 4x+1y+6z = 12 , and oriented clockwise when viewed from the origin
8) Find the circulation of F =(6x+5 y,4y+3z, 2x+1z) around a square of side 7, centered at (1,2,1), lying in the plane 4x+1y+6z = 12 , and oriented clockwise when viewed from the origin
Use Stokes' Theorem to evaluate integral_C F middot dr. C is oriented counterclockwise as viewed from above. F(x, y,...
Use Stokes' Theorem to evaluate integral_C F middot dr. C is oriented counterclockwise as viewed from above. F(x, y, z) = yz i + 8xz j + e^xy k C is the circle x^2 + y^2 = 1, z = 2.
12) Use Stokes' Theorem to calculate the circulation of the field } = 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.
Table 14.4 Fundamental Theoremsdtb)-a) or Calculus Fundamental Theorem f.dr-un-nA) of Line Integr...
need help with #4. need to identify best theorem to use and find
solution.
Table 14.4 Fundamental Theoremsdtb)-a) or Calculus Fundamental Theorem f.dr-un-nA) of Line Integrals Green's Theorem Circulation form) Stokes' Theorem F-nds Divergence Theorem Evaluate the line integral for the following problems over the given regions: 1. F (2xy,x2 C:r(t) (9-2.),0sts3 3X3dy-3y3dz; C is the circle of radius 4 centered at the origin with clockwise orientation. 2. 3. ye""ds; C is the path r(t) (t,3t,-6t), for Ost s In8...
6. Estimates from geometric definitiions: (a) Suppose divF2z. Estimate the ux of F through a sphere of radius 0.01 centered at (b) Suppose curlF-(z + 4)it (2-ทั+ (:-3)E, estimate circulation of F around a circle C of radius 0.1, centered at the origin, if C is on the ry- yz-, and rz-plane respectively oriented counter-clockwise when viewed from the positive z, positive a, and positive y-axis respectively 7. Three small squares Ci,C2, Cs each with sides 0.1, centered at the...
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...
1. About circulation, circulation density and curl: Given curl( F) = z27-2mit cos(12 + y2) (a) Find the circulation density circnF (P) where P= (1,1,1) around the normal i-2- k. (b) Estimate the circulation for F around C, a circle of radius 0.01 centered at P- (1,1, 1), on the z-1 plane, oriented clockwise when viewed from the origin. (c) Find the maximum circulation density for F at P- (1,1, 1).
1. About circulation, circulation density and curl: Given curl(...
(1 point) Evaluate the circulation of yi zj+6yk around a square of side 7. centered at the origin, lying in the yz-plane, and oriented counterclockwise when viewed from the positive x-axis CirculationF dr-
(1 point) Evaluate the circulation of yi zj+6yk around a square of side 7. centered at the origin, lying in the yz-plane, and oriented counterclockwise when viewed from the positive x-axis CirculationF dr-
8) Find the circulation of F =(6x+5 y,4y+3z, 2x+1z) around a square of side 7, centered at (1,2,1), lying in the plane 4x+1y+6z = 12 , and oriented clockwise when viewed from the origin
8) Find the circulation of F =(6x+5 y,4y+3z, 2x+1z) around a square of side 7, centered at (1,2,1), lying in the plane 4x+1y+6z = 12 , and oriented clockwise when viewed from the origin
Use Stokes' Theorem to evaluate integral_C F middot dr. C is oriented counterclockwise as viewed from above. F(x, y, z) = yz i + 8xz j + e^xy k C is the circle x^2 + y^2 = 1, z = 2.
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.
need help with #4. need to identify best theorem to use and find
solution.
Table 14.4 Fundamental Theoremsdtb)-a) or Calculus Fundamental Theorem f.dr-un-nA) of Line Integrals Green's Theorem Circulation form) Stokes' Theorem F-nds Divergence Theorem Evaluate the line integral for the following problems over the given regions: 1. F (2xy,x2 C:r(t) (9-2.),0sts3 3X3dy-3y3dz; C is the circle of radius 4 centered at the origin with clockwise orientation. 2. 3. ye""ds; C is the path r(t) (t,3t,-6t), for Ost s In8...
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