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...
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...
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-
6. (4 pts) Vectors VÀ and VB generate a square in the plane x +2y + 3z = 1, as shown in the left figure. A smooth vector field F in the square behaves as shown in the right figure. В ID 18 12 10 0 B 10 14 16 18 А Assume that the greatest circulation density of T at P is 5 and at Q is 2. (a) Find curl at P. (b) Find curlī at Q. (c)...
GIVEN: Ω isthe portion of the surface of the sphere centered at the origin of radius 3 above 1.2 1(xy, z) the plane, z-2: Ω: the field F = (x, x,x). a) FIND the flux of VrF through Ω in the given direction: n has positive 2-component. HINT: (radius a)on Q:(spherical coordinates) b) Parameterize the path,c-a2, (r,g,z)asin g dode with orientation to agree with the given n for Ω ANS: (a) 5 c) With positive orientation,an -e DETERMINE: F.ds ANS:...
PLEASE DO LETTER d.) PLEASE DO LETTER f.) The plane from e.) is 4(x-2)+6(y-1)+(z-1)=0 or 4x+6y+z=15 15. The temperature on an unevenly heated metal plate positioned in the first quadrant of the xy-plane is given by 25xy + 25 C(x, y) = 7 (x - 1)2 + (y - 1)2 +1° Assume that temperature is measured in degrees Celsius and that x and y are each measured in inches. (Note: At no point in the following questions should you expand...