15.3 Line Integrals Find Flux of Vector Field F across Closed Plane Curve F=xi + yj;...

Question

Question

15.3 Line Integrals Find Flux of Vector Field F across Closed Plane Curve F=xi + yj; the curve C is the counterclockwise path

Answer 1

Answer #1

C div FdA Ilux across C = 0 Fondo Es div F da = S 3 (0)4 da = lada xty cas = 2x Area of circle of radius 5 = 2x Tx 5 = 2x11x2

Answer 2

Similar Homework Help Questions

can you solve this vector problems? Find the outward flux of the vector field F(x, y,...

can you solve this vector problems? Find the outward flux of the vector field F(x, y, z) = (xi + yj + zk)/(x 2 + y 2 + z 2 ) 3/2 across the ellipsoid 4x^2 + 9y^2 + z^2 = 1. 6. (12 pts.) Find the outward flux of the vector field F(r,y, ) (ri yj+ zk)/(x2 + y2 22)3/2 across the ellipsoid 4r2 +9y2 + z2 = 1 6. (12 pts.) Find the outward flux of the vector...
Evaluate the surface integral F dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F...

Evaluate the surface integral F dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) -xi yj+3 k S is the boundary of the region enclosed by the cylinder x2 + z2-1 and the planes y 0 and x y 2 Evaluate the surface integral F dS for the given vector field F and the oriented surface...
Using Green's Theorem, find the outward flux of F across the closed curve C with counterclockwise...

Using Green's Theorem, find the outward flux of F across the closed curve C with counterclockwise 6) F=(x2 + y2)i + (x - y)j is the rectangle with vertices at (0,0),(6.0).(6,7), and (0,7) Rotated counterclockwise Flux GI IS ONE DA (09) 5700 T (6,0) (9)

Could you solve this problem? realted to vector field calculus Find the circulation of the vector...

Could you solve this problem? realted to vector field calculus Find the circulation of the vector field P(ar, y)i +Q(x, y)j F(ar,y) where 2-y P(x, y) = 9x2 + (y - 2)2 -2 y 9r2 + (y+ 2)?'| Q(x, y) = 9r2 + (y- 2)? * 9xr2 + (y + 2)2' around the simple closed curve C = Ci U C2, where C1 is the path along the line y = x from (-3, -3) to (3,3), and C2 is...
xi+ yj + zk 3. Given the vector field in space F(x, y, z) = or...

xi+ yj + zk 3. Given the vector field in space F(x, y, z) = or more conveniently, (.x2 + y2 + 22)3/2 1 Fr) where r = xi + yj + zk and r= ||1|| = x2 + y2 + x2 (instead of p) 73 r (a) [10 pts) Find the divergence of F, that is, V.F. (b) (10 pts] Directly evaluate the surface integral [/F F.Nds where S is the unit sphere 22 + y2 + z2 1...
Please help me how to solve this problem Find the circulation of the vector field F(x,...

Please help me how to solve this problem Find the circulation of the vector field F(x, y) = P(x, y)i + Q(x, y)j where P(x, y) = [2 − y] / [9x^2 + (y − 2)^2] + [−2 − y / [9x^2 + (y + 2)^2] , Q(x, y) = x / [9x^2 + (y − 2)^2] + x / [9x ^2 + (y + 2)^2] , around the simple closed curve C = C1 ∪ C2, where C1 is...

Find the circulation and flux of the field F around and across the closed semicircular path...

Find the circulation and flux of the field F around and across the closed semicircular path that consists of the semicircular arch r(t)=(a cost)i +(a sint)j, Ostst, followed by the line segment rz(t)=ti, -ast sa F = x’i+y? j
Evaluate the surface integral F dot dS for the given vector field F and the oriented...

Evaluate the surface integral F dot dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. 24. F(x, y, z) = -xi - yj + z’k, S is the part of the cone z = x2 + y2 between the planes z 1 and 2 3 with downward orientation
Flux of F(x,y)= x î + yj across the circle x2 + y2 = 4 (anticlockwise)...

Flux of F(x,y)= x î + yj across the circle x2 + y2 = 4 (anticlockwise) is 877 со - 8 TT Can not find

3) (11 points) Consider the vector field Use the Fundamental Theorem of lLine Integrals to find the work done by F along any curve from 41. 1Le) to B(2. el) 4) (10 points) Consider the vec...

3) (11 points) Consider the vector field Use the Fundamental Theorem of lLine Integrals to find the work done by F along any curve from 41. 1Le) to B(2. el) 4) (10 points) Consider the vector field F(x.y)-(r-yi+r+y)j and the circle C: r y-9. Verify Green's Theorem by calculating the outward flux of F across C (12 points) Find the absolute extreme values of the function .-2-4--3 on the closed triangular region in the xy-plane bounded by the lines x...