Find the flux in the upward z direction of the vector field F(x, y, z) = (xz³, yz³, (x² + y²)²) through S, where S is the portion of the surface z = 5 – x² – y² lying above z = 1.

Q: Find the flux of the vector field F(x, y, z) = 3xi+3yj+6zk across the portion of the surface z = 25…

A: The flux F across the surface is given by ϕ=∫σF·nds=∬RF·∇GdA

Q: Find the flux of the vector field F = (y, z, x) across the part of the plane z = 4+ x + 3y above the…

A: The surface integrals compute the flux of fields across surfaces,                   So,…

Q: Use the divergence theorem to find the outward flux of the vector field F(x, y, z) = 4x²i + 5y²j +…

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Q: Find the flux of the vector field F = (y, – z, x) across the part of the plane z = 4 + x + 2y above…

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Q: Use the divergence theorem to calculate the flux of the vector field F(x, y, z) = −1xyi – 2yzj —…

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Q: calculate the flux of the vector field through the given surface F = zi + (y −1)j + 5xk, and S is…

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Q: Find a flux of the vector field ä(M)= (2z– y)i +6xj + yk through a part of the surface S: x - 4y+2z…

A: Given, a→M=2z-yi^ +6x j^ +y k^ Also given surface is, S: x-4y+2z-4=0 So the normal vector to the…

Q: Find the flux of the field F(x, y, z) = z2 i + x j - 3 z k outward through the surface cut from the…

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Q: Find the flux of the vector field F (x, y, z) = (e-y, -y, x sin z) across the positively oriented…

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Q: ind the flux of the vector field F = yzi + 7yj + yk over the sphere x2 + y2 + z2 = 4.

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Q: Find the flux of the vector field F(x,y,z) = xi + yj+ 2zk across o, where o is the portion of the…

A: Flux of  a vector field F on the surface S   =∫∫SF ds We will use divergence theorem  If surface S…

Q: Find the flux of the vector field F = (y, – z, x) - 2, - across the part of the plane z = 2 + 3x +…

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Q: Compute the net outward flux of the vector field F = (x i + y j + z k)/ (x2 + y2 + z2)^(3/2) across…

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Q: 2. Use Gauss' Theorem to compute the outward flux of the vector field F(r) = (x, y, z²) through the…

A: Outward flux by using gauss divergence theorem

Q: Find the net flux of the vector field F(x, y, z) = (2x, - 2y, z) over the closed surface enclosed by…

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Q: Find the flux of the vector field F = (y, - z, x) across the part of the plane z = 4+ 2x + 3y above…

A: The given vector field is, F→=y, -z,  x. The given part of the plane is z=4+2x+3y And the rectangle…

Q: Use the divergence theorem to calculate the flux of the vector field F(x, y, a) + (2y-3')] + 7k…

A: Solution :

Q: Use the divergence theorem to find the outward flux of the vector field F(x,y,z)=3x2i+1y2j+2z2k…

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Q: Find the net outward flux of F = a x r across any smoothclosed surface in ℝ3, where a is a constant…

A: Net outward flux is ∇.F ∇=i∂∂x+j∂∂y+k∂∂za=a1i+a2j+a3kr=xi+yj+zk

Q: Find the flux of the vector field F(x, y, z) = (y z, y, æz) across the surface S, where S is the…

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Q: Q2) Find the flux of the vector field F(x,y,z) = (x,y, z) , where the surface S is the portion of…

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Q: Find the flux of the vector field F(x, y, z) = (yz, y°, xz) %3D across the surface S, where S is the…

A: Given

Q: Find the outward flux of the vector field F = (x°, y°, z²) across the surface of the region that is…

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Q: Find the flux of the vector field F(x, y, 2) = yj + k where o is the portion of the cone =' = 4(x² +…

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Q: Evaluate the outward flux of the vector field F = (2x² – 5e" + sin(z²), –4ry + In(x*), 5z – 3x²y®)…

A: We can see that the region given here is closed, so…

Q: Find the flux of F over the surface S of equation z2 = x2 + y2 , 0 ≤ z ≤ 3 and parameterized by x =…

A: Let E be a three-dimensional solid bounded by a piecewise smooth closed surface S that has…

Q: Calculate the flux of the vector field through the given surface.  F = 2i −3j + 6x2yk through the…

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Q: Find the flux of the vector field F across the surface S in the indicated direction. F =x3y 2i+yj…

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Q: 2. Use Gauss' Theorem to compute the outward flux of the vector field F(r) = (x, y, z²) through the…

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Q: Let S be the part of the plane 2x + 4y + z = 4 which lies in the first octant, oriented upward. Find…

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Q: 2. Find the flux of the vector field F(x,y,z) = xi + yj + 2zk across o, where o is the portion of…

A: The given problem is to find the flux of the given vector field over the given portion of cone…

Q: 4. Use the Divergence Theorem to find the outward flux of the vector field F(x,y, z) = v3;1 v3;173…

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Q: Find the flux of the vector field F = (y, – z, x) across the part of the plane z = 3+ 4x + 2y above

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Q: Let Q be the solid region bounded by the surface S of equation given by z2 = x2 + y2 , 0 ≤ z ≤ 3,…

A: Find outward flux of the vector field G(x, y, z) = x2 i+ y2 j+ z2 k with Q the solid region bounded…

Q: Compute the flux of the vector field F = zi + 8xk through the parameterized surface S oriented…

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Q: Find the flux of the vector field F(x,y,z) = xi – yj + zk across o, where o is the portion of the…

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Q: Find the flux of the vector field F = across the part of the plane | z = 2 + x + 3y above the…

A: Given: F¯=y,-z,x z=2+x+3y The formula to determine the flux is: ∫S∫F·nds=∫D∫(-agx-bgy+c)dA Here…

Q: Find the flux of the constant vector field i = -4 i – 5j- 2 k through a square plate of area 16 in…

A: The solution is given below

Q: Find the surface integral to evaluate the flux of the vector field F=, where S is the surface of the…

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Q: 3. Find the flux of the vector field F(x,y,z) = xi+ yj + 2zk across o, where o is the portion of the…

A: Find your answer below

Q: The flux of the curl of the vector field F(x, y, z) = (y², x, z) through the surface E = {(x, y, z)…

A: Here first we find the curl of the given vector field using formula Curl…

Q: Compute the flux of the vector field F(x,y,z)=5xj+2yk→through the surface S, where S is the part of…

A: Flux problem...

Q: Find the flux of the curl of the vector field F(x, y, z) = [(z2 −4) cos(xyz), 3x+y,(z2 −4) sin(ex…

A: Surface is oriented outwards. And -2 <= z <= 2

Q: Find the flux of the vector field F = xi - 3y j - 2z k through the part of the plane 2.x + 3y + z =…

A: The given problem is to find the flux of vector field F through the part of the plane given in the…

Q: Let S be the part of the plane 2x + 5y + z = 4 which lies in the first octant, oriented upward. Find…

A: Given, S be the part of the plane                        2x+5y+z=4        which lies in the first…

Q: Find the flux of the force field F(x, y, 2) = (2, x + r², 1 – a² + y) across the portion of the…

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Q: Compute the flux of the vector field F = zi + 8xj through the parameterized surface S oriented…

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Q: Find the flux of the vector field F = [x,y,z] through the oriented surface S: z= x^2 + y^2, z <= 1…

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Q: Find the flux of the vector field (y, x, z) in the negative z direction through the part of the…

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Q: Find the work done by the force field F(x, y, z) = (x – y², y – z², z – x2) on a particle that moves…

A: We have to find the work done by the force field F(x,y,z)=&lt;x-y2, y-z2, z-x2&gt; on a particle…