Find the flux of the vector field F = (y,- z, z) across the part of the plane z = 4 + 3z + 2y above the rectangle [0, 2] x [0, 3] with upwards orientation. %3D

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 field F = 2xy i + 2yz j + 2xz k upward across the portion of the plane x + y +…

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Q: What is the flux of the vector field F(x, y, z) = [9y, 2xy, 4yz + 234xy] through the unit cube [0,1]…

A: We find the flux of the vector field F(x, y, z) = [9y, 2xy, 4yz + 234xy] through the unit cube [0,1]…

Q: Find the outward flux of the vector field F = (x³, y³, z²) across the surface of the region that is…

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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: Calculate the flux of the vector field of (xv.z = r-)i +0= 4xz) i +xzk across the box bounded by *=y…

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Q: Calculate the flux of the vector field F(x, y, z) = 5i + 2j+ zk through the closed circular cylinder…

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Q: Find the flux of the vector field F(x, y, z) = ri across the outward oriented sphere %3D

A: In this question, we find the flux of the vector field f(x,y,z)=xi The surface is a sphere of radius…

Q: Calculate the flux of the vector field V = 5i through a square of sides 4 m in the y-z plane (0 s ys…

A: Given V = 5i Area oriented towards positive x direction

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: 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 = (z, y°, through the helicoid with parameterization r(u, v) =…

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

A: Solution :

Q: Compute the flux of the vector field F = 2xi + 5yj through the cylindrical surface shown below, if a…

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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: Compute the flux of the vector field F = 3xzi + 5yk through the surface S, which is the hemisphere…

A: The flux is given byflux =∫S  F→·n^  dShere,n^=x, y, zx2+y2+z2 in spherical coordinatesF→·n^ =x, y,…

Q: Calculate the flux of the vector field (x°, y), out of the annular region between the a + y? = 16…

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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: Calculate the flux of the vector field (x, y³), out of the annular region between the x? + y? = 1…

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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: Q1 Use Stokes theorem to compute the flux of the curl of a vector field F = (2x – y)ĩ – yz? j- y²zk…

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Q: Find the flux of the vector field F = (y, - a, z) through the helicoid with parameterization r(u, v)…

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Q: Compute the flux of the vector field F == through the surface S where S is the surface bounded by r…

A: Given thatF→=fr,fθ,fz=r2+sin2θ,rsincosθ,3z∂∂rrfr=∂∂rr22+sin2θ=2r2+sin2θ& ∂∂θfθ=∂∂θr…

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: Compute the flux of the vector field F = across sphere a? + y² + z² = 9.

A: Let F be a vector field and S be the boundary of the surface D. To find the flux of the vector…

Q: Find the flux of the vector field F(x, y, z) =(x)i+(y)j+(z)k through the surface S of the…

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Q: Calculate the flux of the vector field F = (0, z, y) through the surface E: 2u?v? E:{y= u with…

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Q: disk

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Q: The outward flux of the vector field F(x, y, z) = (x, y, z?) across the boundary of D = {(x, y, z) E…

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Q: Compute the flux

A: Compute the flux

Q: A helicoid H is described by r(u, v) : (u cos(v), u sin(v), v) for 0 < u < 5 and 0 < v < 2n (with…

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

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

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Q: Compute the flux of the vector field F = xi + yj + zk through the surface S, which is a closed…

A: Given F=xi+yj+zk ,-3&lt;=x&lt;=3,r=1

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: Compute the flux of the vector field F = xi + yj through the surface S, which is the part of the…

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Q: 2u?u? Σ: y = u with 0<u < 2,0 < v< 1. Z = V

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Q: Compute the flux of the vector field F(x, y, z) = 41 + 45 + Sk through the rectangular region with…

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Q: Evaluate the flux, in the specified direction, of the vector field across the surface. F(x, y, z) =…

A: To calculate the flux, we shall use the standard formula of flux in terms of the vector form of the…

Q: A hot air balloon is shaped like a truncated sphere like the figure. The gases escape through the…

A: Given a hot air balloon has a truncated spherical shape. The velocity vector field  Vx,y,z=∇×Fx,y,z…

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 = 2xzi + 5yk through the surface S, which is the hemisphere…

A: In this question, we find the flux for the given vector field across the surface of the hemisphere.

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: Verify Stokes' Theorem holds for the vector field F = yz i + x k where S is the portion of the plane…

A: The given vector field is F=yzi^+xk^ where S is the portion of the plane 3x+2y+6z=6 in the first…

Q: Calculate the flux of the vector field through the given surface. F = zi + 2xj + 3yk, and S is the…

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Q: Calculate the vector field flow f➝ (x,y,z) = (xy, y2, z) through the outer surface of solid T in the…

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