Find the flux of the vector field F(x, y, z) = ri across the outward oriented sphere %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 vector field V(x, y, z) = 3xy²i + 5x²yj + 2z³k out of the unit sphere. Flux =

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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: Let v = (x*z, 2 – 4xyz, xz) be the velocity field of a fluid. Compute the flux of v across the…

A: Given, v→=x2z,2-4xyz,xz225x2+16z2=y-202 Then, calculating div v→ div…

Q: Find the curl of the vector field F(x, y, z)= e sin yi - e cos yj.

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

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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: Use the divergence theorem to calculate the flux of the vector field F(x, y, z)=-3ry-ly:j-Szak…

A: To find- Use the divergence theorem to calculate the flux of the vector field F→x, y, z = -3xyi^ -…

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 Stokes' Theorem to compute the flux of the curl of the vector field F = (e² – y, x + e²",…

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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: Use the divergence theorem to calculate the flux of the vector field F(x, y, z) = x°i + (5y – 5x*y)j…

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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: Use the Divergence Theorem to compute the net outward flux of the vector field F across the boundary…

A: Given The given vector field is F=3z+x,7x-9y,y+5z Region between the spheres of radius 1 and 4.

Q: Find the outward flux of the vector field F (x, y, z) = x³i + y³j+(z³ + xz)k across the surface of…

A: The vector field given is as follows: Fx, y, z=x3i^+y3j^+z3+xzk^ We are asked to find the outward…

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: 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: 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: Let S be the part of the plane 4x + 3y + z = 4 which lies in the first octant, oriented upward. Use…

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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: Compute the flux of F = (r, y, z*) across the cone z = x2 + y?, %3D 0<<1, in the downward direction.

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Q: disk

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

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Q: Show that the work done by a constant force field F = a i + b j + c k in moving a particle along any…

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Q: Compute the flux

A: Compute the flux

Q: Find the counterclockwise circulation and the outward flux of the field F = (-sin y)i + (x cos y)j…

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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(x,y,z) = xi – yj + zk across o, where o is the portion of the…

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Q: The vector field F = ( z, z²) has a scalar potential in the region R = {(x, y, z) E R° : x² + y? >…

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Q: (a) Set up a double integral for calculating the flux of the vector field F(x,y,z) = yi +5j − xzk…

A: Let r(x,z)=x,x2+z2,z Then the flux is given by, Flux=∬F.dS=∬F.(rx×rz)dxdz Here, rx=1,2x,0  ;…

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: 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: Use the Divergence Theorem to find the outward flux of the vector field F(x,y, z) = x³i + y³j+z³k…

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Q: Compute the flux of the vector field F(x, y, z) = 3xj + 3yk through the surface S, where S is the…

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Q: 6) Given the vector field F = (-x,-y,-z) '(x²+y2+z²)3/2! write the integral to calculate the outward…

A: First we parameterize field F then we calculate the Flux across the sphere using following formula:

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

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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: 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 outward flux of the vector field i- .+72 across the surface of the region that is enclosed…

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

A: We have find the flux of the given vector field through the parameterized surface S oriented upward.

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

A: Given  plane  2x+2y+z=4

Q: Sketch the vector field F(x, y) = 3i + 5j and calculate the flux then the circulation of F| along…

A: (1) The equation of line segment is: x+3-2+3=y-1-5-1=tx+3=t⇒x=t-3y-1=-6t⇒y=-6t+1 The curve…

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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