Find the divergence of the field F. F = 8x 5 i + 3y 5 j + 2z 5 k   a) 65   b) 8x4 + 3y4 + 2z4   c) 0   d) 40x4 + 15y4 + 10z4

Q: Determine the divergence of vector field E = 3x²x + 2zŷ + x²z2 at (2, –4, 0).

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Q: Find the divergence of the field. F = (2x+7y-8z)i + (5x +3y+6z)j + (-6x-y+2z)H div F =

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Q: The gradient of a scalar field V is a vector that represents both magnitude and the direction of the…

A: Given : The gradient of a scaler field V is a vector that represents both magnitude and direction…

Q: Give an example of a nonzero vector field F such that curl(F) = 0 and div(F) = 0.

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Q: Assume that Ax, y, z) is a vector field whose i component is only in terms of y and z, whose j…

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Q: If ϕ=3xy+2x2yz−12xz3ϕ=3xy+2x2yz−12xz3, Find ∇×(∇ϕ)

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 9) Check whether the vector field F = (-cos x cos y, sin x sin y, - sec² z) is a gradient vector…

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Q: Find the divergence of the field. F=(-x+8y - 3z)i+ (8x- 4y + 3z)j+ (- 4x- y- 3z)k

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Q: Show that the outward flux of a constant vector field across any closed surface to which the…

A: We have to Show that the outward flux of a constant vector field across any closed surface to which…

Q: Use the Divergence Theorem to compute the flux across the sphere x2+y2+z2 = 1 within the vector…

A: The answer is as follows:

Q: A vector field is described as F = (-z + 7x, x³y²z=1,3x + 2z²). (i) Calculate curl F. (ii) Determine…

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Q: Verify that the work performed along the segment P Q by the constant ~ vector field F = (2, -1, 4)…

A: We have given; vector field F = (2, -1, 4) (a) P = (0, 0, 0), Q = (4 , 3, 5) (b) P = (3, 2, 3), Q =…

Q: Evaluate the work done between point 1 and point 2 for the conservative field F. F 3D6xi+ 6уј+ 6z k;…

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Q: Show that the vector field F = ( -z, 0, x) is orthogonal to the position ----+ vector OP at each…

A: Given data: The vector field in the Cartesian co-ordinates is given by, F=-z i+x k.  Here, I and k…

Q: Find the divergence of the vector field. F(x, y, z)= 6x¹0i-10xy ¹0j O divF(x, y, z) = 60x⁹-100xy⁹ O…

A: To find the divergence of the given vector field.

Q: Show that F = (2xy + z³)ï + (x²)j+3xz²k is a conservative field. Find the scalar potential and the…

A: Given F = 2xy+z3 i ; x2j + 3xz2kThe objective is to show that given vector fieldis coonservative…

Q: Why does a two-dimensional vector field with zero divergence ona region have zero outward flux…

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Q: 5. Compute div F and curl F if F = (2x – cos y)i – x²e32j + (z² – 7x)k. 6. Determine if the vector…

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Q: Compute the curl of the vector field F⃗ =7zi⃗ +6yj⃗ +4xk⃗

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Q: Use the divergence theorem to calculate the flux of the vector field F = x3i - 3x2yj + 6zk through…

A: The divergence theorem is defined by the formula, ϕ=∮∂VF·ndS=∮V∇·FdV Consider the given vector…

Q: Find the divergence of the vector field. F(x, y, z)= 7x¹i, 7xy7j O divF(x, y, z) = 7x³¡— Ţxy³j…

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Q: 1. Give an example of a vector field F(x, y) in 2-space such that F has constant direction but || F…

A: The solution are next step

Q: Find the divergence of the field. F= (4x + 5y + 7z)i + (8x - 8y + 3z)j + (2x - 7y + 4z)k div F =

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Q: (a) Determine whether the field F(r, y, 2) = (-2, 2, -2az - 62) is conservative or not.

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: Sketch a two-dimensional vector field that has zero divergenceeverywhere in the plane.

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Q: Compute the flux of the vector field (x2, - xy*), out of the rectangle with vertices (0,0), (4,0),…

A: Given,

Q: Compute the flux of the vector field (x, (æ°, – ay*), out of the rectangle with vertices (0,0),…

A: To compute the flux of the vector field x3,-xy4, out of the rectanglewith vertices 0,0,2,0,2,4…

Q: What is the flux of the vector field (x2,y2,z1 ) through a cuboid with x ranging from 0 to 8.3, y…

A: use divergence theorem

Q: Calculate the divergence of the scalar field F(x,y)=3x2+siny.

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Q: Find the divergence of the field F. F = 8x 5 i + 3y 5 j + 2z 5 k 8x4 + 3y4 + 2z4 O 40x4 + 15y4 +…

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Q: Explain how to compute the divergence of the vector field F = ⟨ƒ, g, h⟩ .

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Q: What is the divergence of a vector field? How can you interpret it?

A: Divergence of a vector field:

Q: Express (5x + 7y, 8x + 5y, 0) as the sum of a curl free vector field and a divergence free vector…

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Q: Find the divergence of the field. F = (- 6x + 8y – 4z)i + (- 8x – 5y + 3z)j+ (x + 5y + 2z)k div F =

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Q: Therefore, div(curl G) = sin(y) – sin(y) + 8 = Since div(curl G) is different from 0, we conclude…

A: Given that:div(curl G)=siny-siny+8=

Q: A smooth vector field F has div F(5, 2, 5) = 2. Estimate the flux of F out of a small sphere of…

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Q: Consider the vector field F = ⟨ 1 , y ⟩ .Compute the path integral of this field along the path:…

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Q: The vector field F is shown in the xy-plane and looks the same in all other horizontal planes. (In…

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Q: Find the line integral of the field F = over the straight-line path from (1,1,1,) to (2,2,2).

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Q: i) Show that F is a conservative vector field.

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Q: Express (5x + 7y, 8x + 5y, 0) as the sum of a curl free vector field and a divergence free vector…

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Q: 3. Show that the vector field F = -C with C> 0, is conservative and find its potential.

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Q: Let F(x, y, z) =⟨3x2y+az, x3,3x+ 3z2⟩ be a vector field. For what values of a is F conservative?

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Q: Give an example of a vector field F (x, y, z) that has value 0 on precisely one line and such that…

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Q: Select the option that gives the vector field that could correspond to this arrow map.

A: The vector field is when a vector is assigned to each point in the given space. The cartesian form…

Q: Evaluate the work done between point 1 and point 2 for the conservative field F. F = 8 sin 8x cos 5y…

A: We have to find work done.

Q: Since the divergence of an inverse-square field is zero, the flux of an inverse-square field across…

A: it is false as

Q: Give an example of a non-zero vector field that is not irrotational and not incompressible.

A: We find an example of a non-zero vector field that is not irrotational and not incompressible.