Use Divergence Theorem to find the outward flux of field F = (-5x³ – 5y)i + (yz + 1)j + xyzk through the cube bounded by planes a

Q: Use the Divergence Theorem to compute the net outward flux of the field F=(2x, 3y, -z)  across the…

A: To calculate the net outward flux of the given vector field across the given surface

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

A:

Q: Verify that the Divergence Theorem is true for the vector field F on the region E. Give the flux.…

A:

Q: Find the divergence of the vector field F at the given point. F(x, y, z) = xyzi + xz2j + 4yz²k; (5,…

A: Recall divergence is a scalar and has formula enclosed in next page

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…

A:

Q: Consider vector field: F = e i-cos y j+ sin² z k. Obtain divergence and curl for F at points (0,,).

A:

Q: Let F be the vector field (ze"z + yz², xz², xeaz + 2xyz) (a) Find the divergence of F.

A: We will find out the required value.

Q: Compute the flux, || Foñds, across the slanted face of the tetrahedron 2 = 4-1- y bounded in the…

A:

Q: Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F and…

A: To use Green's theorem to find the counterclockwise circulation and outward flux for the field F and…

Q: .) Compute the flux of the vector field F = 4x + 4yj through the surface S, which is the part of the…

A:

Q: 3. Use the Divergence Theorem to find the flux of the vector field F = (5x+ 4y?z – 162³) i +…

A:

Q: I. Use the Divergence Theorem: (² F. ds = Ifv. Fav SSS E = to calculate the flux of the field F…

A: Divergence theorem uses  Double integration converts into triple integration.

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: Use the divergence of the vector field to compute F(x, y) = (tan-¹ (2x) fo tan¯¹ (2x) 4 where is the…

A:

Q: 4. (a) Show that the divergence theorem holds for the vector field F = 2xî + yz} – 3z²k where o is…

A:

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

A: Solution :

Q: Find the net outward flux of the fieldF = ⟨bz - cy, cx - az, ay - bx⟩ across any smooth closed…

A: The vector field is F=bz-cy,cx-az,ay-bx where a, b, and c are constants.

Q: Use the extended divergence theorem to compute the total flux of the vector field F(x, y, z) = −3x^2…

A: The function given to us is F→=-3x2+2xz-y, 7y3-6y, 9x2+4z2-3x. We are asked to find the total flux…

Q: Use the Divergence Theorem to compute the net outward flux of the field F=<x,2y,-z> across the…

A: From the Divergence theorem, for a positively oriented boundary surface (outward Normal) of region E…

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: 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.

A:

Q: Calculate the integral line of vector field F(x,y) around the circle x²+y²=1 oriented…

A: Given that Fx,y=-2yx2+y24+2x,2xx2+y2/4+xy+1. The the integral line of vector field F(x,y) around the…

Q: Find the line integral F.dr of the vector field F=ax] over a curve C defined by a C rectangle in the…

A:

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

A: Given: F→=xi→+yj→ z=36-x2+y2 ds=1+∂z∂x2+∂z∂y2dxdy       =1+4x2+4y2dxdy   and…

Q: Use the Divergence Theorem to compute the net outward flux of the vector field F = (x, - y,z") the…

A:

Q: Find the flux of the field F up through the part of the 1+ xy paraboloid z = 1 – x² – y? that…

A: FORMULA: Flux=∬F.n^ dS According to Stokes theorem, ∬F.n^ dS =∬∇×F . n^ dS According to the…

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

A:

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

A:

Q: Verify Stoke's theorem for the vector field F = (2x - y) I- yz*J-yzK over the upper half surface of…

A: Stokes theorem is used

Q: If F = Pi+ Qj+Rk is a vector field on R and P, Q. and R have continuous second-order partial…

A: Given:F=Pi+Qj+Rk is a vector field  in ℝ3To show that:∇.curl F=0

Q: 5. (a) Verify Gauss' Divergence Theorem for the vector field F = yî+x²j– zk and the volume V given…

A: 5.(a)The Gauss' Divergence theorem is,

Q: Use the extended divergence theorem to compute the total flux of the vector field F(x, y, 2) 3D…

A:

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<=x<=3,r=1

Q: Verify Stoke's theorem for the vector field F = (2x - y) I– yz"J - y z K over the upper half surface…

A:

Q: Consider the vector field F(x,y,z)=(−3x^2,8(x+y)^2,9(x+y+z)^2). Find the divergence and curl of FF.…

A:

Q: 4- Evaluate the surface integral of the vector field F = = [ax, by, cz] over the sphere a2 + y² + z²…

A: From the given problem:   F→=axi+byj+czk   Sphere:  x2+y2+z2=36.   From the divergence theorem:…

Q: Verify that the Divergence Theorem is true for the vector field F on the region E. Give the flux.…

A: According to the divergence theorem:

Q: Let C be the curve of intersection of z = 1 – 2x2 and the cylinder x2 + y2 = 1 oriented…

A:

Q: Find the counterclockwise circulation and outward flux of the field F = 7xyi + -5y²j C enclosed by…

A: Introduction: Let C be a piecewise smooth, simple closed curve enclosing a region R in the plane.…

Q: 4- Evaluate the surface integral of the vector field F = [ax, by, cz] over the sphere r² + y² + 2² =…

A:

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

A:

Q: Compute the flux of the vector field F = 2xi + 2yj through the surface S, which is the part of the…

A:

Q: Verify that the Divergence Theorem is true for the vector field F on the region E. Give the flux.…

A:

Q: : Verify the divergence theorem for A=4xi +(2Y+z Vector field ) | +(52-2x)k in the regim beunded by…

A: According to the given information, it is required to verify the divergence theorem for a vector…

Q: a) What is the flux of the constant vector field F = (a, b, c) through any closed surface? b) Is the…

A: Given That : A constant  vector field F=a,b,c and F=x3,y3,z3 To Find : i) The Flux through of…