(b) Solve the electric flux through a paraboloid z = x? +y² – 16 that lies below plane %3D z= 0. It is oriented by an outward unit normal vector with = 3xî + 4yĵ – 5z²k. (c) Determine the flux of the vector field F = x³i – 2yĵ + 7z²& across a cone z = x2 + y2 + 3 that lies in between the planes z = 4 and z = 8 by using Gauss's theorem.

Q: Compute the upward flux of the vector field Ĥ(x, y, z) = (x, 0, 2z) across the portion of the…

A:

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

A:

Q: Consider the solid E determined by the inequalities x² + y² + z≤ 4, and let S denote the surface…

A: Here we will use Stokes theorem  to calculate  flux of curl (F) on surface S bounded by curve C…

Q: Compute the flux of the vector field F = xi + 5yj through the cylindrical surface as shown in the…

A:

Q: Suppose we have part of a hyperboloid of two sheets -4x? -4y? + z? = 9 where z 20 (so the upper…

A: Equation of hyperboloid of two sheets is: −4x2−4y2+z2=9 Where z≥0 and z≤15

Q: Find the flux of the vector field F across the surface S in the indicated direction. F = 3x2j -z2 k;…

A: F = 3x2 j -z2 k,y = 2x2,0≤z≤2,-1≤x≤1.

Q: Compute the flux of the vector field F(x, y, z) = (2y, 3, –2xz) through the surface S, which is the…

A: Given vector field is, Fx,y,z=2y,3,-2xz. The given surface is, y=x2+z2  and  x2+z2≤1. Now for the…

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 outward flux of the field F = (x + y)î + yĵ + zk across the closed surface: S: z = 16x² -…

A:

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

A:

Q: The flow of a gas with a density of δ = 0.001 kg/m2 over the closed curve r(t) = (-sin t)i + (cos…

A: Given that

Q: Consider the gradient vector field V = Vg of the function g(x, y) = x² + y² + e*²-y´ cos(2xy).…

A: We will use the Divergence Theorem in 2D to solve the given flux integral.

Q: Is the two-dimensional vector field V = -2y 2x a possible velocity field x²+y² 'x² +y² for an…

A: For a two dimensional incompressible for a vector field V=ui+vj. ∂u∂x+∂v∂y=0

Q: 4. Compute the outward flux of the vector field F(r) = (r, y', =') through the unit sphere r² + y² +…

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

Q: 4. The vector field F(x, y) = (x² – y²)i+ 10-Rj-2zrk represents the velocity of a gas flowing in…

A:

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

A:

Q: 5. Find the outward flux of the vector field F(x, y,z) = x²i + y°j+z²k through the first octant…

A:

Q: 2. Let C be the curve of intersection between the cylinder r2+y = 1 and r-2y+z = 0, oriented…

A: The complete solutions are given below

Q: 2.) Calculate the curve integral over the vector field V(17, y) = ( * -2²y xy? for the positive…

A: Disclaimer: Since you have asked for a handwritten solution and currently we are not providing any…

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

A: Solution :

Q: The flow of a gas with a density of d = 0.001 kg/m2 over the closed curve r(t) = (-sin t)i + (cos…

A: Given information:

Q: (c) Determine the flux of the vector field F = x³î – 2yĵ + 7z²k across a cone z = Jx2 + y2 + 3 that…

A:

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

A:

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

A:

Q: (a) Compute the flux of the field F = r i+yj-zk across the cylindrical surface a + z = 1, 0 <y53…

A: If E be a  solid region bounded by surface of S with positive orientation then for a vector field…

Q: Find the flux of the field F = 4x i + 4y j + 2 k outward (normal away from the z-axis) through 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: Find the flux of the vector field F = (y, – z, x) across the 2 + 4x + 3y above the rectangle part of…

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

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

A:

Q: Compute the flux

A: Compute the flux

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

A:

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

A:

Q: 2.4) Use the divergence theorem to find the outward flux of the vector field F(x, y, x) = x³i+ y³j+…

A: The divergence of the given vector field is  ∇·F=∂∂xx3+∂∂yy3+∂∂zz3=3x2+3y2+3z2 Let, S be the surface…

Q: Given the radial field (x, y, z) (x² + y² + z²)³/2 |r|3/2 Find the outward flux across the sphere of…

A: Image is attached with detailed solution.

Q: Find the outward flux of the field F = 3xz2 i + y j - z3 k across the surface of the solid in the…

A:

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: he temperature in a temperature-controlled chamber is given by a 3D scalar field Tlx, y, 2) = Ax®yz…

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

Q: Find the outward flux of the field F = xz i + yz j + k across the surface of the upper cap cut from…

A:

Q: Consider the conservative vector field 4 8 F(x, y, z) = – 3y²cos (3nz),37y sin (3tz) – x2). 2xz, %3D…

A:

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: 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: Find the flux of the field F = z k across the portion of the sphere x2 + y2 + z2 = a2 in the first…

A:

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

A: The objective is to find the flux.

Q: 12. Find the flux of the field F(x, y, z) = 4xi + 4yj + 2k outward (away from z-axis) through the…

A:

Q: Find the work done by the force field F(x, y) = xyi+ x²j on a ,2 particle that moves along the curve…

A: Consider the given force field Fx,y=xyi+x2j Then, F⇀x,y=xy,y Write in parametric form y=t  then…

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

A:

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…

Q: Compute the flux of the vector field F = 2xi + 3yj through the cylindrical surface shown below, if a…

A: We have to compute the flux of the  given vector field.