Calculate the flow of the vector field coming out of the surface
S of the volume below. The volume inside this surface is π.
Calculate the flow of the vector field coming out of the surface S of the volume below. The vol...
1) An object moves from point A to point B. Calculate the work done on the object by the force vector field: 2) Calculate, in two different ways, the flow of the vector field coming out of the surface S of the volume below. The volume inside this surface is π. We were unable to transcribe this image(3,0,2) We were unable to transcribe this imageS3 (z = 1 + x) (3,0,2) S3 (z = 1 + x)
Let S be the surface reproduced below and parameterized by b) Calculate Vector Field Flow through S, if the surface is oriented at point (2, 0, 0) by the normal vector ⃗n = ⃗k.u, u) = (2-u We were unable to transcribe this image
Let R be delimited by and and S being surface R, outwardly. Now give us the vector field F(x,y,z)=ij + calculate flux integral We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image(z + sin ( 2)) +(y + cos(r3 +(22 + sin(zy))k
We can combine the scalar potential V and the vector potential A to a combined 4-vector potential: Calculate the components of a 4x4 electromagnetic field tensor: with the contravariant vector: from the electric field and the magnetic field We were unable to transcribe this imageWe were unable to transcribe this imageい() ct OA Ot We were unable to transcribe this image い() ct OA Ot
Suppose that the vector field, , is continuously differentiable and satisfies in the interior of the domain , open and bounded, whose boundary is a smooth surface (at least class) , steerable. Show that cannot be tangent to in every point of the surface We were unable to transcribe this imagedivF = 0,Fi + OyF2 +0. F3 > 0 Ωε P3 We were unable to transcribe this image11 We were unable to transcribe this imageWe were unable to transcribe this...
For any vector field F⃗ and any scalar function f we define a new field a) Assuming that the appropriate partial derivatives are continuous, show the following formula: b) Let ⃗x = x⃗i + y ⃗j + z ⃗k and the vector field Use the formula found in a) to answer the following question: is there a number p such that F⃗ is incompressible (that is, its divergence is zero)? f F)(x,y,z) = f(x,y,z)F(x,y, z) We were unable to transcribe...
a) A vector field F is called incompressible if div F = 0. Show that a vector field of the form F = <f(y,z),g(x,z),h(x,y)> is incompressible. b) Suppose that S is a closed surface (a boundary of a solid in three dimensional space) and that F is an incompressible vector field. Show that the flux of F through S is 0. c)Show that if f and g are defined on R3 and C is a closed curve in R3 then...
(a) Use surface integral(s) to calculate the flux of the vector field or through the given surface. (b) Use the divergence theorem to calculate the flux of the vector field through the given surface. 4. F(x, y, z) =x2yi - 2yzj + x2y2k; S is the surface of the rectangular solid in the first octant bounded by the planes x= 1,y=2, and z=3. Show your work and give an exact answer.
a) The following vector field State whether the divergence of at point A is positive, negative or zero. b) Say if the rotational of at point B is a null vector, which points in the direction of the z-axis or points in the negative direction of z. We were unable to transcribe this image履 2 0 2 4 We were unable to transcribe this imageWe were unable to transcribe this image 履 2 0 2 4
Calculate the flow of the vector field F (picture) across the surface of the solid W defined by the paraboloid z = 4-x^2-y^2 and the xy plane, with normal outside W F(x, y, z) = (x3,2xz2, 3y2z)