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Flux of a Vector Field
209945 Flux of a Vector Field Please note this:
In my textbook theta is angle from Z-axis to the vector-r
Phi is the angle from the x-axis to the vector projection on the x-y plane
Compute the total flux...of the vector field...out through sphere
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Find the flux of the vector field.
39368 Find the flux of the vector field. Let S be the part of the plane 2x + y + z = 1 which lies in the first octant, oriented upward. Find the flux of the vector field
F = 3i + 3j + 3k across the surface S.
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Counterclockwise circulation and outward flux
180251 Counterclockwise circulation and outward flux Use Green's Theorem to find the counterclockwise circulation and outward flux for the vector field F(x,y)= xyi + x^2j and the curve C, where C is the boundary of the region enclosed by the parabola
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Flux of Vector Field Across a Surface
108962 Flux of Vector Field Across a Surface Let S be the part of the plane which lies in the first octant, oriented upward. Find the flux of the vector field across the surface S.
Please see the attached file for the fully formatted problems.
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quantities relateed to the vector field
110254 Vector Fields 1 Calculate the divergence and curl of the vector field F(x,y,z) = 2xi+3yj+4zk.
2 Find the potential of the function for the conservative vector field:
F(x,y,z) = (y+z)i + (x+z)j + (x+y)k.
3 Use Green's theorem
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Stroke's Theorem and Direct Evaluation
We know that for every point P(x,y,z) on S, its direction vector is (x,y,z), so we have
=
= =
(b) Find the flux of the vector field
F(x,y,z) = (y-x)i + (x+y)j + y k across the side of the triangle with vertices at (1,0,0), (0,1,0) and (
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Vector Fields, Fundamental Theorem of Line Integrals
Let be a vector field whose components have continuous first order partial derivatives. Then,
First we find the divergence of the vector
Then
So the flux outward is
6.
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The law of Biot and savart
Use the law of Biot and savart to find the magnetic field at the point P (a,-a) in the x-y plane. Then find the magnetic field at the point Q whose coordinates are (2a, -a).
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Vector Fields and Surface Integrals
128239 Vector Fields and Surface Integrals Find the flux of the vector field F(x, y, z) = (y, 0, z2) out of the unit sphere S. In other words, find the surface
integral ∫∫S (y, 0, z2) * dS, where the sphere S is oriented by the outward normal.