Divergence Theorem for more general regions Use the Divergence Theorem to compute the net outward flux of the following vector fields across the boundary of the given regions D. F = <<z - x, x - y, 2y - z>>, D is the region between the spheres of radius 2 and 4 centered at the origin.

djeljenike 2020-11-08 Answered
Divergence Theorem for more general regions Use the Divergence Theorem to compute the net outward flux of the following vector fields across the boundary of the given regions D.
F=zx,xy,2yz, D is the region between the spheres of radius 2 and 4 centered at the origin.
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Aamina Herring
Answered 2020-11-09 Author has 85 answers
Step 1
Given vector field is F=zx,xy,2yz.
Compute the derivative of the above vector field.
F=x(zx)+y(xy)+z(2yz)
=-1-1-1=-3
Step 2
Now calculate the net outward flux.
DFdV=D(3)dV
=-3(Volume of a sphere)
=3(43π(r23r13))
=4π(4323)[r1=2,r2=4]
=224π
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