Question
Asked Jul 26, 2019
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Use the Divergence Theorem to compute the net outward flux of the field

F=<x,2y,-z> across the surface​ S, where S is the boundary of the tetrahedron in the first octant formed by the plane x+y+z=2
 
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Expert Answer

Step 1

From the Divergence theorem, for a positively oriented boundary surface (outward Normal) of region E the flux is equal to triple integral of divF over the region E.

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Step 2

Find the range of x,y and z as follows. Also observe that the plane is on the first quadrant.

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The range of z varies from value of Z= 0 to value of z on plane z 2 - x-y which implies 0sz2-xy The range of y varies from value of y =0 to value of z on plane y 2-x which implies 0s ys2-x The range ofx varies from value of x = 0 to value ofz on plane x = 2 which implies 0Sxs2

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Step 3

The divF can be calculated as fo...

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divF = div((x,2y,-z)) (2y)+(-z) ôz =1+2-1 = 2

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Calculus

Integration

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