7. Using the divergence theorem compute the outward flux of the vector field F(x, y, z) = x°i+ y³j+10k over the boundary of the region between the upper hemispheres of radius 1 and 2 centered at the origin with bases in the xy-plane.
7. Using the divergence theorem compute the outward flux of the vector field F(x, y, z) = x°i+ y³j+10k over the boundary of the region between the upper hemispheres of radius 1 and 2 centered at the origin with bases in the xy-plane.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Step 1
step:-1
Divergence Theorem:-
Given that
Step:-2
Using spherical co-ordinates, so take
In this picture, we can see the upper hemisphere forms circle in x y- plane, so
As given hemisphere of radius 1 and 2 center at origin so,
and as hemisphere,
Step:-3
Using above divergence theorem we have
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