Verify the divergence theorem fa. A· dS = V.A dv %3D for each of the following cases: (a) A = xy'a, + y'a, + y°za, and S is the surface of the cuboid defined by 0 < x < 1, 0 < y < 1,0 < z < 1 (b) A = 2rza, + 3z sin ø a, – 4 rcos o a̟ and S is the surface of the wedge 0 < r< 2, 0 < ¢ < 45°, 0
Verify the divergence theorem fa. A· dS = V.A dv %3D for each of the following cases: (a) A = xy'a, + y'a, + y°za, and S is the surface of the cuboid defined by 0 < x < 1, 0 < y < 1,0 < z < 1 (b) A = 2rza, + 3z sin ø a, – 4 rcos o a̟ and S is the surface of the wedge 0 < r< 2, 0 < ¢ < 45°, 0
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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Transcribed Image Text:Q4.
Verify the divergence theorem
A· dS :
V· A dv
S.
for each of the following cases:
(a) A = xy'a, + y'a, + y°za, and S is the surface of the cuboid defined by 0 < x < 1,
0 < y < 1,0 <z < 1
(b) A = 2rza, + 3z sin ø as – 4 rcos o a̟ and S is the surface of the wedge 0 < r< 2,
0 < ¢ < 45°, 0< z< 5
(c) A = R'a, + Rsin 0 cos o a, and S is the surface of a quarter of a sphere defined by
0 < R< 3,0 << ¢ < T/2, 0 <0 < T/2.
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