11. (a) Let B be a closed region in R³ bounded by a simple closed surface S and let the vector field F be defined and continuously differentiable throughout B. Rewrite SLLe div FdV in terms of a surface integral over S. (b) Let B be a ball centred at 0 with radius 2 and let S be the sphere of radius 2, which bounds B. Let F(x, y, z) = r/(r + 2) with r (x, y, z) and r = |r]. Using Gauss's divergence theorem or otherwise compute SI. div FdV. Hint: You may use that the surface area of a sphere with radius 2 is given by 167.
11. (a) Let B be a closed region in R³ bounded by a simple closed surface S and let the vector field F be defined and continuously differentiable throughout B. Rewrite SLLe div FdV in terms of a surface integral over S. (b) Let B be a ball centred at 0 with radius 2 and let S be the sphere of radius 2, which bounds B. Let F(x, y, z) = r/(r + 2) with r (x, y, z) and r = |r]. Using Gauss's divergence theorem or otherwise compute SI. div FdV. Hint: You may use that the surface area of a sphere with radius 2 is given by 167.
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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![11. (a) Let B be a closed region in R³ bounded by a simple closed surface S and let the vector
field F be defined and continuously differentiable throughout B. Rewrite SLLe div FdV in
terms of a surface integral over S.
(b) Let B be a ball centred at 0 with radius 2 and let S be the sphere of radius 2, which
bounds B. Let F(x, y, z) = r/(r + 2) with r
(x, y, z) and r =
|r]. Using Gauss's
divergence theorem or otherwise compute
SI.
div FdV.
Hint: You may use that the surface area of a sphere with radius 2 is given by 167.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F04346a1f-846d-4fc3-9d9a-e6702b1151f6%2F7f21c1ce-c6fb-4768-b563-421348fc437e%2Fqm59wvb_processed.png&w=3840&q=75)
Transcribed Image Text:11. (a) Let B be a closed region in R³ bounded by a simple closed surface S and let the vector
field F be defined and continuously differentiable throughout B. Rewrite SLLe div FdV in
terms of a surface integral over S.
(b) Let B be a ball centred at 0 with radius 2 and let S be the sphere of radius 2, which
bounds B. Let F(x, y, z) = r/(r + 2) with r
(x, y, z) and r =
|r]. Using Gauss's
divergence theorem or otherwise compute
SI.
div FdV.
Hint: You may use that the surface area of a sphere with radius 2 is given by 167.
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