For the vector field: F = (x + y)i + (y + z)j + (z + x)k 1) Compute the flux out of the cube bounded by the planes {x = 1}, {y = 1}, {z = 1} in the positive octant {x ≥ 0, y ≥ 0, z ≥ 0}, use the divergence theorem 2) Now what if the cube is shifted and rotated to another portion in space, but still having the same dimension (i.e., it is still a 1 × 1 × 1 cube). Will your answer of part a change? 3) Is there a vector field G such that F=∇×G?
For the vector field: F = (x + y)i + (y + z)j + (z + x)k 1) Compute the flux out of the cube bounded by the planes {x = 1}, {y = 1}, {z = 1} in the positive octant {x ≥ 0, y ≥ 0, z ≥ 0}, use the divergence theorem 2) Now what if the cube is shifted and rotated to another portion in space, but still having the same dimension (i.e., it is still a 1 × 1 × 1 cube). Will your answer of part a change? 3) Is there a vector field G such that F=∇×G?
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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F = (x + y)i + (y + z)j + (z + x)k
1) Compute the flux out of the cube bounded by the planes {x = 1}, {y = 1}, {z = 1} in the positive octant {x ≥ 0, y ≥ 0, z ≥ 0}, use the divergence theorem
2) Now what if the cube is shifted and rotated to another portion in space, but still having the same dimension (i.e., it is still a 1 × 1 × 1 cube). Will your answer of part a change?
3) Is there a vector field G such that F=∇×G?
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