Consider a 3-dimensional radial vector field F(r) = r p3 1 p2 er, where ||r|| = √√√x² + y² + z². r = Prove that the flux of the vector field F outward from the origin-centered sphere of radius R does not depend on the radius R of the sphere. Hint: On the surface of the sphere, n = er. Answer: 4T

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Consider a 3-dimensional radial vector field
F(r)
=
r
where =
r
p3
1
p²
er,
||r|| = √√√x² + y² + z².
Prove that the flux of the vector field F outward from the
origin-centered sphere of radius R does not depend on
the radius R of the sphere.
Hint: On the surface of the sphere, n = er.
Answer: 4π
Transcribed Image Text:Consider a 3-dimensional radial vector field F(r) = r where = r p3 1 p² er, ||r|| = √√√x² + y² + z². Prove that the flux of the vector field F outward from the origin-centered sphere of radius R does not depend on the radius R of the sphere. Hint: On the surface of the sphere, n = er. Answer: 4π
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