Insights Blog
-- Browse All Articles --
Physics Articles
Physics Tutorials
Physics Guides
Physics FAQ
Math Articles
Math Tutorials
Math Guides
Math FAQ
Education Articles
Education Guides
Bio/Chem Articles
Technology Guides
Computer Science Tutorials
Forums
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Menu
Log in
Register
Navigation
More options
Contact us
Close Menu
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Forums
Homework Help
Calculus and Beyond Homework Help
Gauss' Theorem - Net Flux Out - Comparing two vector Fields
Reply to thread
Message
[QUOTE="Master1022, post: 6321337, member: 650268"] [B]Homework Statement:[/B] Vector field [itex] F = \begin{pmatrix} x^2 \\ 2y^2 \\ 3z \end{pmatrix} [/itex] has net out flux of [itex] 4 \pi [/itex] for a unit sphere centred at the origin. If we are now given a vector field [itex] F_1 = \begin{pmatrix} x^2 \\ 2y^2 \\ 3(z+1) \end{pmatrix} [/itex], then how does the net out flux compare if we consider a unit sphere centred at (1,0,0) - is it bigger or smaller? [B]Relevant Equations:[/B] Gauss' Theorem Hi, I just have a quick question about a problem involving Gauss' Theorem. [B]Question: [/B]Vector field [itex] F = \begin{pmatrix} x^2 \\ 2y^2 \\ 3z \end{pmatrix} [/itex] has net out flux of [itex] 4 \pi [/itex] for a unit sphere centred at the origin (calculated in earlier part of question). If we are now given a vector field [itex] F_1 = \begin{pmatrix} x^2 \\ 2y^2 \\ 3(z+1) \end{pmatrix} [/itex], then how does the net out flux compare if we consider a unit sphere centred at (1,0,0) - [B]is it bigger or smaller (than the 4 [itex] \pi [/itex] calculated earlier)?[/B] This is the final part of the question and is worth very few marks, suggesting that I shouldn't need to do any calculations, but I am having trouble arriving at an answer intuitively. The whole question has been about Gauss' Law. [B]Method:[/B] I am stuck and do not know what else to do beyond the realisation that [itex] \nabla \cdot \vec F_1 = \nabla \cdot \vec F [/itex]. Other initial thoughts that I have include: - This sphere is completely in the +ve regions of the x-axis - Some points of interest are on the surface of the new sphere: (0,0,0) and (x,y,z=-1) I would appreciate any help. Kind regards [/QUOTE]
Insert quotes…
Post reply
Forums
Homework Help
Calculus and Beyond Homework Help
Gauss' Theorem - Net Flux Out - Comparing two vector Fields
Back
Top