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
Advanced Physics Homework Help
Finding flux through ellipsoid in Cylindrical Coordinates
Reply to thread
Message
[QUOTE="BrianA., post: 4985049, member: 539706"] [h2]Homework Statement [/h2] Using Cylindrical coordinates, find the total flux through the surface of the ellipsoid defined by x[SUP]2[/SUP] + y[SUP]2[/SUP] + ¼z[SUP]2[/SUP] = 1 due to an electric field [B]E[/B] = x[B]x[/B] + y[B]y[/B] + z[B]z[/B] (bold denoting vectors | [B]x,y,z[/B] being the unit vectors) Calculate ∇⋅[B]E[/B] and then confirm the Gauss's Law [h2]Homework Equations[/h2] Cylindrical Coordinates being used: (s,φ,z) Conversion to Cylindrical Coordinates: x = scosφ y = ssinφ z= z Surface Element of a Cylinder: da = sdφdz [h2]The Attempt at a Solution[/h2] I converted the ellipsoids equation into cylindrical, so it looks like: s[SUP]2[/SUP]cos[SUP]2[/SUP]φ + s[SUP]2[/SUP]sin[SUP]2[/SUP]φ + ¼z[SUP]2[/SUP] = 1 solving for s looks like s = √(1-¼z[SUP]2[/SUP]) I solved for both the volume and surface area of the ellipse through integration. Surface Area was as Follows: ∫ (from -2 to 2) ∫ (from 0 to 2π) sdφdz = ∫∫ √(1-¼z[SUP]2[/SUP]) dφdz = 2π[SUP]2[/SUP] How to use this to find Flux, I am unsure of. I know to convert [B]E[/B] to cylindrical so [B]E [/B]= scosφ[B]x[/B] + ssinφ[B]y[/B] + z[B]z[/B], but don't know what to do about the unit vectors. [B][/B] Is the flux just ∫[B]E⋅[/B][I]d[/I][B]a [/B]? and if so, how do I take the dot product and what do I do about the unit vectors? [/QUOTE]
Insert quotes…
Post reply
Forums
Homework Help
Advanced Physics Homework Help
Finding flux through ellipsoid in Cylindrical Coordinates
Back
Top