My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum

LinkBack Thread Tools Display Modes
August 5th, 2017, 01:44 AM   #1
Joined: Aug 2017
From: Germany

Posts: 1
Thanks: 0

Flux of the vector field through the surface

Hello! I need help with determining the flux of the vector field. I'm enclosing link to my math.stackexchange question.
Vid is offline  
August 5th, 2017, 04:23 AM   #2
Math Team
Joined: Jan 2015
From: Alabama

Posts: 3,264
Thanks: 902

To begin with, you are mistaken about the surface. It is not any part of a sphere. Looking at just the first octant, the surface consists of straight lines connecting points on the two given semi-circles. We can take, as parametric equations for the surface, y= z= s, for $0\le s\le 1$, and, for each s, x lies on the line between 0 and $\sqrt{1- s^2}$: $x= t\sqrt{1- s^2}$ for $0\le t\le 1$.

We can write that as the vector function $\vec{V}= t\sqrt{1- s^2}\vec{i}+ s\vec{j}+ s\vec{k}$. Differentiating with respect to s, $\vec{V_s}= -\frac{2st}{\sqrt{1- s^2}\vec{i}+ \vec{j}+ \vec{k}$. Differentiating with respect to t, $\vec{V_t}= \sqrt{1- s^2}\vec{i}$. The "vector differential of surface area" is given by the cross product of those vectors, $\sqrt{1- s^2}$(\vec{j}- \vec{k}\right)dsdt$. To find the flux of the given vector function through that surface, take the dot product of the vector function, written in terms of s and t, and the vector differential of surface area and integrate.

Last edited by Country Boy; August 5th, 2017 at 04:34 AM.
Country Boy is offline  

  My Math Forum > College Math Forum > Calculus

field, flux, surface, vector

Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Surface (Flux) Integrals adammeek Calculus 0 July 29th, 2016 04:18 AM
Volume induced by a vector field across a moving surface coderodde Calculus 0 April 18th, 2015 09:46 AM
vector field and flux cummings123 Calculus 3 October 17th, 2012 04:41 PM
Vector Calculus Divergence of a Vector Field MasterOfDisaster Calculus 2 September 26th, 2011 10:17 AM
Vector Field 2 OSearcy4 Calculus 2 October 27th, 2009 07:39 PM

Copyright © 2019 My Math Forum. All rights reserved.