Potential of a Rectangular Pipe by Laplace's Equation

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SUMMARY

The discussion centers on solving a problem related to the potential of a rectangular pipe using Laplace's Equation. The user seeks validation for their approach to part b, where they applied the negative divergence operator (-(del)). They express uncertainty about graphing their solution and request guidance on how to tackle part c, indicating a lack of prior examples in class. Additionally, the conversation touches on the use of LaTeX for formatting mathematical expressions, confirming its availability for users in the forum.

PREREQUISITES
  • Understanding of Laplace's Equation
  • Familiarity with vector calculus, specifically the divergence operator
  • Basic knowledge of graphing solutions in mathematical contexts
  • Proficiency in LaTeX for mathematical typesetting
NEXT STEPS
  • Review the application of Laplace's Equation in potential theory
  • Learn about graphing techniques for solutions to partial differential equations
  • Explore advanced vector calculus concepts, including divergence and curl
  • Familiarize yourself with LaTeX formatting for mathematical expressions
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Students studying physics or engineering, particularly those focusing on fluid dynamics or electromagnetism, as well as educators looking to enhance their teaching methods in mathematical problem-solving.

DrPapper
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Homework Statement



EM HW7.jpg

Homework Equations


Is my part a correct and am I on the right track for part b? If not please give me some suggestions to get me closer to the right track. Also, how would I even begin c.? We have literally done no examples like this in class.

The Attempt at a Solution


Solution to a.)
em.png


For b. I simply took -(del) on it. But I have no idea how to graph my solution. Is there a better way to approach this?

ON A SEPARATE NOTE, ARE WE STILL ABLE TO DO LATEX ON HERE? I THINK THERE USED TO BE AN EDITOR AT THE BOTTOM OF THE PAGE FOR TESTING YOUR WRITING IN BEFORE LOADING IT TO THIS FORM.
 
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I would be a lot more helpful if you posted your work. I'm much more inclined to look over your work and see if you did it correctly rather than spending the time to do the problem on my own from scratch to see if my answer matches yours.

Yes, you can still do LaTeX on here. Under the text box, there's a link to a LaTeX guide.
 
vela said:
I would be a lot more helpful if you posted your work. I'm much more inclined to look over your work and see if you did it correctly rather than spending the time to do the problem on my own from scratch to see if my answer matches yours.

Yes, you can still do LaTeX on here. Under the text box, there's a link to a LaTeX guide.
Yes, next time I'll need to upload some scans, there was quite a bit of work to type out. I had about 4 pages of work, lol, and I really didn't want to do it in standard script - gets really really messy. I wish the latex preview box was still down at the bottom. But I think I've figured this problem out in the meantime. :D Thanks for looking at least. I'll put up my work etc.. if it's wrong when it gets returned.
 

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