Waste less time on Facebook — follow Brilliant.
×

Need help in proof of 2 very important theorems!

Well, if anyone starts learning electricity and magnetism(or in particular Vol.2 of Feynman lectures, as that is my site of learning), one always gets these 2 important theorems for sure -

\[\displaystyle \text{1. Gauss' Theorem -} \int_{S}{C.n dS} = \int_{V}{\nabla.C dV}\] such that C is any vector, S area, V volume and \(\nabla.C\) is the divergence of C.

\[\displaystyle \text{2. Stokes' Theorem -} \int_{line}{C ds} = \int_{S}{{(\nabla \times C)}_{n} dS}\] such that C is any vector, \(\int_{line}{}\) means line integral, \(\nabla \times C\) is curl of C.

Now, I want proofs of both these strong theorems. Please if anyone can help me in any way, care to do so. Thanks in anticipation!

Note by Kartik Sharma
2 years, 8 months ago

No vote yet
1 vote

  Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 \( 2 \times 3 \)
2^{34} \( 2^{34} \)
a_{i-1} \( a_{i-1} \)
\frac{2}{3} \( \frac{2}{3} \)
\sqrt{2} \( \sqrt{2} \)
\sum_{i=1}^3 \( \sum_{i=1}^3 \)
\sin \theta \( \sin \theta \)
\boxed{123} \( \boxed{123} \)

Comments

Sort by:

Top Newest

The given theorems are particular cases of a very strong theorem in differential geometry/Calculus on Manifolds, called generalized Stokes' theorem; although applied to electricity concepts. You can see any vector calculus book for particular cases proof and Michael Spicak's Calculus on Manifolds or Rudin's Principles of Mathematical Analysis for the proof of general case. As for proof corresponding to Physical case, you could refer Piyush A Kundu's Electricity textbook.

Vidyarthi S - 9 months, 3 weeks ago

Log in to reply

Do you still need help with it or have you found out a way to solve it yourself ?

Azhaghu Roopesh M - 2 years, 8 months ago

Log in to reply

Still need! That's why I have shared the set! Check out others also! Well, I have one proof with some assumptions but I want a 'proper mathematical proof'!

Kartik Sharma - 2 years, 8 months ago

Log in to reply

Good problems should be challenging but not tedious. Unrelated to this thread but just a reminder/word of advice.

Jake Lai - 2 years, 7 months ago

Log in to reply

@Jake Lai Oh yeah! That's right. I was thinking of that while sharing them but then I thought there isn't any 'tedious' type of thing in mathematics. If calculations is what you are saying, then you have a calculator, I wouldn't mind.

Kartik Sharma - 2 years, 7 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...