Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

145 submissions , 122 unreviewed
3,930 questions , 1,398 unanswered
4,851 answers , 20,616 comments
1,470 users with positive rep
501 active unimported users
More ...

Scale-Invariant component of Capacitance

+ 2 like - 0 dislike
1438 views

I'm wondering if there is any good insight of how to evaluate a given capacitive geometry in such a way that it would be expressed as a function that depends only on two components:

  1. as a geometric component $C_g$, that depends on the shape of the capacitor
  2. as a scale-dependant component, $C_s$. In particular, that would depend on square laws on capacitive surfaces, like in graphene. Or in the case of fractal surfaces, with some weird non-integral exponent between 2 and 3.

In other words, the capacitance expressed as a function of two parameters:

$$ C = C( \textbf{g} , L ) $$

where $\textbf{g}$ represents the scale-free geometric information of the capacitor, and L the scale parameter

Is there an easy physical intuition that allows to roughly predict what shape might be optimal for a capacitor at a given scale? is the one with the most folds up to the minimal allowed scale? does it matter how nested the folds are, or the structure of the nesting?

And more interestingly, what properties of the capacitor geometry makes it worse or better capacitor than the same geometry at a different scale?

asked Sep 1, 2015 in General Physics by CharlesJQuarra (510 points) [ revision history ]
edited Sep 1, 2015 by CharlesJQuarra

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
$\varnothing\hbar$ysicsOverflow
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
To avoid this verification in future, please log in or register.




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...