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3:49 AM
@vzn Actually no I was not aware of the headline at the time of writing. I have some students doing a project on the restricted 3-body problem...
and they had never heard of 2010 or the reference to the Lagrange points there... maybe there is none and I’m just mistaken.
Hi GooD MoRninG..
Two Capacitors $C_1 = 2\mu F$ and $C_2 = 6\mu F$ are charged separately to the same potential of 120v.
(a) Connect the negative plate of $C_1$ to the positive plate of $C_2$ (like open circuit).
(b) Connect the negative plate of $C_1$ to the positive plate of $C_2$ and connect the positive plate of $C_1$ to the negative plate of $C_2$ (like closed circuit).
Find the charge on each capacitor in (a) and (b)
Pls help me out how to solve this situation????????
1 hour later…
5:23 AM
Hi! So I am learning multivariable calculus, and I have a doubt. In one of my assignments, I was asked to prove that if a multivariable function had continuous first partial derivatives on a domain $D$, then that function is continuous as well.
Now, when I tried working out the problem, I noticed that continuity of first partial derivatives wasn't a necessary condition. With only the condition that the partial derivatives are defined everywhere on the domain $D$, I could prove that function was continuous on the domain $D$.
Hi @JohnRennie Sir Pls look at my question. How to solve it. I have two answers $120\mu C$ & $360\mu C$
5:44 AM
@FakeMod Solved!
6:09 AM
@123 if you connect the capacitors like this then the charges cannot change:
The topmost charge of +240 μC cannot change because the charge has nowhere to go, and likewise the bottommost charge of -720 μC. And the charges on the two plates of a capacitor have to be equal and opposite.
@123 if you connect them in a loop, as in (b), then you'll get this:
1 hour later…
7:26 AM
Thanks a lot @JohnRennie .
You rock... I made a mistake in loop i am connecting it as series not parallel. That's why i got wrong answer.
7:40 AM
@JohnRennie Does capacitance of capacitors change or always same whether it is connected in series, parallel or separate. Pls explain.
7:53 AM
Hey I was wondering if I could ask something about condensed matter theory and theoretical chemistry here.
Theories in chemistry and Condensed matter physics both are about the physics at length scales of atoms.I think that they are interested in different kinds of phenomena, but the underlying motivation is similar in the sense that they try to explain emergent phenomena using some effective models.
Is this the right way to think about these two fields? Could anyone throw some light on this?
8:24 AM
@Charlie in principle there can be other changes that leave the stationary points invariant (e.g. if you just add the Lagrangian to itself the stationary points obviously also don't change), but the total time derivatives are the only ones that leave the stationary points invariant regardless of the specific form of the Lagrangian
9:01 AM
Who is gnat? They seem to be a profilic voter in several communities, but when I open their profile, it says they're only a member of the community I'm looking from
@NiharKarve Users can choose to hide communities they're part of in that overview, this user has probably hidden all their communities so you only see the one you're currently on
Incredible, they've cast 14,000 votes - that's more than Qmechanic!
9:30 AM
@NiharKarve gnat and Qmechanic are the fourth and fifth most prolific voters on physics.SE, see physics.stackexchange.com/users?tab=Voters&filter=all
@ACuriousMind Yep, that's where I saw it
10:07 AM
is Diff(M) always infinite-dimensional (in physically relevant cases)?
I'd like to learn a bit about gravity as a gauge theory, but I don't really want to learn about infinite-dimensional manifolds/groups first
It's a linear combination of $\partial_{\mu}, \partial_{\mu} \partial_{\nu},...$ derivatives so of course it's infinite dimensional
oh yes, of course
thank you
the gauge group of GR is not Diff(M)
I don't see any notes framing GR in terms of diff really
@NiharKarve these are good, still thinking about the GR sections every now and then though
see physics.stackexchange.com/q/346793/50583 and its linked questions for discussions on what gets "gauged" in the context of GR
10:09 AM
By the guy who first thought this stuff up
I was inspired by physics.stackexchange.com/questions/4359 and the like
I'd like to understand the shortcomings of that formulation
Q: Gravity as a gauge theory

riemanniumCurrently, (classical) gravity (General Relativity) is NOT a gauge theory (at least in the sense of a Yang-Mills theory). Why should "classical" gravity be some (non-trivial or "special" or extended) gauge theory? Should quantum gravity be a gauge theory? Remark: There are some contradictory c...

thanks all
10:41 AM
A: General relativity as a gauge theory of the Poincaré algebra

NikitaMain idea to introduce gauge field for every generator, is to provide invariance under some group of transformation, in your case under group of diffeomorphism and local Lorentz transformations (local version of global Poincaré group). This logic is very similar to gauge invariance, where we intr...

That's pretty good
Last quote of this answer
A: GR as a gauge theory: there's a Lorentz-valued spin connection, but what about a translation-valued connection?

A.V.S.In 2+1 dimensions general relativity with Einstein–Hilbert action with or without cosmological constant is equivalent to a gauge theory with a gauge group one of $\mathrm{ISO}(2,1)$, $\mathrm{SO}(3,1)$ or $\mathrm{SO}(2,2)$ (depending on the presence of cosmological constant and its sign) and a ...

makes the same point about the action being linear vs quadratic as the paper I linked to above, this seems to be a really big issue
11:17 AM
@ACuriousMind ah ok ty
2 hours later…
12:53 PM
Q: Feature Preview: Table Support

Ham VockeNo waffling, right to the point: What? When? Where? Table support 2020-11-23 Meta Stack Exchange & DBA Meta More table support week of 2020-11-30 DBA Stack Exchange Even more table support week of 2020-12-07 Network-wide launch (if no major issues found) That's right. It's finally...

... since it seems this won't be featured on MSE
huh, neat

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