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Why does [math]\frac{\partial\rho}{\partial t}=0[/math] in magnetostatics?
I like to think as follows:
Consider the Maxwell's equations. The static case, the one that leads us to electrostatics and magnetostatics regimes, can be defined in such a way that the electric and magnetic field does not evolve with time, i.e.
[math] \frac{\del}{\del t} \mathbf{E} = 0 [/math]
[math] \frac{\del}{\del t} \mathbf{B} = 0 [/math]
In this case, the Maxwell's equations read
[math] \mathbf{\nabla \cdot} \mathbf{B} = 0 [/math]
[math] \mathbf{\nabla \times} \mathbf{B} = \mu_{0} \mathbf{J} [/math]
[math] \mathbf{\nabla \cdot} \mathbf{E} = \frac{\rho}{\epsilon_{0}} [/math]
[math] \mathbf{\nabla \times} \mathbf{E} = 0[/math]
Taking the time derivative (partial) of the third eq. above, we have (i think you know some vector calculus, and why the manipulations below are valid)
[math] \frac{\del}{\del t} (\mathbf{\nabla \cdot} \mathbf{E}) = \mathbf{\nabla \cdot} (\frac{\del}{\del t} \mathbf{E}) = \frac{1}{\epsilon_{0}} \frac{\del \rho}{\del t} [/math]
Since we're in the static electromagnetic field case,
[math] 0 = \frac{1}{\epsilon_{0}} \frac{\del \rho}{\del t} [/math]
Therefore,
[math] 0 = \frac{\del \rho}{\del t} [/math]
Sorry, forgot it was $\partial$.
I'm used to packages kappa
Is it worth getting an AS in electrical engineering if I want to get a BS in computer engineering?
Puttus Chromosomus Bagus
I should add, the reason I'm considering doing this is because I want something to fall back on if I realize I'm too much of a brainlet to complete the degree.
because 'statics' implies steady state i.e. partial derivative with respect to time of any function equals zero, duh
Why does hot water clean better than cold water?
Sorry in advance for not using [math] tags but I'm feeling kind of lazy.
If we had some propositional function (not v1 or v2) if and only if (v1 implies v2), what would it be in DNF?
I got (v1 and v2) or (v1 and not v2) or (not v1 and v2) or (not v1 and not v2) from a truth table. Is this correct or am I way off base?
warm water has a higher solubility product. it's more reactive.
Greater kinetic activity makes it easier to remove dirt or grease or whatever, and the higher temperature kills more bacteria.
Can a nuetron decay into a proton?
If 2 wire , A1 and A2 with opposite current direction is coincide to one another, will the resultant magnetic field cancel out each other?
Suppose that the current on A1 is higher, , do I just have to draw the magnetic field of A1 considering A1>A2?
Do people consider me stupid despite that I learn computer programming and other kind of knowledge through Lynda.com?
When I'm minimizing a DFA using the table filling method, should I include the dead state on the table?
Because when i include it, in the end it gives me a pair between the dead state and the starting state, which doesn't make sense. (and also ruins my DFA's function)
Absolutely
How to gitgud at calc 2? I struggled with the introduction of Integrals in Calc 1 and we’re starting pretty quickly in Calc 2. I would like to be able to see a integration problem like
Integral[sqrt(25-x^2)]dx and be able to understand the way to get the answer 25pi/2. Introduction of trig and all is just blowing my mind. What can I do?
if I were to continually breed short people contiually to get shorter people, would they be healthy, or would they have simmilar issues that people with dwarfism have?
Practice
In math everything boils down to practice
Is a nuclear plant really that big of a risk this day and age? If it produces clean energy, why aren't there more of them?
they would be healthy
as healthy as a chihuahua dog
frightened and shivering all the time
also cute
It really comes down to memorization.
If you see things with square roots and [math]x^{2}[/math], it usually implies arctrig integrals.
when looking at [math]\int \sqrt{25-x^{2}} \;
\mathrm{d} x[/math] we recognize the arcsin function (I've added the picture as a resource) where [math]a^{2}[/math] is 25, meaning a is 5.
This means the integral is [math]arcsin\left ( \frac{x}{5} \right ) + \mathrm{C}[/math]
whoops forgot the picture
Is Algebra by Shen-Gelfand a good book?
>Is Algebra by Shen-Gelfand a good book?
Why don't you read it and find out?
How do I know when to use a bar graph or line graph?
how can i figure out what wavelengths of light would be scattered by a molecule, given IR and Raman spectra?
e.g. The Raman spectrum of XeF4 shows bands at 161, 291 and 586 cm–1, whilst
in the IR spectrum bands are observed at 218, 524 and 554 cm–1. Calculate the wavelengths of light scattered by a sample of XeF4 when it is illuminated by a HeNe laser (632.81 nm).
is it just the wavelengths of light that correspond to the difference in wavenumbers for the Raman spectra?
On Earth there's relatively catastrophic events like earthquakes, tsunamis, etc.
Are there analogs on the universal scale, something that greatly disturbs a massive area of space? I don't mean things like black holes since they're more 'permanent'
if p
p=2 q=3
O shit, yea asuuming both primes are odd.
>Homo neanderthalen/sci/s
plural Homo neardenthalen/sci/
>O shit, yea asuuming both primes are odd.
No:
Assume q divides p^2-1.
Since p^2-1=(p+1)(p-1) and q is prime, q either divides p+1 or p-1.
Since p
are scalars just 1x1 matrices?
we like stupid questions here
discord gg/c37NwyB
>are scalars just 1x1 matrices?
math.stackexchange.com
Fuck, I was starting to look with primality tests and shit and it was just basic algebra... thnx bro.
by what process do you get to use these symbols
and where can i learn how to use it
also what does TEX mean on top of the reply window?
a bar graph is used when you want to compare data between several different sources, like cities, bank accounts, or whatever else.
a line graph is used when you have a single measurement, with one independent and one dependent variable, like money and time, or jews vs days, or even how many cookies a bakery makes vs hours its open.
>Magnetostatics is the study of magnetic fields in systems where the currents are steady (not changing with time). It is the magnetic analogue of electrostatics, where the charges are stationary
Because ideal constant current sources aren't real so you'll never have one indefinitely charging a capacitor. In real life it will hit it's max supply voltage and the current will taper off.
If you do it properly no, it's hardly a risk, but that implies anyone will finance a money sink without cutting corners.
What's the difference between mass and weight ?
I'm pretty sure mass is just the quantity of "matter" in it and is therefore static for a given object
My friend argue that within a system with 0 gravity or force pushing it, the mass of an object become 0
Which one is it ?
mass is a way to quantify how resistant you are to changes in force, which is why it's sometimes called a measure of inertia (e.g. moment of inertia)
the mass is intrinsic and a property of matter, so what you're made of determines your mass
weight is the measurement of how much force there is between you and whatever planet you're on, so when we talk about weight here we're talking about Gm1m2/r^2 where r is the radius of the earth and m1 is the mass of the earth (and G is the gravitational constant)
so a system with 0 gravity means 0 weight, not 0 mass
also you have to be underageb& to not already know this
Thanks, also I'm 28 so not exactly underage
The biggest obstacle is that they're incredibly expensive, and are potentially a high-risk investment (they'd be prohibitively high-risk in a free market, but that isn't the issue; no-one builds them nowadays unless the government legislates to provide some guarantee of future income).
Also, you have no idea what the clean-up costs are going to be like in 30-50 years time (the licensing process revolves around making damn sure you can't just fold the business once the reactor reaches end-of-life and the future consists of all costs and no income).
Suppose [math]H(t)=\left(H_{ij}(t)\right)[/math] is a square matrix. How does [math]\frac{d}{dt}[/math] operate on [math]H[/math]?
Are you looking for an answer other than coordinate-wise?
Are you saying the differential operator is treated like a scalar and distributed to all of the elements of the matrix?
>Are you saying the differential operator is treated like a scalar and distributed to all of the elements of the matrix?
Are you looking for a different answer?
What is honestly the difference between an [math]n\times 1[/math] matrix and a vector? Why even call it a column vector if it's not exactly the same thing?
>What is honestly the difference between an n×1 matrix and a vector?
A vector is an element of a vector space.
An nx1 matrix is an ordered n-tuple
For example, consider the 3 dimensional vector space of polynomials with real coefficients and degree at most 2
Then 1+3x is a vector, but its '3x1 matrix representation' with the basis 1,x,x^2 is [1,3,0]
OOOOOOH so the column vector is just the coordinate of the vector?
Yes.
Assuming one day we can made really fast spaceships, would weird relativistic effects harm the human body if we went fast enough?
This board is useless waste of space.
>This board is useless waste of space.
Haven't you got a white supremacy thread to bump?
>Haven't you got a white supremacy thread to bump?
Are you okay?
Doing better than you by the look of things.
What's wrong with this place?
Why are you guys so fucking weak?
>Why are you guys so fucking weak?
I'm not a "guy".
>Doing better than you by the look of things.
Your delusions of white supremacy threads indicate otherwise.
I'm sorry, maybe my description wasn't precise enough.
Should I just call it a nigger hate thread?
Sorry I misgendered you. Tits of GTFO.
>nigger
Why the racism?
That is what they are called in their homeland.
Why the racist shitposting every day?
Why do Veeky Forums put up with it?
Come on now.
You seemed so brave a minute ago.
Why so quite all of the sudden?
Why are you so fucking weak?
What's wrong with you Veeky Forums?
>Why so quite all of the sudden?
Just pretending to be retarded I expect.
They're probably laughing that the joke's on you for replying.
They are /pol/tards?
Worse, they are cucked by poltards.
You can literally do anything you want to Veeky Forums and they will take it.
Some will even thank you.
For the challenge question, what I did was
[eqn]\frac{n_{1}}{4}+\frac{n_{2}}{8}=5-n_{1}(p-\frac{1}{4})-n_{2}(q-\frac{1}{8})[/eqn], by making n2=2 I get [eqn]n_{1}=\frac{5-2q}{p}[/eqn]. The solution given in the book is 1/2, but it could as easily be 2/1 by making p=1, q=1/2.
Is the book wrong or did I make a mistake somewhere?
Forgot the picture.
dumb answer
Scalars form a 1D vector space and so do 1x1 matrices. So they are isomorphic and you can essentially do anything you can with one with the other.
Just balls deep Electrical Engineering with Computer Engineering, I'm in a major that's less related to EE and my average semester still floats around 16-18 credit hours.
t. EE and MatSci student
They are isomorphic.
They are isomorphic.
[math] V^* \cong V [/math]
One is a linear functional, the other one is a vector.
>Why do Veeky Forums put up with it?
There is a report function. There is a hide function.
why are improper fractions improper?
i understand why they are, the numerator being larger than the denominator, i just don't get how that makes them improper.
They are not improper. Nobody uses that term for fractions except like retarded teachers in elementary schools.
The only thing that you might consider "improper" about a fraction a/b is when gcd(a,b)=/=1.
>So they are isomorphic and you can essentially do anything you can with one with the other.
You can multiply any matrix by a scalar, you can't multiply any matrix by a 1x1 matrix.
>Why the racist shitposting every day?
I don't know; ask yourself why you're abusing racial slurs on a science and math board.
>Why are you so fucking weak?
Do you really need to swear? It invalidates your post.
it says this is wrong.
am i retarded? this isn't for marks.
What forces will be acting on a ping-pong ball at the exact moment it touches the ground?
We have that $X_1, \dots, X_n, \dots $ are iid random variables with $X_i \equiv X$ for all $i$, where $X$ is absolutely integrable.
Define $S_n = X_1 + \dots + X_n$ where $X_i, 1 \le i \le n$ are random variables.
Tao states this sparsification Trick:
> Next, we apply a sparsification trick. Let ${0 < \epsilon < 1}.$ Suppose
that we knew that, almost surely, ${S_{n_m}/{n_m}}$ converged to ${{\bf
E} X}$ for ${n=n_m}$ of the form ${n_m := \lfloor (1+\epsilon)^m \rfloor}$
for some integer ${m}$. Then, for all other values of ${n}$, we see that
asymptotically, ${S_n/n}$ can only fluctuate by a multiplicative factor
of ${1+O(\epsilon)}$, thanks to the monotone nature of ${S_n}$. Because of
this and countable additivity, we see that it suffices to show that
${S_{n_m}/{n_m}}$ converges to ${{\bf E} X}$. Actually, it will be enough
to show that almost surely, one has ${|S_{n_m}/{n_m} - {\bf E} X| \leq
\epsilon}$ for all but finitely many ${m}$.
Why can $S_n /n$ asymptotically only fluctuate by a multiplicative factor of $1 + O( \epsilon)$ ?
Is it orgo or ochem or organic?
What is the difference between taking a derivative of a limit and of a function? In what way are those two different? I always thought that you only take derivatives of functions to get a derived function that gives slope at each point of the graph of the function we derived from...
When doing implicit derivation, why are we doing what we're doing? I can't seem to find an explanation on the internet. Why do we derive x normally, and y has to be multiplied by dy/dx specifically? What if I had other symbols? What's the reasoning behind it? In school we haven't used dy/dx or d/dx or any Leibniz notation whatsoever ONCE, then all of a sudden, BOOM class, I'm just gonna put this dy/dx here outta fucking nowhere, without even explaining what Leibniz notation IS (we only ever used y and y', but suddenly a wild d/dx dy/dx appears), because fuck you that's why.
I WANNA KNOW WHY I DO THE SHIT THAT I DO, I DON'T WANNA PLUG AND CHUG LIKE A MONKEY!!
All you need to know additionally to understand it is the pic related and a def o deriviative, as a slope of the tangent of the curve at a given point.
>I DON'T WANNA PLUG AND CHUG LIKE A MONKEY
The topic you're """"studying"""" requires it, since only monkeys use it.
>Taylor sequences
So, looking at the definitions, the part I do not get how you can deduce from the inequality above theese two integrals? I get from where the inequality comes from (absolute value), I know the rest of the proof when we follow with the integrals, but how would you know that integrating in this way would be the next step? Is it just a "lucky shot" or is there an explaination in baby steps that connects it with the inequality above?
see calculus and algebra are the most bullshit, counter-intuitive areas of mathematics, you'll have to accept the fact that you are forced to be a monkey while working with them
>calculus
>area of mathematics
>caring about """intuition"""
You are one of the monkeys I was talking about.
>algebra
I doubt you have studied even the basics of it.
how does everyone think about classical entropy, im happy with microstates, but i cant fathom an extensive, measurable quantity that has no physical meaning other than a vague notion of 'the dispersal of or avaliable energy'
>entropy
No such thing.
whats dG/dT then?
Did I get it right?