Instead you are supposed to imagine a string in the $x$-direction which moves in a wave-like motion. Each point of the string is identified by some $x$, and its displacement from the mean at time $t$- the position where the string is flat - is what $y(x,t)$ describes.
@ACuriousMind Instead you are supposed to imagine a string in the $x$-direction which moves in a wave-like motion. Each point of the string is identified by some $x$, and its displacement from the mean at time $t$- the position where the string is flat - is what $y(x,t)$ describes. this is confusing
@JacobP.J The string has some length $L$. We refer to one end of the string as the place with $x=0$ and the other as having $x=L$. Any $x$ in between just means the corresponding point in between. We think of the string as continuous here and do not care whether it has "constituent particles".
By "the position where the string is flat" I mean that we have to choose some zero for the $y$-direction. If all points of the string have $y(x,t_0)$ at some point in time $t_0$, then the string is a line along the $x$-axis at that moment
@Abcd If you surround that charge with a sphere then all those flux lines have to pass through that sphere. But if you surround it with a cube then still all those flux lines have to pass through the cube.
@Abcd it doesn't matter what shape the surrounding surface is, the same flux lines still pass through it.
@Abcd flux lines can only begin or end on a charge. If you have some closed surface with no charge inside it, and a charge outside the surface, then any flux line from that charge must go in the surface and then back out again because it can't end inside the closed surface.
Also, why are you insisting on thinking in terms of "solid angle"? The inuitive notion of a closed surface is simply a surface that encloses some region of space such that you cannot leave that region without going through the surface.
@Abcd so suppose the point charge produces a total flux $F$, then since all the flux lines go out to infinity all that flux $F$ must pass through the surface of the cone. Yes?
@Abcd the gaussian surface is an imaginary surface not a real object. Any real object will have a non-zero polarisibility so things start getting complicated.
The gaussian surface is just some geometric object we imagine surrounding the charge (or charges).
@Slereah That is not true in all generality, for instance consider the infinite-dimensional Graßmann algebra that you get from an infinite direct sum of finite-dimensional ones: All souls are still nilpotent, since the direct sum allows only finite sums.
@Slereah If you have $N$ variables, then $z^{N+1}$ will always consist of a sum of monomes in which at least one variable occurs twice as a factor. Since $\theta_i^2 = 0$, $z^{N+1} = 0$.
The same argument does not work for infinite variables: No matter how high you choose the exponent, you can always find summands that survive.
@Slereah Sort of. Look at $\theta_1 + \theta_2\theta_3 + \theta_4\theta_5\theta_6\theta_7 +\dots$, where the $i$-th summand is the product of $2^{i - 1}$ Graßmann variables that did not occur yet.
If you look at its finite equivalents, you find that in $2^n$ dimensions, $z^n \neq 0$ (instead I think it's $n! \omega$ where $\omega$ is the top-degree element, i.e. the product of all $2^n$ distinct variables)
In infinite dimensions, the pattern which makes the power non-zero for exponents smaller than $n$ continues for all exponents: Some summands cancel, and all summands that remain have a positive sign in front of them after sorting the variables in ascending order of their indices, so they cannot cancel.
then the if$ function takes up the three topmost elements of the stack, looks at the third topmost and sees if it's a one or a zero, and depending on that it puts the second topmost or second topmost on top of the stack
so if the top of the stack was empty, it now runs output.nonnull and moves on
and if the top of the stack had object X, then it now has X then pop$ and it runs pop$, which takes whatever is below it in the stack and prints it out
and that's how you do simple logic in .bst language
and if you mess up and you let something slip onto the stack where you're expecting some function to find something else.... well, you're fucked.
Consider a pair of objects in elliptical orbits around a common center of mass. For all considerations of angular motion and torque, the pivot point of interest is the center of mass in this discussion.
The only forces occurring point directly towards the center of mass, and cannot cause a torqu...
