What is Infinite: Definition and 1000 Discussions

Homework Statement A) Three infinite, current-carrying wires are arranged as shown below. In terms of the given quantities, determine the magnitude and direction of the magnetic force per length acting upon wire 2. (Part A.jpg attached) B) Three infinite, current-carrying wires are arranged as...

Homework Statement A charged sheet with charge density ##\sigma## is described by ##-\infty<x<0,-\infty<y<\infty, z = 0##. Find the electric field at ##(0,0,z)##. Homework Equations Electric field of continuous density charged body from the Coulomb law: $$E = \frac{1}{4\pi...

For a series to be convergent,it must have a finite sum,i.e.,limiting value of sum.As the sum of n terms approaches a limit,it means that the nth term is getting smaller and tending to 0,but why is not the converse true?Should not the sum approach a finite value if the nth term of the series is...

Is there a simple closed-form solution for the following infinite series? ##F(a,b,c) = \sum_{j=0}^\infty \frac{(j+a)!}{(j+b)! (j+c)!}## where ##a, b, c## are positive integers?

Homework Statement Show that ##\displaystyle \bigcup_{n=2}^\infty \left[ \frac{1}{n} , \frac{n}{n+1} \right] = (0,1)##. Homework EquationsThe Attempt at a Solution I'm not sure how to show this rigorously. It is sufficient to note that ##\lim_{n\to\infty} \frac{1}{n} = 0## and that...

<Moderator's note: Moved from a technical forum and thus no template.> 1. Homework Statement Is this proof correct? Let K>0, and choose N such that N >= K2, then for all n in the naturals, and n>=N, sqrt(n)+7>=sqrt(N)>=K Is this proof correct? Please tell me

Evaluation of \displaystyle \sum_{r=1}^\infty \left(\frac{1}{36r^2-1}+\frac{2}{(36r^2-1)^2}\right)

##\displaystyle \sum_{n=1}^\infty\frac{1}{n^2+n/2}## converges by the direct comparison test: ##\displaystyle \left|\frac{1}{n^2+n/2}\right| \le \left|\frac{1}{n^2}\right|##, and ##\displaystyle \sum_{n=1}^\infty\frac{1}{n^2} = \frac{\pi^2}{6}##. But what if we want to show that ##\displaystyle...

It is said (hopefully no need to give references for such a common statement) that the electromagnetic field of a given charged particle is infinite in range (albeit converging to zero as the distance goes to infinity). However, given that charged particles apparently did not exist at the...

For 0 < x< 1, find the sum: \[\frac{2x-1}{1-x+x^2}+\frac{4x^3-2x}{1-x^2+x^4}+\frac{8x^7-4x^3}{1-x^4+x^8}+ ...\]

Homework Statement Consider an electromagnetic field in an empty space in the region ##0 \leq z \leq a## with the following non-zero components: $$E_x = -B_0\frac{\omega a}{\pi}\sin\left(\frac{\pi z}{a}\right)\sin\left( ky-\omega t\right)\\ B_z = B_0\frac{ka}{\pi}\sin\left(\frac{\pi...

A question came up with some friends recently that googling hasn't turned up a satisfying answer to. Simply put: If the world was flat and infinite (ignoring all the stupidity of this) how far could you see from sea level before the atmosphere itself is preventing any light reaching you...

For a particle trapped in a region of length L the de broglie wave for the 1st excited state is a pure sine wave from 0 to 2pi for which the particle momentum can be calculated as 2h/L from de broglie relation Whereas from energy quantisation relation p=nh/2L where n is the state integer,for...

First we have to agree on the definition of infinite: https://en.m.wikipedia.org/wiki/Actual_infinity So: - Potentially infinite is the process of continued and potentially endless iteration (IE a limit). - Actually Infinite is the result of an unbounded number of iterations; IE NOT DEFINED...

...to give a number? https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2016/lecture-notes/MIT8_04S16_LecNotes5.pdf On page 6, it says, " Matrix mechanics, was worked out in 1925 by Werner Heisenberg and clarified by Max Born and Pascual Jordan. Note that, if we were to write xˆ...

Homework Statement A crystal is a periodic lattice of positively and negatively charged ions. (a) Consider an infinite one-dimensional crystal of alternating charges +q and −q, separated by distance d...

Homework Statement Let ##H = \langle x \rangle##. Assume ##|x| = \infty##. Show that if ##H = \langle x^a \rangle## then ##a = \pm 1## Homework EquationsThe Attempt at a Solution Here is my attempt: Suppose that ##H = \langle x^a \rangle##. Then, for arbitrary ##b \in \mathbb{Z}##, ##x^b =...

While I was was numerically integrating the magnetic field caused by an infinite array of magnetic moments, I observed the interesting limit ( limit (1) in the image). It may seem difficult to prove it mathematically but from the physics point of view, I think it can be proved relatively...

Hi I have read one excellent explanation on the question I am posting again, at another thread on PF, because I am not able to completely understand the concept. Please spare some more time. I need help to understand how an electric field due to an infinite sheet of charge can be uniform where...

Could someone tell me in what sense the following photo of Hilbert is a infinite dimensional Hilbert Space? It's shown in a pdf I'm reading. Perhaps I'm putting the chariot in front of the horses as one would say here in our country, by considering infinite as infinite dimensional?

1. Charge is distributed through an infinitely long cylinder of radius R in such a way that the charge density is proportional to the distance from the central axis: ß = A r, where A is a constant and ß is the density. (a) Calculate the total charge contained in a segment of the cylinder of...

Hello! I am reading about image charges for an infinite plane and a charge above the plane. In the book I am reading (Griffiths) the author says (and uses this results several times) that the field below the plane is 0. How do we know this? The method of the mirror charges gives the V above the...

The electric field of an infinite conductor of net charge Q along the x-y plane is easily found using Gauss's Law: $$ \vec E(x, y) = \frac {\lambda} {2\pi \epsilon}\frac {[(x-x_c)\hat x + (y-y_c)\hat y]} {[(x - x_c)^2 + (y - y_c)^2]^3}, $$ where ##x_c## and ##y_c## mark the location of the...

Homework Statement 3 - 2 , 1 km wires ( so acting like infinite wires ) , both have same current , no direction specified , , separated by 1 meter distance and having between them a magnetic force of module 0.02 N . find the current i= Homework Equationsthe definition of 1 ampere has same...

Suppose for the sake of argument someone said the outward speed of light is infinite and the return speed is c/2, creating a two-way speed of c. Wouldn't this violate the conservation of momentum? p = E/c. That means on the way out, the momentum of light would be zero, but on the way back it...

I'm curious...

Hi. I'm trying to get an idea how to look at the beginning, before the cosmic background radiation (CBR) and what we can detect with our eyes, and what we can assume about earlier times than light was around. I was looking into the red shift effect effect, as not only a measure of relative...

For finite matrices ##A## and ##B## we have Tr(AB)=Tr(BA) What happens in case of infinite matrices?

I was watching a conference on YouTube about cosmology and one of the speakers was Anthony Aguirre. He was giving a lecture on different cosmological models that are infinite in time as well as space. Here is a link to one of his papers and one of the models he was presenting. There is not much...

What is effective mass? What is zero and infinite effective mass?

In Zettili's Quantum Mechanics, page 477, he wants to determine the energy and wave function of the ground state of three non-interacting identical spin 1/2 particles confined in a one-dimensional infinite potential well of length a. He states that one possible configuration of the ground state...

The problem statement can be seen here http://www.feynmanlectures.caltech.edu/info/exercises/infinite_pulleys.html Since each pulley is presumably massless, it must have no net force on it and so the tension of each rope is half of the one above it. If we let T be the tension acting on m0...

So for a story I'm writing, there is a character with the ability to absorb force and store it (the force never impacts but its absorption works like pausing a movie). The force can be released (or resumed) through use of a circular space called a "rune". The character can control the size/area...

Homework Statement Homework EquationsThe Attempt at a Solution So the book is saying that this series diverges, i have learned my lesson and have stopped doubting the authors of this book but i don't understand how this series diverges. ok i can use the comparison test using 1/3n and 1/3n...

Homework Statement Homework EquationsThe Attempt at a Solution So my understanding of this so far is that the whole infinite series from 1 to infinities summation minus the first six terms summation is equal to 0.0002..? This is so confusing. So how does that mean that the sum will lie...

Homework Statement If the Green's function of the electric field in a system is G(x,x')=e^{-i(x-x')^2} I want to calculate the phase of the electric field at x if the source is uniformly distributed at x'=-\infty to x'=\infty Homework EquationsThe Attempt at a Solution Then, the phase of...

Homework Statement An infinitely long cylinder of radius a has its axis along the z-direction. It has Magnetization ##M=M_0(s/a)^2\hat{\phi}## in cylindrical coordinates where ##M_0## is a constant and s is the perpendicular distance from the axis. Find the values of ##\vec{B}## and ##\vec{H}##...

Homework Statement Figure 6.47 shows a horizontal infinite straight wire with current I1 pointing into the page, passing a height z above a square horizontal loop with side length l and current I2. Two of the sides of the square are parallel to the wire. As with a circular ring, this square...

If we measure one conjugate variable in an uncertainty relation precisely , i.e., so its standard deviation is zero, then by the HUP the sd of the other one is either infinite or undefined. But what about the cases when the other conjugate variable has limits: e.g., there cannot be an infinite...

Homework Statement Two infinitely large conducting plates with excess charge 2Q and 3Q are placed parallel to one another, and at a small distance from one another. How are the charges 2Q and 3Q distributed? You may assume that infinitely large sheets of charge produce electric fields that are...

Dear Everybody, I need some help with find M in the definition of the convergence for infinite series. The question ask, Prove that for $-1<r<1$, we have $\sum_{n=0}^{\infty} r^n=\frac{1}{1-r}$. Work: Let $\sum_{n=0}^{k} r^n=S_k$. Let $\varepsilon>0$, we must an $M\in\Bbb{N}$ such that $k\ge...

Is infinity truly infinite if it has something else in it? Put differently, say there's an infinite volume of water that has some rocks in it, is the volume of water truly infinite? Though there's a place where there's no water?

In school we are taught that sunlight contains all different frequencies of light. Also that each frequency has it's own unique wavelength and energy (per photon). So my question is that if there are infinitely many different wavelengths of light (much like infinitely many numbers in an...

Homework Statement 2. Homework Equations Ohm's law and Kirchoff's voltage law The Attempt at a Solution My solution is a bit long so I will just briefly explain it. First, we find the total equivalent resistance. Since the circuit extends to infinity, it is equal to replacing the second...

The Feynman LECTURES ON PHYSICS (NEW MILLENNIUM EDITION) by FEYNMAN•LEIGHTON•SANDS VOLUME II discusses radiation from an infinite sheet of switched-on constant current in section "18-4 A traveling field" on page 18-15. The solution shows a constant E field and constant B field at a given point...

Hello Everyone. I am searching for some clarity on this points. Thanks for your help: Based on Schrodinger wave mechanics formulation of quantum mechanics, the states of a system are represented by wavefunctions (normalizable or not) and operators (the observables) by instructions i.e...

I´m not sure, whether this little challenge has been posted before. I have searched the forum and didn´t find it. It might still be a duplicate though ... Find the sum of fractions $$\frac{2}{3\cdot5}+\frac{2\cdot4}{3\cdot5\cdot7}+\frac{2\cdot4\cdot6}{3\cdot5\cdot7\cdot9}+...$$

Homework Statement Homework Equations F=ma F=Gm1m2/r2 Gauss' Law? The Attempt at a Solution I'm not sure if I should be using Gauss' Law for this question, because I've never heard of it or learned about it. I'm currently taking multi-variable calculus (gradients, vectors, etc.). From what I...

The problem I'd like to calculate the value of this sum: $$3 \sum^\infty_{k=1}\frac{1}{2k^2-k}$$The attempt ## 3 \sum^\infty_{k=1}\frac{1}{2k^2-k} = [k=t/2] = 3 \sum^\infty_{t=2}\frac{1}{2 \left( \frac{t}{2} \right)^2-\frac{t}{2}} = 3 \sum^\infty_{t=2}\frac{1}{ \frac{t^2}{2} - \frac{t}{2}} = 3...

Homework Statement When I have a disk with radius r then naturally the area is πr^2. Then I want to do this by calculus and my first step is simply taking πrdr. But the correct way is to take 2πrdr. To me this is really confusing, because I would never take 2πr dr (circumference x width)...