Ring Definition and 1000 Threads

Homework Statement Text description: Let V(z) be the potential of a ring of charge on the axis of symmetry at distance z from the center. Obtain the first two non-vanishing terms of the multipole expansion for V(z) with z>>a where a is the radius of the ring. Can you see by symmetry that the...

Homework Statement NUMBER 271 Homework Equations Not Really Sure The Attempt at a Solution No Idea where to start, I looked up the law of Tangents and it seems to do with that. Please help! :) I am also confident that it has to do with equilibrium?

Can someone here help me fill in the gaps of my understanding for this problem? I would appreciate it. **Problem:** If $f(x) \in \mathbb{C}[x]$ is a nonzero polynomial of degree $n$, prove that the ring $R=\frac{\mathbb{C}[x]}{(f)}$ has finitely many distinct ideals. How many distinct ideals...

Homework Statement find the inverse of r in R = F[x]/<h>. r = 1 + t - t^2 F = Z_7 (integers modulo 7), h = x^3 + x^2 -1 Homework Equations None The Attempt at a Solution The polynomial on bottom is of degree 3, so R will look like: R = {a + bt + ct^2 | a,b,c are elements of z_7 and x^3 = 1 -...

Homework Statement A ring of charge is situated in the x‐y plane centered about the origin. The ring has a uniformly distributed charge Q = ‐10 nC and a radius R = 2.0 cm. a. Find the electric potential at a distance z = 5.0 cm above the origin on the z=axis. b. Find the electric field at a...

A bead of mass m is threaded on a metal hoop of radius R. There is a coefficient of kinetic friction µk between the bead and the hoop. It is given a push to start it sliding around the hoop with initial speed v0 . The hoop is located on the space station, so you can ignore gravity Find the...

At least that is the interpretation of the scientists - 200 times larger than the system around Saturn, and thick enough to make a complicated light curve during stellar transit. The transit happened in 2007 and took nearly two months. A gap in the ring system hints at an exomoon. As they just...

So the free particle wave functions are of the type: ψ(x) = Aexp(ikx) + Bexp(-ikx) (1) In a problem I am doing I am supposed to find the energy levels for a particle which is sliding on a frictionless ring and the exercise says that to do so I should use the fact that ψ(x+L)=ψ(x) (2) BUT...

I need help understanding the following solution for the given problem. The problem is as follows: Given a field $F$, the set of all formal power series $p(t)=a_0+a_1 t+a_2 t^2 + \ldots$ with $a_i \in F$ forms a ring $F[[t]]$. Determine the ideals of the ring. The solution: Let $I$ be an...

(I assume that the three section headings below form the template referred to below) 1. Homework Statement n identical equi-distant particles are distributed equi-distantly around the circumference of a ring of radius r in space. Each particles is of mass m, so the total mass of the ring is...

I don't understand this page, https://www.proofwiki.org/wiki/Kernel_of_Ring_Homomorphism_is_Subring, but how can this be a true statement? Wouldn't a ring morphism map the multiplicitive identity to itself? So it wouldn't be in the kernel, so how could the kernel be a subring? I happened upon...

Hello, I asked somebody a question, and didn't understood his answer. Can someone explain it to me ? My question was : Is there a valuation ring in ℚ(x,y), lying above the ideal <x,y> in the ring ℚ[x,y], whose residual field is a non-trivial extension of ℚ ? Here is his answer: This is not too...

I attended the navy day celebrations and the marine commandos demonstrated a bomb blast by setting a time bomb in a small installation at the middle of the sea. The commandos dived from their boat and set the explosives from underwater. After the explosion, what I saw first was a cloud of black...

This is probably a stupid question. Let R be a domain, K its field of fractions, L a finite (say) extension of K, and S the integral closure of R in L. Is the quotient field of S equal to L ? I believe that not, but I have no counter-example.

What is a gravity tidal torque on a simple circular ring, inclined at some angle i? I can't find a solution for this simple problem, despite the ring's idea is frequently used in the precession problems, for example in the Earth's axis precession case. How this can be computed effectively?

Homework Statement A block of mass ##m## slides on a frictionless table. It is constrained to move inside a ring of radius ##l## which is fixed on the table. At ##t=0##, the block is moving along the inside of the ring with tangential velocity ##v_0##. The coefficient of friction between the...

Homework Statement A 25.0 g copper ring at 0°C has an inner diameter of D = 2.71585 cm. A hollow aluminum sphere at 88.0°C has a diameter of d = 2.72019 cm. The sphere is placed on top of the ring (see the figure), and the two are allowed to come to thermal equilibrium, with no heat lost to the...

Say if I magnetize a hollow cylindrical ring magnet by placing a staight current carrying wire along its axis. It will be magnetized with magnetic field lines running inside the cylinder clockwise or anticlockwise! So there will be no magnetic field lines outside the iron body? If I have a...

Homework Statement Six of the electrons from benzene C6H6 form a delocalized conjugated π-bond. We will model it as a "particle on a ring" with ring radius a, particle (electron) mass m, and "moment of inertia" I = ma2. After obtaining the energy diagram, we will fill in these 6 electrons...

Homework Statement A metal ring of mass m and radius R is placed on a smooth horizontal table and is set rotating about its own axis with a constant angular speed ω. What is the tension in the ring ?Homework EquationsThe Attempt at a Solution Consider a small element ds=rdθ .Tension T acts at...

I know it is very unlikely such thing exists because QM can prevent CTLs However, what observer would see near such singularity? As ring is timelike, for an observer it won't be a ring at all, but a point, correct? That point should be visible (naked) because there are no horizons between an...

Hey! (Wave) Let the ring of the integer $p$-adic numbers $\mathbb{Z}_p$. Could you explain me the following sentences? (Worried) It is a principal ideal domain. $$$$ The function $\epsilon_p: \mathbb{Z} \to \mathbb{Z}_p$ is an embedding. (So, $\mathbb{Z}$ is considered $\subseteq...

I think I'm not understanding some conceptual part of rotational kinematics because all the questions seem connected. I want to figure it out as best I can so please don't solve it but any hints in the right direction would be really appreciated, thanks! The Question: A stiff piece of wire is...

Homework Statement A) If ab+ba = 1 and a^3 = a in a ring, show that a^2 = 1 Homework Equations none The Attempt at a Solution Little confused. If we know that a^3 = a, can't we just multiply each on the right or left side by a^-1 to get a^2 = 1? Or could we only do that if the ring is said...

Homework Statement Show that 0 is the only in R if and only if a^2 = 0 implies a = 0. Homework Equations none The Attempt at a Solution So I'm not sure if I'm doing this right. a^2 = a*a = 0. Therefore, either a or a is zero. The reason I'm not sure about this is because I'm thinking...

Can someone please help me get started on the following problem: Show that if A is a left unital Artinian ring, then: ... whenever x, y \in A ... we have ... xy = 1 \Longrightarrow yx = 1.Peter

I am reading "Introduction to Ring Theory" by P. M. Cohn (Springer Undergraduate Mathematics Series) In Chapter 2: Linear Algebras and Artinian Rings, on Page 66 we find a definition of right Artinian rings ... The relevant text in Cohn's book is as...

Homework Statement Show that ##\vec{E}_x## on the axis of a ring charge [I'm assuming they meant "of charge Q"] of radius "r" has its maximum value at ##x=\pm \frac{r}{\sqrt{2}}## Homework Equations Linear charge density ##\lambda=\frac{Q}{2\pi R}## ##dQ=\lambda ds = \frac{Qd\theta}{2\pi}##...

Hi there, I have been researching an optical Ring Resonator and have been given the following values: FSR=100GHz, Q=10000, Wavelength (λ)=1.55um (micro), ng=3.7 and neff=2.3. Using these values I was asked to calculate the k value (coupling coefficient), length of ring, length of the...

Homework Statement Thin rod of the length l is placed with one of its ends placed at the center Oof the thin ring of radius R as shown, perpendicular to the plane of the ring. Rod is charged with total charge Q that is distributed along the rod’s length with the linear charge density...

I am reading "Introduction to Ring Theory" by P. M. Cohn (Springer Undergraduate Mathematics Series) In Chapter 1: Basics, on Page 33 we find a definition of a module homomorphism (or R-linear mapping) and a definition of Hom. I need help to interpret one of Cohn's expressions when he deals...

Hello, I have a conducting copper ring of inner radius a and outer radius b. point charges Q pass through the centre of this ring for time dt. so I guess I'm suppose to get a step function of induced current or something similar. 1)what is the equation relating the charge Q to the...

Homework Statement Suppose you design an apparatus in which a uniformly charged disk of radius R is to produce an electric field. The field magnitude is most important along the central perpendicular axis of the disk, at a point P at distance 2R from the disk. Cost analysis suggests that you...

Is -(x^-1) = (-x)^-1 true for all nonzero x in any ring, where x^-1 denotes the multiplicative inverse of x?

Z = field of integers . If R is a ring and k is an element of Z, write kR = {kr | r is an element of R}. It is not too difficult to verify that {k is an element of Z | kR = 0} is an additive subgroup of Z. I am confused on how kR would equal 0? Wouldn't that mean that k would have to...

i'm trying to model the combustion of a pressurized gas (nitrous oxide) inside of a paraffin ring. What I'm trying to figure out is the amount of paraffin that will be burning per unit time. What I'm assuming is that the gas is totally covering the inside of the wax ring and Ideal Gas law. I'm...

Dear Friends, Please tell me the differences created in ring theory problems when 1.Unity is taken in integral domains. 2. Unity is not taken in integral domains. Do results become more general in the second case. Why one standard way not adopted worldwide by all authors because...

Hi all. I started a thread a while back about RF mixer design. I didn't know what to do or what design to choose. You guys laid some options for me and after some research and time I have finally decided that I will go for a double balanced, ring diode topology. Here is a schematic from google...

Hi, Can somebody give me the formula for pull force of ring magnet(permanent. not solenoid or electric) on a metal rod. Also is the formula for pull force by a solenoid given below correct. If not let me know the correct one for the below. Force = ((N x I)^2 x μ x A) / (2 x g^2) N =...

Homework Statement Let R be the ring of all 2*2 matrices, over Zp, p a prime. Let G be the set of elements x in the ring R such that det x ≠ 0. Prove that G is a group. Homework Equations Matrix is invertible in ring R. The Attempt at a Solution Group properties and ring properties...

Homework Statement Let R be the ring of all 2*2 matrices over Zp, p a prime,. Show that if det(a b c d) = ad - bc ≠ 0, then (a b c d) is invertible in R.Homework Equations The Attempt at a Solution I don't know how to start if Zp, with p a prime, is the clause. I know that since ad- bc ≠ 0, it...

Homework Statement Consider a particle on a ring with radius R in a plane. The Hamiltonian is H_0 = -\frac{\hbar^2}{2mR^2}\frac{d^2}{d\phi^2} The wavefunction at t=0 is \psi=ASin\phi Find the mean value of the observable Sin\phi Homework Equations The eigenfunction are \psi_n =...

So I'm trying to solve old qualifying exam problems, one of which is a particle on a ring with a constant electric field perturbation. The un-perturbed problem is straightforward, and we then add a constant electric field in the x-direction (the ring lies in the xy-plane) of magnitude E...

I could use some guidance as to how I would analyse the stresses in a ring girder similar to the one shown in the attached picture. I have found the stress in the columns that support the ring but I do not know how to find the maximum stress in the ring. The best I have been able to come up with...

Let S={p,q,r} and S=(S,+,*) a ring with identity. Let p be the identity for + and q the identity for *. Use the equation r*(r+q)=r*r+r*q to deduce that r*r=q. Attempt of a solution r*r=r*(r+q)- r*q =r*r+r*q - r*q But I'm not finding a clever way to deduce what is required. Any type of help...

Hello everyone. I am world-building for a fantasy setting. I've had an idea and I'm not sure if it's feasible or not. I'm trying to model a non-standard world type and I wanted to see if I'm on the right track. The idea is for a ring world. The outside is habitable. I've already got a...

There are several threads on the Bell paradox, plus the article in the FAQ forum, but I must be missing something here. Forget for a moment about 2 ships. Let's take one ship, which an observer at the front and the other at the rear. The ship is undergoing a constant 1G acceleration. The...

I am reading Joseph Rotman's book Advanced Modern Algebra. I need help with Problem 2.20 on page 94. Problem 2.20 reads as follows: 2.20. Prove that if R is a commutative ring then R[x] is never a field. Could someone please help me get started on this problem. Peter ***EDIT*** Presumably...

Homework Statement In the figure below two point mass m, over the ring with mass M and radius R, are released from the rest in the highest point and there is no friction in the system. What is the maximum amount of m/M for which the ring doesn't leave the surface? Homework Equations According...

Homework Statement Consider a ring-shaped body in a fixed position with mass M. A particle with mass m is placed at a distance x from the center of the ring and perpendicular to its plane. Calculate the gravitational potential energy U of the system (the picture has a small sphere...