Ring Definition and 1000 Threads

Homework Statement Consider a circular ring of wire of radius a that resides in the x-y plane through the origin. The center of the ring coincides with the origin and you can regard the thickness of the wire to be infinitesimal. a. Given that a current I flows in the ring, find an...

Hello, This is my first post on this forum, and I'm not used to the english mathematical vocabulary, I'll try my best to explain what is my problem. Let (A,+,x) be a ring, ans S be the subset of the indempotents of A, i.e S={x\in A , x^2=x} . I must show that if S is a finite set, then S has...

Is it true that polynomials of the form : f_n= x^n+x^{n-1}+\cdots+x^{k+1}+ax^k+ax^{k-1}+\cdots+a where \gcd(n+1,k+1)=1 , a\in \mathbb{Z^{+}} , a is odd number , a>1, and a_1\neq 1 are irreducible over the ring of integers \mathbb{Z}...

Most introductory physics textbooks derive the following formula for the gravitational field for a point mass on the on the axis of the ring: g_{x} = -\frac{Gmx}{(x^2 + a^2)^{1.5} } where, m = total mass of ring x = distance from point mass to ring center a = radius of ring Is...

Homework Statement A ring can rotate about a horizontal axis(x), and a diameter placed on the x-axis. A uniform field is perpendicular to the ring -B0*y. The diameter of the ring is D. it spins with constant angular velocity ω around the x-axis. At at time t = 0 the ring is entirely in the xy...

This is about the electric field of a ring with radius r, at a distance z from center, along the axis of the ring. The ring carries a uniform line charge λ . We always say that the radial component of the field cancels out due to symmetry. Can somebody tell how to prove it mathematically...

A statement in a book of analysis I have says: (Q,+, .) is a commutative ring with an identity element. I assume by its notation (Q,+,.) is a tuple.(correct?) There are several questions that come to mind: 1. Why is there an order between Q,+ and . ? 2. As far as I know, a tuple is an...

Homework Statement What is the centre of the ring of the quaternions defined by: \mathbf{H}=\{ \begin{pmatrix} a & b \\ -\bar{b} & \bar{a} \end{pmatrix} | a,b \in \mathbf{C} \}? Homework Equations The definition of the centre of a ring: The centre Z of a ring R is defined by Z(R)=\{A...

hi i need the schrödinger equation for a particle(electron) in a ring under the influence of a magnetic field that goes through perpendicular to the plane of the ring and i want to consider the spin too. Well, the particle in the ring is pretty easy: - \frac{ \hbar^2}{2mr^2}...

Homework Statement Write down the Schrödinger equation for a particle inside a circle of radius R Homework Equations - Gradientψ(r,θ)=Eψ(r,θ) The Attempt at a Solution Take the gradient in spherical form and set r = R; θ=90;∅ as 0 Then you are left with the first two...

Homework Statement Consider the bead threaded on a cicular hoop of example 7.6 (pg 260), working in a frame that rotates with the hoop. find the equation of motion of the bead, and check that your result agrees with eq 7. 69. Using a free body diagram explain the result 7.71 for...

Homework Statement [PLAIN]http://img695.imageshack.us/img695/3864/unled1dxu.jpg Homework Equations F=(mv^2)/r The Attempt at a Solution NetForce=0 N-W=0 === A free body diagram of the car at the bottom would just incorporate a downwards W force and an upwards N force together equalling 0...

Homework Statement A point charge Q is located at point P(0,-4,0) while a 10nc charge is uniformly distributed along a semicircular ring as shown in the figure. find the value of Q such that E(0,0,0)=0 Homework Equations Q=ρLdl dl = ρd∅ (because ρ and z are constant)...

1. Homework Statement A ring of mass M and radius R lies on its side on a frictionless table. It is pivoted to the table at its rim. A bug of mass m walks around the ring with speed v, starting at the pivot. What is the rotational velocity of the ring when the bug (a) is halfway around and...

Hi everyone, Homework Statement Let a charge Q be uniformly distributed on a circular ring defined by a < \rho < b. Find D at (0,0,h). Homework Equations E = kQ/r2 ar D = \epsilono E The Attempt at a Solution Well I thought I had this figured out, but I was wrong and I still...

Homework Statement Are chain and ring forms of glucose isomers? They aren't, because they have the same structure, right? Homework Equations The Attempt at a Solution

I researched this some, but could not find a method to calculate the radius of the ring singularity in a Kerr black hole. I would think it is a function only of black hole mass and angular velocity. Please let me know if there is some reports or papers on this.

Hi, I have found many papers using analytical methods to calculate the static twist in piston rings. All the papers that i found have used the results of that analytical tool but no one explained how the tool works. Can anyone find a paper in which the analysis to calculate piston ring twist is...

Homework Statement Solve for the Electric force exerted on a Particle a distance z above a uniform ring of charge Q. Determine the potential energy of the charge where the charge lies directly in the center. Homework Equations F=kq1q1/r^2 The Attempt at a Solution Knowing E=F/q I...

The Problem is as follows: A ring of diameter 7.50 is fixed in place and carries a charge of 5.50 uniformly spread over its circumference. A) How much work does it take to move a tiny 3.80 micro-columb charged ball of mass 2.00g from very far away to the center of the ring? B) What...

Homework Statement A ring falls through a horseshoe magnet. Before reaching the magnet, is the current induced in the ring clockwise or counterclockwise? What about after the ring has passed through the magnet? The answers are clockwise before the ring passes through, and...

Homework Statement I need help specifically with b. The inner diameter of a steel ring is 2.0000 cm, and the diameter of an aluminum disk is 2.0100 cm. Both are at 430 C. At what common temperature will the disk fit precisely into the hole in the steel ring? b) If after the aluminum disk is...

In a token ring LAN (IEEE 802.5) what are the differences between "Single token", "Multiple token" e "Single packet"? Thanks in advance.

Homework Statement \mathbb{Z}[x]/(x^3-x) \rightarrow \mathbb{Z} Show that is ring homomorphism, and count the number of homomorphism..? Homework Equations The Attempt at a Solution the map f is homomorphism if, f(x+y)=f(x)+f(y) f(xy)=f(x)f(y) I think, I must find a...

Homework Statement You have an iron ring, hung near a solenoid which has an iron core inserted within. [PLAIN]http://img843.imageshack.us/img843/1623/imgsole.jpg Below are the questions and answers my book provided. I highly suspect the reasoning and i seek PF members to evaluate how true it...

Homework Statement E=(kqz)/(z^2+a^2)^1.5 Through calculus i found that the max occurs at z=a/sqrt(2) and z=-a/sqrt(2) and I think the negative one is the minimum. That answer was given in the book also. The ring has radius a. It wants me to graph E versus z. I'm a little confused on how to...

Ok, I understand that the liquid crystal structure expands and contracts in response to thermal fluctuations and that the structure is made of layers... and only the wavelengths that mach exactly or are half (or quarter and so on) can have constructive interference, thus, only those wavelengths...

consider the image i have uploaded, it shows 4 ring-shaped magnets of different sizes each pair of concentric magnets are held in position relative to each other, and the lower pair is also affixed to the ground, i.e. the upper pair of magnets is free to move blue and red faces show the...

You just can't make this stuff up. http://news.yahoo.com/greek-police-smash-violent-doughnut-ring-213853411.html

Suppose that there is an integer n>1, such that an=a for all elements of some ring. If m is a positive integer and am=0 for some a , then I have to show that a=0. Please suggest.

I found that the endomorphism group over an elliptic curve is isomorphic to a complex quadratic order: End(E)\simeq \mathbb{Z}[\delta]=\mathbb{Z}+\delta\mathbb{Z}, where \delta=\frac{\sqrt{\Delta}}{2} if \Delta is even \delta=\frac{1+\sqrt{\Delta}}{2} if \Delta is odd Does anyone know where...

This is more of a practical question - what is the proper way to remove the retaining ring shown below? Note that it does not contain lug holes, so I am not sure whether retaining/snap-ring or circlip pliers would be capable of removing the ring.

How to calculate the deflection in ring, fixed at center, with a radial point force acting at some point(let say at theta=0) ? I have derived complete set of equations. Now how to apply boundary conditions ? to get a complete solution of 4th order equation, I need 4 B.C's, but here...

Let R be a commutative ring with 1. If there exists a non-zero R-module M such that every submodule of M is free, then R is a PID. I remember proving something similar to this, assuming submodules of all R-modules are free, but I'm not too sure about this question. The direction I am headed in...

I have got a doubt regarding the situation when a ring rolls in a non-uniform magnetic field. We can see that the flux linkage is increasing (considering dB/dt to be positive). So EMF should be induced in the loop. But if we join any two points, say the instantaneous axis of rotation and the...

http://today.msnbc.msn.com/id/44002915/ns/us/_news-crime_and_courts/#.TjmjfGFKO_I There was over 100 terabytes of child pornography swapped here. From the indictment I've read the rules required to be in the site. Here's the indictment document...

Homework Statement Consider \frac{\mathbb Z_2[X]}{X^2+1}, is this ring isomorphic to \mathbb Z_2 \oplus \mathbb Z_2, \mathbb Z_4 or \mathbb F_4 or to none of these? Homework Equations / The Attempt at a Solution - \mathbb F_4 No, because \mathbb Z_2[X] is a principle ideal domain...

As we know for the average Undergrad attempting to grasp (and understand) these abstract mathematical concepts can be challenging to say the least. I was (and still am in some sense :P) in that boat. Does anyone have any Analogies or creative ways of explaining these and getting their meaning...

Hello, I have to find the maximum rpm of the shaft that has ring mounted on the shaft with interference fit of 0.002". I want to know at what rpm the ring will come loose from the shaft? and If I run the shaft at 7000rpm at 400 degree Celsius, is the interference fit of 002" enough...

Homework Statement There is a vertical ring with a bead strung on it. The vertical ring spins at 4 revolutions per second, and the the bead moves up the ring at what angle from the bottom of the ring will the bead be at equilibrium? Is it possible for the bead to make it all the way up to the...

Homework Statement A massive ring (radius = a and mass = M) lies on the xy plane. Calculate the force F on a test mass m at position z on the z axis. Now assume a = 1 and GMm/a2 = 1 in some system of units. (a) What is the force on m at z = 0? I got the answer for this its 0 (b) What...

large number of magnets attached to a fixed non magnetic circular ring. Another non magnetic smaller radius ring with equal number of magnets is taken. Here magnets are attached such a way that like polls of the magnets of bigger and smaller rings are facing each other. Due to repulsive force...

Homework Statement A circular metal ring, as shown on the diagram below, is constructed so as to expand or contract freely. In a region with a constant magnetic field Bo oriented perpendicular to it, the ring expands, with its radius growing with time as r=r0(1+\alphat2). As the ring expands...

I got this question from another forum and it's driving me crazy. Find all triples of odd primes, p,q,r such that p^2+1 is divisible by q, q^2+1 is divisible by r and r^2+1 is divisible by p. Two such triples are 5,13,17 and 17,29,421. If we assume p<q<r, then there are no other such triples...

Hi, All: Could someone please tell me or give me a ref. on the basic properties of Gl(n,R) ; R a ring; possibly a division ring, and Gl(n,R) the group (under composition) of matrices invertible over R ? (I imagine we need a ring R with 1 , to talk about invertibility). I...

It may seems like simple homework question but it is industrial question with actual condition & I am struggling for the answer & also asked this question on other website but not get any reply. So ,please help me 'O' ring Internal Diameter(ID) ID=4 mm with tolerance is + & - 0.15mm...

Hi there, I'm attempting a science experiment to create a magnetic suspension field that can hold magnetic objects in place in mid air. Since a Magnetic field isn't flat a single magnet would be pointless as the opposing object is continually sliding off it, so I looked at creating a ring...

Homework Statement Let \phi: R \to S be a ring homomorphism from R to S. What can you say about \phi if its image \text{im}\phi is an ideal of S? What can you say about \phi if its kernel \ker \phi is a subring (w unity) of R? The Attempt at a Solution I think the second one...

Homework Statement Let R be a ring and S be any set. Let R^S be the set of set-functions S \to R . Endow R^S with a ring structure such that if S is a singleton, then R^S is just a copy of R. The Attempt at a Solution It seems to me that the obvious (and perhaps only?) way to...