Ring Definition and 1000 Threads

Homework Statement Consider the quotient ring ##F = \mathbb{Z}_3 [x] / \langle x^2 + 1 \rangle##. Compute the order of the coset ##(x+1) + \langle x^2 + 1 \rangle## in the group of units ##F*##. Homework EquationsThe Attempt at a Solution I was thinking that I just continually compute powers...

Homework Statement A charge ##Q## is distributed unifromly around a thin ring of radius ##b## which lies in ##xy## plane with its centre at the origin. Locate the point on the positive ##z## axis where the electric field is strongest ? Homework Equations The Attempt at a Solution...

Homework Statement T/F: Every ring with unity has at least two units Homework EquationsThe Attempt at a Solution I thought that the answer was true, because if a ring ##R## has unity ##1##, then ##1 \cdot 1 = 1## and ##(-1) \cdot (-1) = 1##. Where am I going wrong?

Homework Statement A box is sliding with constant acceleration a to the right. Inside the box there is a quarter of a circle upon which a frictionless ring can slide. Find the angle theta in terms of the other given variables. Picture in solution Homework Equations F=ma, etc. basic stuff...

Homework Statement Show that ##\mathbb{Z} [\sqrt{d}] = \{a+b \sqrt{d} \ | \ a,b,d \in \mathbb{Z} \}## is an integral domain Homework EquationsThe Attempt at a Solution Do I have to go through all of the axioms to do this? For example, do I have to show that it is an abelian group under...

Hey, is it possible to have a cylindrical ring (made of permanent magnet) and a magnetic sphere sitting inside it and staying in one place without touching the inner sides of the ring and not falling through? The object doesn't necessarily have to be a sphere. If it would work with any other...

So I know that in general, for the ring of ##n \times n## matrices, if ##AB = 0##, then it is not necessarily true that ##A=0## or ##B=0##. However, in other rings, for example the integers ##\mathbb{Z}##, I know that this statement is true. So what property is the ring of matrices lacking such...

<Mentor's note: Moved from a technical forum and thus no template.> A ring's kinetic energy is integral of 0.5v2 dm. Distance X is rΘ, and Θ is defined as distance traveled/radius, so X is r*distance traveled / r. Velocity V is X divided by time, so V is r*distance traveled / rt, and I define...

[Mentor's note : No template as this thread was moved from the technical forums] Hi all! I am working on finding the Lagrangian for the situation stated in the title. This is actually a Wolfram Mathematica demonstration as well in which they give you the Lagrangian. I am working on re-deriving...

My professor drew the following molecule on the board and asked us how many pi electrons this aromatic molecule has. Everyone in the class said 14, as there are 7 double bonds, with two pi electrons from each bond. He told us that there are only 10 pi electrons in this molecule, refused...

Homework Statement A uniform ring of mass m and radius r is projected horizontally with velocity v on a rough horizontal floor,so that it starts off with a pure sliding motion and it acquires a pure rolling motion after moving a distance d.If the coeffcient of friction between ground and ring...

Homework Statement A cylindrical magnet with its axis vertical provides a radial magnetic field. A thin, circular aluminium ring that is co-axial with the magnet falls through the magnetic field. By finding an expression for the current in the ring when it is falling at the speed v, or...

Homework Statement From ##\mathbb{Z}_3## to ##\mathbb{Z}_{15}## Homework EquationsThe Attempt at a Solution I know how to do this if we assumed that the rings had to be unital. In that case, there can be no non-trivial homomorphism. However, in my book rings don't need unity, and so a...

Homework Statement A rigid ring is fixed with three bearings evenly spaced around its circunference, which allow it to rotate but not to displace in the radial direction. An external force is applied in a fixed point P of the ring which moves with the ring. The bearings have friction. These...

I am reading Stephen Lovett's book, "Abstract Algebra: Structures and Applications" and am currently focused on Section 5.4 Ring Homomorphisms ... I need some help with Exercise 1 of Section 5.4 ... ... ... Exercise 1 reads as follows:Relevant Definitions A ring homomorphism is defined by...

Homework Statement I am reading Stephen Lovett's book, "Abstract Algebra: Structures and Applications" and am currently focused on Section 5.4 Ring Homomorphisms ... I need some help with Exercise 1 of Section 5.4 ... ... ... Exercise 1 reads as follows: Homework Equations The relevant...

Homework Statement [/B] A circular ring of radius "a" has a total charge Q uniformly distributed along the top half. (Q is distributed along the semicircle in quadrants I and II). What is the potential at a point located on the bottom of the ring (observation point is on the ring in quadrant...

Why the center of Newton's ring is dark? though I am thinking the path difference in the center is zero between two reflected rays... so,I will be glad if you give the correct information about that...

I have been thinking around the definition of a unit in a ring and trying to fully understand why the definition is the way it is ... ... Marlow Anderson and Todd Feil, in their book "A First Course in Abstract Algebra: Rings, Groups and Fields (Second Edition), introduce units in a ring with 1...

I have been thinking around the definition of a unit in a ring and trying to fully understand why the definition is the way it is ... ... Marlow Anderson and Todd Feil, in their book "A First Course in Abstract Algebra: Rings, Groups and Fields (Second Edition), introduce units in a ring with 1...

Homework Statement A uniformly charged thin ring has radius 13.0 cm and total charge 21.5 nC . An electron is placed on the ring's axis a distance 32.5 cm from the center of the ring and is constrained to stay on the axis of the ring. The electron is then released from rest. Find the speed of...

Homework Statement A washer made of nonconducting material lies in the x − y plane, with the center at the coordinate origin. The washer has an inner radius a and an outer radius b (so it looks like a disk of radius b with a concentric circular cut-out of radius a). The surface of the washer is...

Homework Statement A metal ring with a radius of 10cm and resistance 0.1Ω passes through a delimited magnetic field, look at the photo posted below. The ring has a velocity of 5m/s, and the magnetic field has the field strength 0.4T. When the ring passes through the magnetic field, at some...

Hi. This is from a high school textbook, in a chapter about eddy currents and Lenz's law. In a), a magnetic field is turned on, in b) it's turned off, which both induces a current in a suspended aluminium ring: I think the direction of the current is wrong in both pictures. Any opinions?

Hi. According to Lenz's law, a conducting ring responds to an increasing external magnetic field with a repelling field and to a decreasing external magnetic field with an attracting one. Thomson's experiment uses an AC coil, so its field strength changes between increasing and decreasing a...

Homework Statement Homework Equations F = mw^2r [/B]The Attempt at a Solution For part a, I can't get the constant of half with the tan a I am getting tan a = w^2l/g

Homework Statement There are a big object and an astronaut in space. How do we calculate the gravitational force between them. I enclose a photo. I have given the mass of an astronaut, the dimensions of this giant ring and density of the ring. There is also a mistake in the photo. The astronaut...

Hello, does anyone know if a solution to EFEs (Einstein's Field Equations) has been found that's analogous to Helmholtz's vortex ring solutions in fluid dynamics?

Hi everyone, While studying surface tension I came across a(numerical example) problem which asks to find the force required to pull a circular glass plate of some given radius from the surface of water(assume plane of plate on water surface). Value of surface tension of water is also given in...

Homework Statement I would like to show that if ##p(x) = \sum_{i=1}^m a_i x^i## and ##q(x) = \sum_{j=1}^n b_j x^j##, then ##p(x)q(x) = \sum_{k=0}^{m+n} \left( \sum_{i+j=k} a_i b_j \right) x^k##, where the polynomial ring is assumed to be commutative. Homework EquationsThe Attempt at a Solution...

Homework Statement Homework Equations ΔL = LαΔT The Attempt at a Solution What I did was to set the diameter of the inside of the brass ring + the change in diameter of the brass ring equal to the diameter of the steel rod + change in the diameter of the steel rod. So, Lbrass + ΔLbrass =...

Homework Statement A ring of radius a is made from a charge wire with a uniform charge density λ. a) Calculate the electric potential due to the ring as a function of distance from its center along the axis of the ring passing through the center, perpendicular to its plane b) If a particle...

Our professor did a demonstration today for our physics II class. She was demonstrating electromagnetic induction with a solenoid and a metal ring. When she slid the ring down the solenoid and passed alternating current through the solenoid, the metal ring was flung upward off the solenoid. My...

1. Homework Statement A flat ring, with radii ##b>a## like on the picture is charged with a surface charge density ##ρ_s=ρ_0\frac{b}{r}## where ##ρ_0=const.## Calculate the potential of the ring on the ##z-axis## by taking the reference point to be in the infinity. Picture below. 2. Homework...

Hey! :o A set $R$ with two operations $+$ und $\cdot$ is a ring, if the following properties are satisfied: $(R, +)$ is a commutative/abelian group Associativity : For all $a,b, c \in R$ it holds that $(a \cdot b)\cdot c = a \cdot (b \cdot c)$. Distributive property : For all $a,b, c...

Homework Statement Find the angle Theta so that the system is in equilibrium Mass of each block: 2 Kg Mass of ring: 4π Kg Homework Equations Static equilibrium: Rotational equilibrium The Attempt at a Solution Static equilibrium: 2g + 2g + 4πg = Normal N = 4g + 4πg Taking...

Homework Statement When iron is irradiated with neutrons an isotope of iron is formed. This isotope is radioactive with a half-value period (half-life) of 45 days. Give the meanings of the terms printed in italics. A steel piston ring of mass 16 g was irradiated with neutrons until its...

Homework Statement Alrighty, so here's my problem in a nutshell: Some particle of mass m is confined to move along a ring of radius R. Since it's on a ring, it has periodic boundary conditions--i.e.: For the boundary defined as ##-\pi R \leq x \leq \pi R##, ## x = -\pi R ## and ## x = \pi R...

Homework Statement Normalized equation for particle in a ring, where V=0 on a ring of radius 'a' and infinite everywhere else. Homework EquationsThe Attempt at a Solution Replcing x by rθ, $$-\frac{\hbar^2}{2I}\frac{\partial^2\psi}{\partial\theta^2}=E\psi$$ By guess, I found out that...

I am reading An Introduction to Rings and Modules With K-Theory in View by A.J. Berrick and M.E. Keating (B&K). I need help to clarify a remark of B&K regarding ring homomorphisms from the zero or trivial ring ... The relevant text from B&K reads as follows...

I am reading An Introduction to Rings and Modules With K-Theory in View by A.J. Berrick and M.E. Keating (B&K). I need help to clarify a remark of B&K regarding ring homomorphisms from the zero or trivial ring ... The relevant text from B&K reads as follows: In the above text from B&K's book...

Homework Statement A ring charge of total charge Q and radius a is concentric with a grounded conducting sphere of radius b, b < a. Determine the potential everywhere. The ring is located in the equatorial plane, so both the sphere and the ring have their center at the same spot. Homework...

Hey guys can we derive the formula of Electric Field Intensity around a uniformly charged ring if yes please share the derivation thanks

Hi, I am new to this forum. I need to design an interference fit for a 1.5 mm thick SS ring. The interference fit is between this ring and another 1.5 mm thick SS sheet metal can without any groove. The ring is bent outwards at a specific angle.(please refer attached image) We know amount of...

Homework Statement A Ring with center in (0,0) and R radius. The charge distribution from the ring is: ψ(θ) = ψo*Sin(θ), where θ is the angle from the x-axis (counterclowise). Negative values of the sine determine negative charge, and 0 no charge at all. What is the field (E) created from this...

Homework Statement This problem involves solving a simple differential equation. A block of mass ##m## slides on a frictionless table. It is constrained to move inside a ring of radius ##l## that is fixed to the table. At t = 0, the block is moving along the inside of the ring (in the...

If you look at this YouTube video you will see an example of a ring vortex made by a dolphin (there are quite a few other examples). The problem is I can't understand why the ring doesn't immediately float to the surface. Only when it breaks up do the bubbles rise. The ring appears to...

If a star with enough mass to become a black hole is rotating before it becomes a black hole, then the singularity of the black hole will actually be a ring singularity. How is it possible?

I am reading T. S. Blyth's book "Module Theory: An Approach to Linear Algebra" ... ... and am currently focussed on Chapter 1: Modules, Vector Spaces and Algebras ... ... I need help with an aspect of Theorem 1.1 part 4 ... Theorem 1.1 in Blyth reads as follows: In the above text, in part 4...

I am reading T. S. Blyth's book "Module Theory: An Approach to Linear Algebra" ... ... and am currently focussed on Chapter 1: Modules, Vector Spaces and Algebras ... ... I need help with an aspect of Theorem 1.1 part 4 ... Theorem 1.1 in Blyth reads as follows:In the above text, in part 4 of...