Ring Definition and 1000 Threads

So I have a ring(red) of uniform charge ##\lambda## per unit length, and I want to calculate the electric potential at the origin (actually on any point of the ring). It is clear that the ring is given by the equation $$r=2 R \sin \theta$$, in polar coordinates, where R is the radius of the...

consider a small element that subtends an angle ##2\Delta \theta## at the center of the ring. balancing the forces on this element gives: (let the field due to the ring be at its circumference be ##E##). $$2T\Delta \theta = E(dq) = E (\frac{Q}{2\pi})(2\Delta \theta)$$ $$T = \frac{EQ}{2\pi}$$ now...

To find ##\delta## for the 1st order, all I need to do is to square the diameter of the 2nd ring and subtract it to the square of the diameter of the first ring. $$\delta_{1st \; order} = {d^2}_{2nd \; ring} - {d^2}_{1st \; ring}$$ To find ##\Delta##, I can use the below equation...

In this photo you see on the right-hand side that the outer wall current is negative and the inner wall current is positive. That is, they are directed in different directions. But if the applied magnetic field is in the z direction as shown, then shouldn't they both be in the same direction do...

Summary:: Please see the attached photo. I have obtained the correct answer, and my solution agrees with the official solution. However, I have some questions about why the solution is correct. (One may have to draw out some diagrams for this problem, it was quite hard to visualise for me.)...

I am just a bit confused here. Would doing this even change the electric field direction at the center at all? I'm thinking no, but a bit of direction would be appreciated. This problem is really simple, I'm just a bit confused.

The physics behind this problem is that an electric field is induced (by Faraday's Law), when the B field is switched on. Charges on the ring now experience a force as given by dF = E dq. Apparently, because of this, the ring starts rotating. I understand that charges in an insulating material...

Admittedly I found similar threads here already but due to my rather lacking math skills I wanted to go through this myself. As for the math side, I see various different equations with which this is treated can someone please provide the formulas for calculating B field from a rotating charged...

I know the solution for the problem of the tension on a rotating ring without gravity (tha is, ##\frac{mR\omega^2}{2\pi}##) - that I find simple enough. But I'm at a loss how can I change it to do with gravity :/ Any help is appreciated! (and apologies for the bad drawing)

a.)N cos θ=mg N sin θ=mrw^2 sin θ cos θ=g/rw^2 b.) My question is reaction force =N ? or =F=mg tanθ ? If it is N then N=mg cosθ =mg^2/r w^2 or N=mg/cosθ =mrw^2 ? Thank you

I have the problem with my solution. I don't know it is correct. Could somebody check it?

The Thompson jumping ring experiment consists in an AC supply connected to a coil with a metal steel core inside. A metal ring is placed around the core. When the AC supply is turned on, the ring suddenly jumps and after a time it starts levitating in a fixed height. I'm a little confused about...

I considered that the lengths of pi/4 and 3pi/4 would be in parallel: 1/R = 1/30 + 1/10 R = 7,5 ohm But the answer is 30 ohm. Where am I missing and how do I calculate the potential of the voltmeter.

I tried finding the potential due to a small element dM of the ring let's say dV, the summation of dV for all the dM's of the ring will give the potential at the point P, but since every element dM of the ring is at a different distance from the point P I am unable to come up with a differential...

I tried considering a little piece of the ring (shaded black below) subtending angle ##d\theta##, and attempted to find the electric field in the vicinity of that piece by a summation of contributions from the rest of the ring: $$dE_x = \frac{dq}{4\pi \epsilon_0 d^2} \cos{\phi} =...

Hi Everyone, I am wondering how to prove an ideal of a ring $R$ which is defined as a coordinates. Let $R$ be the ring of $\mathbb{Z} \times \mathbb{Z}$. Let $I={(a,a)| a\in \mathbb{Z}}$. I determine that the $I$ is a subring of $R$. Next step is to show the multiplication between the elements...

So I have been watching the latest edition of PBS Space Time ( I know, not a proper resource/guide,) and it seems to be a bit confusing as to whether you would hit the ring singularity at the center or not. On the one side he claims that the geodesics end there but on the other he claims you...

Summary:: This question is in relation to finding the mmf of a cast steel ring. Unfortunately I do not know how to post a picture of the page showing the graph. [Mentor Note -- Thread moved from the technical forums so no Homework Template is shown] A cast steel ring has a cross sectional...

I know HNO2 favours diazotisation.So amine reacted and formed diazorised product with N+=NCl- which leaves and gives a carbocation to which OH- attacks.So according to me the answer should be cyclohexane-1,2-diol. But in the answer key,cyclopentane carboxyaldehyde was given as answer. I know it...

This sounds interesting to me. I would appreciate the opinions of more knowledgeable and physics oriented forumists. The paper is in Science (I don't think its open access). Here is the abstract:

I imagine the system where P is in the middle between A and B, and P is also in the middle of light elastic string. Between P and B, there is tension force acting downwards on P. Between A and P, there is tension force acting upwards and because P is in the middle of the elastic string, there...

Proof: ##(\Leftarrow)## Suppose there exists non zero ##b \in R## such that ##bp(x) = 0##. Well, ##R \subset R[x]##, and so by definition of zero divisor, ##p(x)## is a zero divisor. (assuming ##p(x) \neq 0##). ##(\Rightarrow)## Suppose ##p(x)## is a zero divisor in ##R[x]##. Then we can choose...

The increase in radius is due to the centripetal force acting on the ring. The centripetal force acting on each point of the ring is directed towards its center. We can find force using ## F_c = M(\omega)^2R## We can use this ##F_c## in the equation of Hooke's Law to find the elongation Could...

As I`` m learning for an upcoming exam I found an electrodynamics problem I struggle with. In the first task I need to calculate the magnetic dipole moment of a uniformly charged,thin disk with the Radius R and a total charge Q which rotates with a angular speed omega round its symmetry axis...

Here is this week's POTW: ----- Compute the center of the ring $M_n(\Bbb C)$ of all $n\times n$ complex matrices. ----- Remember to read the https://mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to...

Good day I'm trying to calculate the pressure drop in each branch of the following loop ring system I used the following formula to find the pressure drop but i seems that it worked only for the ring, and the branch #2 ( the branch in the middle), the solution given by the professor show...

Okay, I am not even sure how to startr with this question. But here's my theory: First I will need to the electric field produced by the ring using the formula: ##E = k\frac{\lambda a}{(x^2+a^2)^{3/2}}## After finding out electric field produced by ring, am I supposed to find out the...

Quick question about the relativistic energy of a rotating thin ring, hoop or cylinder. Is there any reason why the relativistic energy would be anything different than ##E=\gamma_t m_0 c^2## where ##\gamma_t## depends on the tangential velocity ##v_t## observed by someone at rest with the...

Dear Every one, I am having some difficulties with computing an element in the Integral dihedral group with order 6. Some background information for what is a group ring: A group ring defined as the following from Dummit and Foote: Fix a commutative ring $R$ with identity $1\ne0$ and let...

Dear Everyone, Does every theorem that holds for finite group holds for ring groups? Why or Why not?Thanks Cbarker1

I'm not sure how will this oscillator work. Assume A is low, so B will be high and the capacitor will charge through B-C- 2Mohm. Now even D has gone high, so A will be high and B will be low and C will discharge. I'm not sure how the voltage divider rule across RC will take into effect. I found...

Problem (c) for Discrete Value Ring for a unit I am stuck in the middle of a proof. Here is the background information from Dummit and Foote Abstract Algebra 2nd ed.: Let $K$ be a field. A discrete valuation on $K$ on a function $\nu$: $K^{\times} \to \Bbb{Z}$ satisfying $\nu(a\cdot...

Purpose is to make a ring.

Dear Everyone, I am stuck in the middle of a proof. Here is the background information from Dummit and Foote Abstract Algebra 2nd ed.: Let $K$ be a field. A discrete valuation on $K$ on a function $\nu$: $K^{\times} \to \Bbb{Z}$ satisfying $\nu(a\cdot b)=\nu(a)+\nu(b)$ [i.e. $\nu$ is a...

Dear Everyone, I am stuck on a portion of the sub-ring criterion. The Problem states: "The center of a ring $R$ is $\{z\in R| zr=rz \ \forall r\in R\}$. Prove that the center of the ring is a subring that contains the identity as well as the center of a division ring is a field." I am doing...

Dear Everyone, I am having trouble with an exercise problem. Here is the problem: Dummit and Foote Ed.2 pg 231: "Let $R$ be a ring with 1. Prove that if $u$ is a unit in R then so is $-u$." My Attempt: Suppose $u$ is a unit in $R$. Then, from Prop 1 (4) (if $R$ has an identity, then the...

They seem to mean the almost the same thing, with a field allowing subtraction & division whereas a ring only needs addition & multiplication. Is that a ring can mean "addition" & "multiplication" in some way that isn't between numbers per se, but between whatever abstract things can be dreamed...

Hi. This picture shows an iron ring shielding a static magnetic field: Does this really work, and why? I know that a conductor can shield an electric field (Faraday cage) and a changing magnetic field (Lenz's law), but why would it shield a static field? Especially since iron is a ferromagnet.

What the differences between Field and Ring?

Homework Statement Let ##R## be the ring of all continuous real-valued functions ##f : [0,1] \to \mathbb{R}## with pointwise addition and pointwise multiplication of functions as its two operations. Let ##c \in [0,1]## and denote ##M_c = \{f\in R : f(c) = 0\}##. a) Show that any ##f\in R##...

Homework Statement For a commutative ring ##R## with ##1\neq 0## and a nonzerodivisor ##r \in R##, let ##S## be the set ##S=\{r^n\mid n\in \mathbb{Z}, n\geq 0\}## and denote ##S^{-1}R=R\left[\frac{1}{r}\right]##. Prove that there is a ring isomorphism $$R\left[\frac{1}{r}\right]\cong...

I learned this in college too. I once know the name of these zero friction piston rings but I have forgot. If I knew the name I could do Google search and learn more about them. College professor said, grooves are .020" wide and .020" deep. Pressure drop across the grooves make them act like...

We know that kernel of a homomorphism consists of all the elements that map to the additive identity, 0. Here is my naive question: Why don't we define the kernel as all of the elements that map to the multiplicative identity, 1? Why isn't there a name for the set of all elements that map to the...

Could someone clarify the notion of a ring with identity element $1=0$? Apparently it's just the zero ring, but then why do we always talk about a ring with identity $1 \ne 0$? It's like having to talk about prime $p \ne 1$; instead we don't define $1$ as a prime but also because we would lose...

Homework Statement Let ##S=\{a+bi+cj+dk \mid a,b,c,d \in \mathbb{Z}\}## be the ring of integral Hamiltonian quaternions, where multiplication is defined using the same rules as in ##\mathbb{H}##, the ring of real Hamiltonian quaternions. Define a function $$N:S\to\mathbb{Z}...

Homework Statement A solid sphere, hollow sphere, disk and ring are released simultaneously from top of a incline. Friction is sufficient to prevent slipping of hollow sphere- what will reach the bottom first? Homework Equations a in pure rolling down an incline=gsinθ/(1 + I/mR^2) The Attempt...

Hi all. First, some context. I work for a small seed oil extraction plant where we cold press the seed then solvent extract the residual oil from the presscake. In the solvent extraction plant we use liquid ring pumps to pull the required vacuums. The Plant Vac Pump (PVP) is used in all...

Homework Statement a)recall that electric potential is a scalar quantity. For a circular ring of radius, R', carrying charge, Q, what is the electric potential at a height,y, above the center of the ring? b)Use your above answer to determine the electric potential at a height,y, above the...

Homework Statement Homework Equations charge density equations, electric field equations, The Attempt at a Solution My attempts are attached. The attachment labeled A, is part A. Part B took a lot of paper so there are two attachments labeled B1 and B2. It is really B and C that I am...

Homework Statement The electric field on the axis of a uniformly charged ring has magnitude 360 kN/C at a point 6.2 cm from the ring center. The magnitude 19 cm from the center is 150 kN/C ; in both cases the field points away from the ring. Homework Equations 1. Find the ring's radius. 2...