Ring Definition and 1000 Threads

In this lecture, the lecturer claims that the ##C^{\infty}##-module of smooth vector fields defined on a smooth manifold can lack to admit a basis (not even infinite dimensional). Indeed the set of smooth vector fields can be given an (infinite dimensional) vector space structure over the field...

How to calculate the field due to a uniformly charged ring at a point not on the perpendicular axis of the plane of the ring I have tried using coulomb's law and divergennce of the electric potential but I always stumble with a complicated integeral

https://unionrayo.com/en/100-euclid-discovers-einstein-ring/

So to begin with, I did this: $$ \begin{align*} dm &= \frac{M}{2\pi} d\theta \\ dN &= dm \cdot g = \frac{M}{2\pi} g \, d\theta \\ df &= \mu_k \, dN = \mu_k \frac{M}{2\pi} g \, d\theta \\ f &= \int df = \int_0^{2\pi} \mu_k \frac{M}{2\pi} g \, d\theta \\ f &= \mu_k \frac{M}{2\pi} g...

In principle, the ring is, at any instant, a beam being loaded in the centre, and in a failing state. Thus, to drive the material continuously through the rollers, Force x Velocity = Work done/time = power. 60.P/2.pi.N = T The units pan out, but is the concept correct? The faster the work is...

Showing the motion is simple harmonic seems routine. The 5th equation on p. 674 gives ##E=frac{1}{4\pi\epsilon_0}frac{qx}{(a^2)+(x^2)}^frac{3}{2}##, but matching expressions for ##\omega=k/m## yields only ##x=frac{ea^2}{2}##. Something in the model is escaping me. Thanks for any help offered!

I do not know how to solve this. All I got was to exclude the speed of the ant relative to the ring from the equation for its full speed

Hello, I have a question about the FFT and would like to share my thoughts with you. The background is a problem 30.2-6 from the legendary algorithms book by Cormen. It says that instead of doing an n element FFT over the field of complex numbers, we can use ##\mathbb{Z}_m##, where ##m = 2^{t...

...this element ##r## can only be ##0## correct? The zero ring has only one element which is ##0##.

A bead is kept at the bottom of a vertical frictionless ring , if the ring is given an acceleration a horizontally, what is the maximum angular displacement of the particle? The problem is easily solved from the frame of reference of the moving ring, I am however Intrested in a solution without...

Hi, I have problems with the task part b and g To solve the task, we have received the following information Task b First, I wrote down what the state ##\psi## looks like $$\psi=\frac{1}{\sqrt{N}} \sum\limits_{k}^{} \psi_k$$ $$\psi=\frac{1}{\sqrt{N}} \sum\limits_{k}^{} \frac{1}{\sqrt{N}}...

Let E be a finite nonempty set and let ## \Omega := E^{\mathbb{N}}##be the set of all E-valued sequences ##\omega = (\omega_n)_{n\in \mathbb{N}}F##or any ## \omega_1, \dots,\omega_n \in E ## Let ##[\omega_1, \dots,\omega_n]= \{\omega^, \in \Omega : \omega^,_i = \omega_i \forall i =1,\dots,n...

hello i would to get some help with my homework. 1. true 2. i dont know 3. true 4. i dont know 5, false 6. i dont know about 2,4,6 i really have know idea what to think I really appreciate help

Hi all, I'm attempting to build a jumping ring apparatus (a core of iron with the bottom wrapped with wiring like an electromagnet, so that when a metal ring is placed on top of the coil and a current is run through the coil, the ring jumps up into the air). Looking on the internet, I'm seeing a...

If we consider the coefficient b as the rings impedance, we can consider the effective impedance on the right to be b+Z2 where Z2 is the impedance of the second string. Then because there is no reflection it follows that Z1=b+Z2 or b=Z1-Z2. Is this a valid solution? My professor went through a...

For all the attention we‘ve paid to ring habitats, we haven’t talked that much about the interior design of the central trunk yet, around which the rings rotate. Just having one big hollow ship trunk, about 100 metre in diameter, would be a lot of wasted space. It would also be too easy for...

This is a topic that will be relevant for anyone who plans to use "realistic" artificial gravity (of the centrifugal kind, rather than the "acceleration-based" kind) in their stories - be it on spaceships or space stations: How much of the ring walls has to be dedicated to radiation shielding...

Hi! For this problem, Why is the area of each ring segment dA equal to (2π)(r)(dr)? However, according to google the area of a ring segment (Annulus) is, Many thanks!

Hi! For this problem, The solution is, However, why did they not include constants of integration in their working shown in red? Many thanks!

Square matrices are closed under addition and their own form of multiplication, but in general do not commute. What algebraic structure then describes this, along with polynomials of matrices and allows us to amend with other operations, such as differentiation or integration defined on these...

Am going through this notes...kindly let me know if there is a mistake on highlighted part. I think it ought to be; ##α^2=5+2\sqrt{6}##

This is the diagram provided in the question: The ring is made of conducting material. I was originally asked to find the potential difference between ##a## and ##b##. I did so using the Hall effect (and assuming it would work as per normal in this situation). This got me ##\Delta V = vBl##...

My 15 y/o daughter is in driver's ed. Her teacher passed on some information as fact that seems more like an urban legend. He told the class that an inexperienced driver got into a bad car wreck, and the sudden loss of speed caused her belly button ring to penetrate her entire midsection like...

As can be seen below we have 3 ring magnets. The middel one floats in between the other two. We want to know how to calculate the air friction of the middle ring magnet if this rotates.

My current spaceship design with several ring habitats (6 in my case) works well for worldbuilding purposes, in the sense that the reader should easily be able to tell what types of facilities can be found where on the ship. That’s because the rings distinguish themselves from each other by...

Hi. I have solved the problem below as shown in the attached image. However I'm at a loss to figure out where I am making a mistake, and I know it is indeed a big goof up. Requesting guidance over identification and rectification of this big goof up. (Edit- I can solve this problem in the...

A point charge of value q=8uC is released from rest at a point 1.5m away from the center of the axis of a ring with uniform charge density 3uC/m. The ring has a radius of 10 cm. What is the kinetic energy of this charge when it is 4.5 cm from the center of the charge ring, considering that it is...

As a result of one of our previous discussions, I had drastically cut down the distance between the six rings of my fictional generation ship Exodus to a mere 5 metres. Only recently did it occur to me that the airlocks on each ring existed primarily to allow the first crew to board the ship...

What i don't understand is why we are able to replace the ring with 'two oppositely charged superposed disks'? Just trying to understand.. So we have a uniform charge which means that this'll just be a simplification of the problem than, correct? Thanks in advance.

Ok for ##1##, we also have, ##a⋅0=a⋅(0+0)=a⋅0 + a⋅0 ## We know that ##a⋅0=0 ## by additive cancellation. For ##2.11##, Number ##2##; We first show and prove that ##-b=-1⋅b## adding ##b## on both sides, ##-b+b=0## for the lhs ##-1⋅b +1⋅b=b(-1+1)=b(0)=0## for the rhs therefore...

Homework Statement:: See attached Relevant Equations:: Ring Theory Trying to go through my undergraduate notes on Ring Theory ( in appreciation to my Professor who opened me up to the beautiful World of Math)...anyways see attached... I need some clarity on the zero divisor. I am aware that...

Lets suppose a half ring whit internal radius a and external radius b and height t. We can calculate the resistance of the half ring considering that it is made of a number of parallel resistors each one with resistance given by: R = ρ L/S where L = π·r and S = t·dr. The resistance of each...

We know that $$V_Z=\int_{\textrm{ring}} E\cdot dl$$ We therefore consider ##E=\dfrac{\lambda}{2\pi \varepsilon_0}\cdot \dfrac1r##. Then, $$V_Z=\int_{\textrm{ring}} \dfrac{\lambda}{2\pi \varepsilon_0}\cdot \dfrac1r\, dl = \dfrac{\lambda}{2\pi \varepsilon_0}\dfrac1r \int_{\textrm{ring}}dl=$$...

I have the calculation of the electric field created by a ring of radius ##R## uniformly charged with a linear density of charge ##\lambda## at any point on the axis perpendicular to its surface (##z## axis), but I have some doubts about it. I'll leave you the calculation done first: In ##x##...

Could I ask for a hint as to where to go next with this question please? I've done this first part, to find the reaction on the wall. Here's my diagram: I've labelled the internal forces at B in red. In green I've shown the reaction at the ring. So I need to find sqrt(Rx^2 + Ry^2) = R. So...

Does anyone know of a Kernel I can use to find a ring in a image ?

Greetings, while studying the stress in the rotating thing ring and find out the last equation that says I would like to understand why? Thank you!

I don't understand why there is potential difference between point A and O. Is there any change in magnetic flux experienced by the ring? I think the magnetic field passing through the ring's cross sectional area is constant Thanks

Hi ... How can I find the electric field due to a thin circular ring of radius a and charge q for points outside the plane of the ring? The distance from the center of the ring to the point of the electric field is large compared to the radius of the ring. I have answered it but I don't know if...

hi guys I am trying to calculate the the potential at any point P due to a charged ring with a radius = a, but my answer didn't match the one on the textbook, I tried by using $$ V = \int\frac{\lambda ad\phi}{|\vec{r}-\vec{r'}|} $$ by evaluating the integral and expanding denominator in terms of...

I read that "the azimuthal drift is compromized because the typical life expectancy of ring current particles is only hours to days and thus of the same order of magnitude as the drift period". But, if it is so, why relevant current exist? How could we armonize the fact that the azimuthal drift...

This is the initial setup of the problem: The electric field due to the ring is: $$E = \int\frac{k(dq)}{(\sqrt{R^2 + x^2})^2}\frac{x}{\sqrt{R^2 + x^2}} = \frac{kqx}{(R^2 + x^2)^{3/2}}$$ the force on the rod due to this Electric field produced by the ring is: Consider a differential element...

Hi, I'm not quite sure if I'm correct. I need to find the boundary conditions for 2 ropes ##T_1 \mu_1, T_2 \mu_2## fixed at ##x=0## to a massless ring with a massless damper of force ##F_d - -bv_y## Here what I think, since the ring and the damper is massless ##\sum F_y = 0##. Thus, ##-T_1...

When moving around a circular spinning space station (doughnut shaped) Is there any difference in the direction one goes? Is the energy expenditure the same or different? Would one ever feel like one is climbing? My gut feeling says no, as the person walking has the angular momentum matching...

This is an offshoot of @Angela G 's thread. I don't want to hijack her thread so I decided to create a new one. Original thread https://www.physicsforums.com/threads/unstable-or-stable-electrostatic-equilibrium.1007881/ @kuruman @PeroK @bob012345 If you have the time I'd appreciate your input...

In a previous thread* the field in a charged ring was discussed and it was shown to be not zero except at the center. In *post #45 a video is referenced that says the field diverges as one gets close to the ring and it was argued that at very close distances the field looks like an infinite line...

I have broken the ring into a top arc and a bottom arc. First, let's assume an imaginary charge of +1 C is placed at point P. We will determine the force on this unit charge from top and bottom arcs. The charges in the top arc will result in electric fields that will all cancel each other...

Hello! Long story short, I am interested in installing a snap ring rated for 5 mm diameter shafts over a 6 mm diameter shaft into the appropriate groove. For several reasons, I cannot use other types of retaining rings (i.e. side mount E-style retaining rings, etc). This is the snap ring...

I thought of few scenarios and they ended up as follows: The ring must have an induced current. Due to the symmetry of the ring, if one part of the ring feels a force, the part of the ring radially opposite this part will feel a force opposite in direction, since the current will be opposite in...