Uniform Definition and 1000 Threads

Homework Statement Assume the roller coaster cart rolls along the curved track from point A to point C under the influence of gravity. Assume the friction between the cart and track is negligible. What would be the direction of the carts acceleration at point A? (The question in the image does...

If you have uniform magnetic field, would something like a halbach array which has a non symmetrical magnetic field experience a net force? If not, is there any way to shield one side of a magnet so that it would experience a net force? On a similar note, if you wound a wire around a sphere in...

Any pure state of spin-1/2 particle can be represented by a superposition of spin up and spin-down relative to an arbitrarily direction. lw>=a l+> + b l-> where a^2+b^2=1 If there is no magnetic field, the measurement of the spin is random and we get 50-50 chance to be spin up and spin down...

Homework Statement Find the z -coordinate of the center of mass of the first octant of a sphere of radius R centered at the origin. Assume that the sphere has a uniform density. Homework Equations Mass = Integral of the density function Center of mass for z = Integral of density * z divided...

Greetings all, I apologize for joining your forum just to inquire about something that should be relatively simple, but you seem like a group of physics geeks able to articulate coherent arguments, and I need someone/s to help me see a different perspective on how to make an argument. For the...

Homework Statement An object with mass m = 2 kg is moving in a uniform circular motion with radius r = 2m as shown in the figure. It takes π seconds for the object to travel from θ =0 to θ = 180 degrees. What is the distance traveled by the object in 20 s...

Homework Statement Hi There, I'm having trouble understanding (what I guess should be) a simple concept and so I can't apply it to a project I'm working on (also kind of rusty on torques and mechanics problems) If I have a hinged beam (of uniform weight) and I lift it from one end and stay...

In uniform curved motion , I can get the acceleration from the equation : A = v2/r , but in non uniform the velocity is changing , so will the certipetal acceleration also change ?

Homework Statement Homework Equations $$a^2-b^2=(a-b)(a+b)$$ The Attempt at a Solution $$a^2=\sqrt{1-x_2^2}\,\,\, ,\ \ b^2=\sqrt{1-x_1^2}$$ $$|a^2-b^2|=\left| \sqrt{1-x_2^2}-\sqrt{1-x_1^2} \right|=\left| \sqrt[4]{1-x_2^2} - \sqrt[4]{1-x_1^2} \right|\cdot\left| \sqrt[4]{1-x_2^2} +...

I am reading "Introduction to Real Analysis" (Fourth Edition) by Robert G Bartle and Donald R Sherbert ... I am focused on Chapter 5: Continuous Functions ... I need help in fully understanding an aspect of Example 5.4.6 (b) ...Example 5.4.6 (b) ... ... reads as follows: In the above text...

Could anyone please let me know if breakthrough spark can happen, or, in general, what will happen in the below system? Note 1: the dielectric layers have a much higher breakthrough voltage than humid air. Note 2: the intensity of the electric field that develops in the flow of the humid air is...

Homework Statement Two identical thin rods of length L carry the same uniform line charge distribution (charge per unit length) of . If the two rods are collinear (aligned along the same line), with a distance of d between their nearest ends, calculate the Coulomb force (magnitude and...

Homework Statement Homework EquationsThe Attempt at a Solution Because of the external magnetic field ##\vec B_0 ## , a uniform magnetization will be in the direction of external magnetic field. Because off this uniform magnetization, there will be a uniform magnetic fied in the direction of...

Homework Statement Homework EquationsThe Attempt at a Solution I have a difficulty in the last part of the problem. Let's assume that gradient of a scalar function ## \lambda ## could be added to the vector potential ## \vec A ##. Then, acc. to the condition ## \nabla . \vec A = 0 ##, we get...

i am stuck on question 9 can anyone help me out. thanks

Can a sphere with a frozen - in uniform polarization ## \vec P ## be considered a linear dielectrics? Following the definition of dielectrics given in Griffiths: The electric field inside the sphere, ## \vec E = \frac {-P}{3 \epsilon_0} ## So, ## \vec P ≠ ε_0 χ_e \vec E ## as ## ε_0 χ_e##...

Homework Statement "*Question 44: Uniform Circular Motion Inside Sphere of Charge The tau particle is a negatively charged particle similar to the electron, but of much larger mass - its mass is 3.18 x 10-27 kg, about 3480 times the mass of the electron and about twice the mass of a proton or...

How does look like electric field lines due to change of the uniform magnetic field? Suppose we have a magnetic field between two infunite plates with surface current $i$ which is lineary change with time. Then B-filel is (x - perpendicular to plates, z and y along plates) \begin{equation} B_z =...

In uniform circular motion, direction of particle is changing at every moment but its speed remains the same. If the magnitude of velocity or speed remains the same, change in magnitude of velocity is zero. Then how come radial acceleration can have a calculated value since acceleration = change...

Does #Time have uniform Scale??

1. The problem statement, all variables, and given/known data Suppose you have a wire of length l and a uniform line charge density λ. Find the electric field at the midpoint that is height r above the x-axis Homework Equations (see attached) The Attempt at a Solution To solve, I used the...

So a light signal is sent off some space behind me. At the same time I start accelerating extremely quickly. Even though the light signal will always be faster than me it will never catch up with me. I have difficulties to understand that something that is always faster than you can still never...

I have been unable to determine whether a Halbach Array of permanent magnets would experience a net force in a uniform magnetic field.

Homework Statement In a certain region of space, there is a uniform electric field of magnitude 25.0 V m^-1 directed at 30.0 degrees to the direction of the positive x-axis and at 60.0 degrees to the direction of the positive y-axis. (There is no z component of the electric field.) The electric...

Hello! Can someone explain to me in an intuitive way the difference between pointwise and uniform convergence of a series of complex functions ##f_n(z)##? Form what I understand, the difference is that when choosing an "N" such that for all ##n \ge N## something is less than ##\epsilon##, in the...

Hi. I have this power serie (2^n/n)*z^n that runs from n=1 to infinity, and I have to show whether it's uniform konvergence on [-1/3, 1/3] or not. I hope someone can help me with this.

In https://en.wikipedia.org/wiki/Galilean_transformation it is shown that translation is different from uniform motion. So, isn't translational motion another name for uniform motion?

Homework Statement Charge is distributed uniformly over a large square plane of side l, as shown in the figure below. The charge per unit area is σ. Determine the electric field at a point P a distance z above the center of the plane, in the limit l -> infinity.. Homework Equations please...

I have learned that the electric field between parallel plates are independent of distance since E=V/d so if I increase the distance between parallel plates, the E will decrease, right? if I am right on the previous statement, then why does the electric field are independent of distance?

Homework Statement A cat rides a merry-go-round turning with uniform circular motion. At time t1 = 2.00 s, the cat’s velocity is V1 = (3.00 m/s)i + (4.00 m/s)j , measured on a horizontal xy coordinate system. At t2 = 5.00 s, the cat’s velocity is V2 = (3.00 m/s)i + (4.00 m/s)j. What are (a) the...

Homework Statement Prove that f(x) = 1/(|x|+1) is uniformly continuous on R. Homework EquationsThe Attempt at a Solution This needs to be an e-d proof (epsilon-delta). So I suppose we should start with let e>0, then we want to find a d such that for all x,y in R, if |x-y|<d then...

Homework Statement A non uniform disc of radius R has a mass of M. Its centre of gravity is located at a distance x from the centre. Find the moment of inertia of mass (moi) around the axis perpendicular to the surface passinf through the centre of gravity. Homework Equations Parallel axis...

Does time dilation in relative UNIFORM motion REALLY happen or is it merely a perspective from one reference frame relative to another as in the simple case where objects appear smaller the further away they are from the perspective of an observer in a particular reference frame? Putting it...

Homework Statement A particle of mass m is dropped into a hole drilled straight through the center of the Earth. neglecting rotational effects and friction, show that the particle’s motion is a simple harmonic if it is assumed that the Earth has a uniform mass density. Obtain an expression for...

Homework Statement Uniform Slab: Consider an infinite slab of charge with thickness 2a. We choose the origin inside the slab at an equal distance from both faces (so that the faces of the slab are at z = +a and z = −a). The charge density ρ inside the slab is uniform (i.e., ρ =const). Consider a...

Hello! So I've been working on proving to myself different parts of https://ocw.mit.edu/courses/nuclear-engineering/22-611j-introduction-to-plasma-physics-i-fall-2003/lecture-notes/chap2.pdf packet for several weeks. Under 2.1 Uniform B field, E=0, for the Larmor Radius, I need to know...

I'm doing some special relativity exercises. I have to find $$x(t), v(t)$$ of a charged particle left at rest in $t=0$ in an external constant uniform electric field $$\vec{E}=E_{0} \hat{i}$$, then with that velocity I should find the Liénard–Wiechert radiated power. I will show you what I did...

Homework Statement 2 large plates are separated by a distance d and a space charge of uniform charge density p is placed between them and a potential difference V is applied across the plates. Find the electric field stength at a distance x fromt the positive plate The answer is -V/d...

Homework Statement An electric dipole with magnitude ##p = 0.2Cm## is placed inside a uniform electric field of ##\vec{E} = 100\vec{i} + 70\vec{j} + 40\vec{k} \frac {N} {C}##. The dipole was initially pointing along the +x direction. You then start to rotate it first on xz-plane towards...

Considering that all energy gravitates, why is it assumed that the vacuum energy that we measure inside the gravity well of the Milky Way is consistent throughout space? Is there any real way to know? Would it make any difference in the problem that QM and GR differ in the vacuum energy...

Homework Statement A biker is 40.0m to the east of a flag in a park, heading south at 10m/s. 30.0 seconds later, the biker is 40.0m north of the flag and heading east at 10.0m/s. For the biker in this 30.0s interval, what are: a) the magnitude and direction of the displacement? b) the magnitude...

Homework Statement Can someone explain why f(x) = 1/(b-a) for a<x<b ? Homework EquationsThe Attempt at a Solution shouldn't it be 0? since its a continuous random variable and so that interval from a to b has an infinite number of possible values?

Homework Statement In the notes , it's stated in the first part for non-uniform flow that the gradient of $$S_0$$ , $$S_w$$ and $$i$$ are not the same , But , in the lower part , it's stated in the first part for non-uniform flow that the gradient of $$S_0$$ , $$S_w$$ and $$i$$ are the...

Homework Statement 1. Show that for an arbitrary uniform triangle ABC, with A at (x1, y1), B at (x2,y2), C at (x3, y3), the CM (xcm, ycm), is simply defined by xcm=(x1+x2+x3)/3, and ycm =(y1+y2+y3)/3 Homework Equations xcm = 1/M * ∫xdm ycm = 1/M * ∫ydm M = ∫dm = ∫δdA where δ = M/A = dm/dA...

Hey! :o I want to check the pointwise and uniform convergence for the following sequences or series of functions: $f_n:[0, \infty)\rightarrow \mathbb{R}, f_n(x)=xe^{-nx}$ for all $n\in \mathbb{N}$ $f_n:[0, \infty)\rightarrow \mathbb{R}, f_n(x)=nxe^{-nx}$ for all $n\in \mathbb{N}$...

Homework Statement Let ##Q = \{(x_1,x_2,...,) \in \mathbb{R}^\omega ~|~ \lim x_n = 0 \}##. I would like to show this set is closed in the uniform topology, which is generated by the metric ##\rho(x,y) = \sup d(x_i,y_i)##, where ##d## is the standard bounded metric on ##\mathbb{R}##. Homework...

Homework Statement A uniform plank, of weight 30N and length 3m, resting on two supports. The supports are 0.5m and 2.0m from the left-hand end of the plank. A weight of 18N is suspended from the left-hand end of the plank. By how much should the weight on the left-hand en be increased so...

Homework Statement Let ##f:X \to Y##. Show that ##f## not uniform continuous on ##X## ##\Longleftrightarrow## ##\exists \epsilon > 0## and sequences ##(p_n), (q_n)## in ##X## so that ##d_X(p_n,q_n)\to 0 ## while ##d_Y(f(p_n),f(q_n))\ge \epsilon##. Homework Equations Let ##f:X\to Y##. We say...

Homework Statement A slab of dielectric of thickness a and relative permittivity ε is placed in a uniform external field E whose field lines make angle θ with normals to the surface of the slab. What is the density of polarization charge on the surface of the slab? Neglect end effects...

Hi, I started to study the function of Weierstrass (https://en.wikipedia.org/wiki/Weierstrass_function) And in one part says that the sum of continuous functions is a continuous function. i understand this but the Limiting case is a different history depend of the convergence, so what i need...