Uniform Definition and 1000 Threads

Homework Statement A current carrying wire is bent into a circular loop with radius R and lies in the XY plane. A uniform magnetic field in the +z direction exists through out the plane of the loop. What is the magnetic force exerted on the loop? Homework Equations Fb = I lb sin (theta) The...

I need to prove that the complex power series $\sum\limits_{n=0}^{\infty}a_nz^n$ converges uniformly on the compact disc $|z| \leq r|z_0|,$ assuming that the series converges for some $z_0 \neq 0.$ *I know that the series converges absolutely for every $z,$ such that $|z|<|z_0|.$ Since...

Hello, I am stuck at this exercise: 1. Homework Statement X ~ U(0, a), a > 0 and Y = min(X; a=2). - Find the cumulative distribution function of Y -Is the variable Y continuous ? Homework Equations 3. The Attempt at a Solution [/B] The density function for X is f(t)= 1/a if 0≤t≤a , 0...

So I am starting to learn for the final exam a bit early and I am trying to do this problem with a uniform beam which is reinforced with iron inside. I know how to calculate this if it wasn't for the reinforcement within the concrete. I know that the purpose of the iron reinforcement is to...

Hello, I've been attempting to do these problems from my textbook: 1. Suppose that $$f$$ is a continuous function on a bounded set $$S$$. Prove that the following two conditions are equivalent: (a) The function $$f$$ is uniformly continuous on $$S$$. (b) It is possible to extend $$f$$ to a...

Homework Statement The wait time (after a scheduled arrival time) in minutes for a train to arrive is Uniformly distributed over the interval [0,12]. You observe the wait time for the next 95 trains to arrive. Assume wait times are independent. Part a) What is the approximate probability (to 2...

Hi Guys, new poster here. I am currently doing a practical report on Uniform Circular Motion, where we had to swing a rubber stopper around attached to a length of string and mass. I have to do a write up, including the background theory. I have searched everywhere but I have found no clear...

Homework Statement [/B] a) In a certain region of space, the volume charge density p has a uniform positive value. Can E be uniform in this region? Explain. b) Suppose that in this region of uniform positive p there is a "bubble" within which p=0. Can E be uniform within this bubble? Explain...

Homework Statement Hi all. Please help me with this. A small particle moving with a uniform acceleration a covers a distances X and Y in the first two equal and consecutive intervals of time t. Show that a = Y-X/t². Homework Equations Acceleration is usually v-u/t i.e. rate of change of...

1. A charge density ρ (charge per unit volume) is distributed uniformly throughout a non-conducting cylinder of radius R. What is the magnitude of the electric field a distance r = R/2 from the cylinder's axis? Homework Equations E ∫dA = q(interior)/ε0[/B]3. So I tried doing EA =...

This problem has charge that is not uniform in the inside, but it is still possible to find the electric field as a function of distance outside the slab using Gauss's law. How is this possible if the electric field is not uniform in the slab and plane? Wouldn't the electric field from the...

Homework Statement [/B] Charge is distributed uniformly over a large square plane of side l, as shown in the figure. The charge per unit area (C/m^2) is \sigma . Determine the electric field at a point P a distance z above the center of the plane, in the limit l \to \infty. [Hint: Divide the...

1. Portion of z-axis for which |z| < 2 carries a non uniform charge density of 10|z| (nC/m). Using cylindrical coordinates, determine E in free space at P(0,0,4). Explicitly show your integration.Homework Equations E = (1/4πε0) ∫ dQ*aR/(R2)The Attempt at a Solution...

Homework Statement Find the potential V(r) inside and outside of a uniformly charged sphere with radius R and total charge q. A) Fix first the charge density ρ(r) in the two regions 1: r>R and 2: 0<r<R the results should only be in terms of q and R[/B] Homework Equations ρ= qtot/Vtot dq=...

Hello, I have two jobs,Normal distribution with mean of 4.5 minutes and standard deviation of 1.5 minutes for type 1 and uniformly distributed between 1 and 3 minutes for type 2

Suppose a particle undergoing uniform circular motion completes a cycle, then ##<\vec{v}> = \frac{Δ\vec{r}}{Δt} = \vec{0}##. But then again, isn't it also the mean of the two velocity vectors at that point? And aren't those two velocity vectors equal? So if the velocity at that point were, say...

I've attached an image of part a of the question to this thread. My question is this (the solution to these former homework problems are posted to help us study for exam, which is why know this already): The angle between the two velocity vectors is determined to be pi/2. How? I know that dot...

Homework Statement A thin line of charge is on the x-axis from x = -L/2 to L/2. The charge density is non uniform and given by λ = ax where x are the points on the charge distribution. Calculate the electric field for all points along the y axis. Homework Equations E = kQ/r^2 The Attempt at...

Hi there, I'm trying to brush up on some of my E&M and am comparing treatments of Coulomb's Law in introductory calculus-based texts with higher level material. My understanding was that Coulomb's Law (and by extension, calculation of the electrostatic force on a charged particle using F = qE)...

Homework Statement Electric field at a distance 'a' from the end of a solid uniform charge volume dq = Pdv dv = (pi)(y)(dy) A = (pi)(y) dE = f(dq) Homework Equations What is the starting integral The Attempt at a Solution limits from 0 to b (k)(p)(pi)(y)(dy) E =...

Homework Statement An airplane flies in a loop (a circular path in a vertical plane) of radius 120m . The pilot's head always points toward the center of the loop. The speed of the airplane is not constant; the airplane goes slowest at the top of the loop and fastest at the bottom. At the top...

√Homework Statement Show that the gravitational field due to thin uniform circular plate of radius a at point distant R from center and on the axis passing through the center and perpendicular to the plane of the plate is given by E= -2πGρ[1-R/(a^2+R^2)^1/2] Homework Equations F= GMm/r^2...

Uniform circular motion requires a force perpendicular to the velocity. Therefore, the work done by such a force is zero because the dot product of the force and the path is zero. So there is no energy gain beyond the kinetic energy arising from its constant speed. But if I have a mass (rocket...

Homework Statement A lift ascends from rest with uniform acceleration of 4m/s², then it moves with uniform velocity and finally comes to rest with uniform retardation of 4m/s². If the total distance covered during ascending by the lift is 28m and the total time for ascending 8s respectively...

So I'm reading "An Introduction to Wavelet Analysis" by David F. Walnut and it's saying that the following sequence " (x^n)_{n\in \mathbb{N}} converges uniformly to zero on [-\alpha, \alpha] for all 0 < \alpha < 1 but does not converge uniformly to zero on (-1, 1) " My problem is that isn't...

Homework Statement Given a uniform bar of length L, which point should you hang it from (between 0 and L) so that you get maximum frequency for small oscillations? Homework Equations ... The Attempt at a Solution It seems like a basic problem, but I don´t know how to start. Could you guys...

My book says that for uniform rotational flow, the velocity at any point is proportional to r (v = wr.) In vortex flow, the velocity at any point is proportional to 1/r (angular momentum is conserved.) However, in uniform rotational flow, isn't angular momentum also conserved so the same logic...

Homework Statement Given a uniform plane wave in air as: E_i=40cos(wt- Bz)a_x +30sin(wt- Bz)a_y (a) Find H_i (b) If the wave encounters a perfectly conducting plate normal to the z axis at z = 0, find the reflected wave E_r and H_r. (c) What are the total E and H fields for z < 0?Homework...

Homework Statement [/B] A uniform solid ball of mass m rolls without slipping down a right angled wedge of mass M and angle θ from the horizontal, which itself can slide without friction on a horizontal floor. Find the acceleration of the ball relative to the wedge. 2. The attempt at a...

Homework Statement So a body $m$ is on a uniform circular motion ($\omega = d\theta/dt = \text{constant}$), it is suspended by an inextensible rope with negligeable mass Homework Equations P = mg , didnt know what to put here The Attempt at a Solution So this is what the book did. What I...

Homework Statement Attached file Homework Equations Attached file[/B]The Attempt at a Solution Attached fileSorry, I am in mobile, so i cant Write all the things,

Homework Statement Hi I am supposed to calculate the distance traveled by a particle that is uniformly accelerated with acceleration equal to the Earth's gravity (i.e. a=9.81m/s^2) after 1, 10 and 100 years proper time. Homework Equations We derived in class the four vector which describes the...

[Note by mentor: This thread does not use the homework template because it was moved here from a non-homework forum.] Hello, I have a problem with this exercise. I don't know if my solution is right! Could you check it, please? A proton with kinetic energy Kp is moving in a uniform magnetic...

The position function for a particle moving on a circle (with constant speed) is: ## \vec{r}(t)=\left \langle r\,sin(t), \, r\,cos(t) \right \rangle ## Taking the first and second derivatives, ## \vec{v}(t)=\left \langle -r\,cos(t), \, r\,sin(t) \right \rangle ## ## \vec{a}(t)=\left \langle...

Homework Statement Two particles, each of mass m, are attached one to each end of a diameter PQ of a uniform circular disk, of mass 4m, radius a with its centre at O. The system is free to rotate about a horizontal axis through A, a point on PQ such that OA = b as indicated in the diagram...

Homework Statement Hello, I have to calculate the self-energy of an uniform charged electron with radius R. The distributed charge is e. Homework Equations The SE is given as: E=\frac{1}{2}\int dV \int dV' \frac {\rho(\vec r)\rho(\vec r')}{ |\vec r - \vec r'|} according to the problem sheet...

Homework Statement A construction worker attempts to lift a uniform beam off the floor and raise it to a vertical position. The beam is 2.26 m long and weighs 397 N. At a certain instant the worker holds the beam momentarily at rest with one end a distance d = 1.21 m above the floor, as shown...

Homework Statement If ##X\sim\mathcal{U}(-1,1)## and ##Y = X^2##, is it possible to determine to ##cov(X, Y)##? Homework Equations \begin{align} f_x &= \begin{cases} 1/2, & -1<x<1\\ 0, & \text{otherwise} \end{cases}\\ f_y &= \begin{cases} 1/\sqrt{y}, & 0<x<1\\ 0, & \text{otherwise} \end{cases}...

Homework Statement A 1.60 m long rod rotates about an axis through one end and perpendicular to the rod, with a rotational frequency of 6.91 radians per second. The plane of rotation of the rod is perpendicular to a uniform magnetic field of 0.30 T. Calculate the magnitude of the mf induced...

Is there a formula for the moment of inertia? A thin, uniform density rod is rotating about an axis that is off the end of the rod, so it looks a bit like this: ------- | (------- is the rod and | is the axis of rotation, so the rod is rotating out of the plane of your screen) I just have...

Homework Statement On a banked race track, the smallest circular path on which cars can move has a radius of 116 m, while the largest has a radius of 153 m, as the drawing illustrates. The height of the outer wall is 11.6 m. Find (a) the smallest and (b) the largest speed at which cars can move...

Homework Statement 2. Homework Equations [/B] So the sample mean is 2. the sample variance would be [[(3-1+1)-1]/12]/36 = 8/432. The Attempt at a Solution Is it, P[ (2.1-2)/sqrt(8/432) < z < (2.5-2)/sqrt(8/432)] = 0.232574. The book answer is 0.2312. I just want to be sure.

Homework Statement A uniform rope of length L and mass M is held on a frictionless table by a force F. One fourth of its length (¼L) is hanging over the edge. Find the work required to pull the hanging part back onto the table. Homework Equations W=Fd The Attempt at a Solution I have no...

Homework Statement A centrifuge is a device in which a small container of material is rotated at a high speed on a circular path. Such a device is used in medical laboratories, for instance, to cause the more dense red blood cells to settle through the less dense blood serum and collect at the...

Homework Statement In this question, the Earth is modeled as a uniform sphere of radius 6400km. Objects are released from points just above the Earth's surface at the equator and at the North Pole. Which will fall to the Earth with the greater acceleration and by how much? Homework Equations...

Desloge (1989) published the article: ## '##Non-equivalence of a uniformly accelerating reference frame and a frame at rest in a uniform gravitational field## '##. His result, briefly resumed: a uniform gravitational field is not flat, is quite interesting. But the way he proves the result is...

Consider a test charge is moving in and electric field of a parallel plate capacitor then : Force F = ma In an electric field, F = qE For an electron in field E, qE = ma => a = qE/m As the charge is in uniform electric field "E" will be constant . As "E" is the force per unit charge so...

Homework Statement a) Derive the expression for the potential difference due to two uniform infinite sheet charges at y=5 and y=-5 in free space. b) If V=4V at (0,2,10) find V at (-4,3,1) . The surface charge density on the two sheet charges are ?s=?0 col/m2 [/B]Homework EquationsThe Attempt...

a) Derive the expression for the potential difference due to two uniform infinite sheet charges at y=5 and y=-5 in free space. b) If V=4V at (0,2,10) find V at (-4,3,1) . The surface charge density on the two sheet charges are ?s=?0 col/m2 What you guys be able to help me with this ?

Here's the problem: Two particles of mass $m$ and $M$ undergo uniform circular motion about each other at a separation $R$ under the influence of an attractive force $F$. The angular velocity is $\omega$ radians per second. Show that $$R = \frac{F}{\omega^2} \left( \frac{1}{m} + \frac{1}{M}...