Uniform Definition and 1000 Threads

Hi all, I interested in how can I get low of motion in for orbiting particle in a uniform magnetic field $$\frac{d\vec{r}}{dt} = \vec{\omega}\times\vec{r},\qquad \vec{\omega} = \frac{e\vec{B}}{mc},$$ Of course, rotating about z' axis is very simple. \begin{equation}\label{eq:K}...

Hi, I’m new here and I signed up to ask for some help with a physics problem. I’m not trained, nor am I receiving training, in physics. I’m a bachelor of Geoscience student halfway through my course. The problem I have is with understanding and testing the law of uniform motion (I think that’s...

Not sure what I'm doing here. Not sure how to continue? Please help. Thank you in advance!

Basically, I need help to continue on this question. This is what I have now: Angle of the race track (angle of the grey part): tan(18/(169-108)) = 0.30396 Not sure how to continue?? What am I supposed to do and find next? Thank you in advance! :smile::blushing::oldbiggrin:

So, I volunteered to run a seminar to first year students in my college. They got a question like this for homework recently and a lot of them made a mistake in the calculation. I am not asking for help with the question itself because I know how to do it. However, a lot of students made a...

If ##\tau= 0.0727, N=60, i=1.3, B=1.0,## and ##\theta=15##, I tried the following calculation: ##\tau=NIABsin\theta## ##\tau=NIs^2Bsin\theta## ##s^2=\frac {\tau} {NIBsin\theta}=\frac {.0727} {60*1.3*1*sin(15)}=0.0632 m=6.32 cm## The answer is probably right in front of me, but I don't know what...

So, it's a long way to the solution, but I'm finding it difficult to find a starting point. I'm going to say that as a first step, I should find what the value of the stream function ##\psi## is, at the surface. In order to do this, I need to use the following equation: ##F=\phi+i\psi## If I...

My answer will be no for both (a) and (b) because there is no change in magnetic flux experienced by the circular coil. Am I correct? Thanks

Answer is 37.8 g cm^2 new to latex

Hi, I have this question: If random variable T is uniformly distributed over [a, b] , what is its failure rate? Please help

Hi, I am trying to design uniform field gap electrodes using the Rogowski profile. I've read some papers on it, but I'm completely new to this and I am just having a hard time translating what's in the paper to my Matlab code to produce the same results. I'm not sure if this is the right place...

Hi, I am interested in designing an electrode that reduces the peak e-field intensity at the edges of the electrode. I've read some papers and it looks like there are quite a few. I'm not really familiar with the terms, so I decided to start off with what looks like is one of the simpler ones...

I have a lot of questions about this single concept. You don't have to answer the questions in the order that I ask, if it is convenient to answer them in a different order. 1. When the dipole moment ##\vec{p}## is in the same direction as the electric field (uniform) it has the least potential...

Why do they only think of kinetic energy of motion? Why don't they think of both kinetic of motion and kinetic of rolling energy? So. i think ## L = \frac{1}{2}mv^2 + \frac{1}{2}I \omega^2## ## L = \frac{1}{2}m(r \omega)^2 + \frac{1}{2}(\frac{1}{2}mr^2) \omega^2## ## L = \frac{3}{4} mr^2...

Hey! 😊 Let $0<\alpha \in \mathbb{R}$ and $(f_n)_n$ be a sequence of functions defined on $[0, +\infty)$ by: \begin{equation*}f_n(x)=n^{\alpha}xe^{-nx}\end{equation*} - Show that $(f_n)$ converges pointwise on $[0,+\infty)$. For an integer $m>a$ we have that \begin{equation*}0 \leq...

If I use cartesian co-ordinates, I get: ##\bar{x}=\frac{1}{A}\iint x\, dA=\frac{1}{A} \iint r^2\cos\theta\, dr\, d\theta= \frac{2a\sin\theta}{3\theta}## ##\bar{y}=\frac{1}{A}\iint y\, dA=\frac{1}{A}\iint r^2\sin\theta\, dr\, d\theta= \frac{2a(1-\cos\theta)}{3\theta}## But if I use polar...

I couldn't solve the question. Can you help me?

i did not get how the professor came to such result. In particular: in order to evaluate P[x+y<=z] solved a double integral of the joint density. What i am not getting is did i choose the extreme of integration in order to get as result ##\frac {z^2} {2}##

For: a) Avdol did the work because he is the force that is causing the displacement, right? b) Is there another formula we would have to use? I am confused at how this would work out and what the answer would be.

I need guidance on part c, finding the cdf/pdf of Y. I understand that for X>3, Y=6-X and for X<3, Y=X. For X = 3, Y=3 For part b, I got P(Y>y)= (3-y)/3, for 0≤y<3 Now for part c, I know P(Y>y) relates to the cdf. But the definition of cdf relates to P(Y<y), so I'm guessing I have to do...

I do not have the solutions to this problem so I'm wondering if my attempt is correct. My attempt at solution: We have two surfaces which we can calculate the area of. I think we can use gauss law to find the electric field and then integrate the E-field to find the electric potential. So for...

I am trying to calculate the interaction energy of two interpenetrating spheres of uniform charge density. Here is my work: First I want to calculate the electric potential of one sphere as following; $$\Phi(\mathbf{r})=\frac{1}{4 \pi \epsilon_{0}} \int...

So this was a section taken out from a question which I am trying to do shown below I have drawn a sketch to help me visualise of what is going on I have used Fleming's left hand rule to help me determine what direction the force is facing on each side of the coil. For the last part in...

There are two parts to the question Let's start with part :) I understand the definition of Uniform continuity And I think I'm in the right direction for the solution but I'm not sure of the formal wording. So be it ε>0 Given that yn limyn-xn=0 so For all ε>0 , ∃N∈ℕ so that For all N<n ...

I came across the following question: If g and f are uniform continuity functions In section I, then f + g uniform continuity In section I. I was able to prove it with the help Triangle Inequality . But I thought what would happen if they asked the same question for f-g I'm sorry if my...

This is not really homework, but I'm having trouble understanding it intuitively. I came across this when learning about the space charge layer of a diode. The solution I know simply uses the 1D form of Gauss's law: ##\vec{\nabla} \cdot \vec{E}## = ##\dfrac{\rho}{\epsilon_0}## becomes...

dv/dt is the acceleration, so I thought I could find the acceleration from F = qE = ma = dp/dt. But this is a relativistic case, so the proper acceleration is a = F/mγ3, where v in the gamma is the v of the electron and F = eE. However, I'm not sure if this is correct, because the constant τ...

Hello, I hope you are all having a great day ! I've got a physics test in a couple of days and I have some questions:1. In a calculation, if the acceleration is in m/s², I presume the speed also has to be in m/s and not in km/h ? 2. So with this graph (v with t), I have to find the total...

I am trying to push the boundaries of special relativity with a self-imposed challenge problem. A common derivation of relativistic kinetic energy involves an object to which a constant force is applied. I want to consider a similar scenario, but instead of a point object we now have a uniform...

So to start off, what I will do find the center of mass of each of the rods. So for the top rod, COM is at where y= 0.5 L and COM of the rod at the bottom is at x = 0.5 L. From there, how do I proceed in finding the moment of inertia using parallel axis theorem? Do I simply treat: ##I...

A uniform rod AB of length ℓ is free to rotate about a horizontal axis passing through A. The rod is released from rest from the horizontal position. If the rod gets broken at midpoint C when it becomes vertical, then just after breaking of the rod. Choose multiple answeres from the below...

displacement (x) = 750 m [E] distance = 1100 m I drew a diagram. Now what??

Consider a function ##f\in\mathcal{C}^2## with Lipschitz continuous gradient (with constant ##L##)- we also assume the function is lowerbounded and has at least one minimum. Let ##\{x^k\}_k## be the sequence generated by Gradient Descent algorithm with initial point $x^0$ and step-size...

I have to find pμ(τ) of a particle of mass m and charge q with v(0) = (vx(0), vy(0), vz(0)) in a electric field E parallel to the y-axis and a magnetic field B parallel to z axis, both constant and uniform, with E = B. Here follows what I have done (see pictures below): I wrote 4 differential...

a) We can solve for acceleration by looking at FNETy FNETy = FE (G is negligible) FNETy = m * a The mass (m) of an electron is 9.1093836 x 10-31 kg. The elementary charge (q) of an electron is -1.60217662 x 10-19 C a = ε * q / m a = (4.0 x 102 N/C * 1.6022 x 10-19 C) / 9.1094 x...

I started with the first of the relevant equations, replacing the p with the operator -iħ∇ and expanding the squared term to yield: H = (-ħ^2 / 2m)∇^2 + (iqħ/m)A·∇ + (q^2 / 2m)A^2 + qV But since A = (1/2)B x r (iqħ/m)A·∇ = (iqħ / 2m)(r x ∇)·B = -(q / 2m)L·B = -(qB_0 / 2m)L_z and A^2 =...

All i could think is that the z component of velocity will remain unchnged as there is no force in that direction.And for the x and y component can we imagine the helical motion as a superposition of a circle and a straight line.So for x and y component can we solve for a particle moving in a...

In my textbook when proving continuity implies uniform continuity (which is very similar to the proof given here), BWT is used to find a converging subsequence. I cannot see why this is needed. Referring to the linked proof, if we open up the inequality ##|x_n-y_n|<\frac{1}{n}##, isn't by the...

Hello, I am currently stumped over a question that has to do with the continuous uniform distribution. The question was taken from a stats exam, and while I understand the solution given in the mark scheme, I don't understand why my way of thinking doesn't work. The problem is: The sides of a...

I am reading D. J. H. Garling's book: "A Course in Mathematical Analysis: Volume II: Metric and Topological Spaces, Functions of a Vector Variable" ... ... I am focused on Chapter 11: Metric Spaces and Normed Spaces ... ... I need some help in order to understand some...

I'm not too sure how to use the hint here. What I had so far was this: an odd extension of ##f## implies ##f = \sum_{k=1}^\infty b_k \sin(k x)##. Notice for ##m>n## $$ \left|\sum_{k=1}^m b_k\sin(k x) - \sum_{k=1}^n b_k\sin(k x)\right| = \left| \sum_{k=n+1}^m b_k\sin(k x)\right| \leq...

I am reading D. J. H. Garling's book: "A Course in Mathematical Analysis: Volume II: Metric and Topological Spaces, Functions of a Vector Variable" ... ... I am focused on Chapter 11: Metric Spaces and Normed Spaces ... ... I need some help with an aspect of the proof of Theorem 11.1.11...

I am reading D. J. H. Garling's book: "A Course in Mathematical Analysis: Volume II: Metric and Topological Spaces, Functions of a Vector Variable" ... ... I am focused on Chapter 11: Metric Spaces and Normed Spaces ... ... I need some help with an aspect of the proof of Theorem 11.1.11 ...

+(3/2) standard deviations from the mean = \frac {a+b}{12} + \frac{\sqrt3}{4} (b-a) -(3/2) standard deviations from the mean = \frac {a+b}{12} - \frac{\sqrt3}{4} (b-a) \frac {1}{b-a} \int_a^{\frac {a+b}{12} - \frac{\sqrt3}{4} (b-a)} dx = m_1= \frac {(-11+3\sqrt3)a + (1-3\sqrt3)b}{12(b-a)}...

I'm confused what's meant by a uniform surface current density since this plane has a thickness, It would need a current density distributed through its cross sections, I thought.Edit: I tried solving with proper LaTeX and all my steps, but it looked awful. For outside, I got B=µ_0jd/2. for...

Hello, Let's imagine we have an infinite plane (or large enough compared to the region of interest and measurements) pierced in normal direction by magnetic field B which is uniformly distributed but time varying. For the sake of simplicity we'll presume the magnetic induction is linearly (and...

The photo above is the problem I'm struggling now and the photo below is what I have done so far. By differentiating and integrating the given equation, which is F=-b exp(αv), I tried to express v(t) or a(t) as a function related to t, which is time. But the more I did, the more complicated...

Let ##(x_1,y_1)## and ##(x_2,y_2)## be the point where the rods intersect the ##x,y## plane. I know that on any given point there will be the superpositions of ##E_1=\frac{2\lambda}{4\pi \epsilon_0}\frac{1}{(x-x_1)^2+(y-y_1)^2}\hat{r}_1## and ##E_2=\frac{2\lambda}{4\pi...

In exploring the feasibility of constructing a vacuum chamber, I am trying to calculate the thickness of rectangular polycarbonate sheet needed to withstand 100kPa of pressure, given dimensions of 30.5cm by 61cm (12 by 24 inches) and clamped edges. I have found some calculators that will tell...

I can not understand why ##v_x = -|v|sin(θ)## and ##v_y = |v|cos(θ)## I'm asking about the θ angle. If i move the vector v with my mind to the origin i get that the angle between x'x and the vector in anti clock wise, it's 90+θ not just θ. So why is he using just θ? Does the minus in v_x somehow...