deriving Definition and 1000 Threads

Homework Statement Consider a very thin conducting ring of radius R which contains a total positive charge of +Q coulombs. (a) Derive a formula for the z coordinate which gives the maximum value for the magnitude of E ring (Z)? (b) Suppose that the charged ring is oriented horizontally, as...

I've been sitting at my desk trying to prove this and nothing, already tried googling.. Any help guys? I want to know how to derive it from basic principles. Thanks How I came by it: I'm a high school student and was doing my exam then get asked about drift velocity and it's not even in the...

Hi All, I am currently reading Menzel's "Mathematical Physics" and one part in particular confuses me. When he is introducing Riemannian Geometry he derives the Christoffel symbols almost out of thin air. He starts by differentiating a vector with respect to a coordinate system...

Hi I know the general equation for shear stress in beams is this: Shear Stress τ = F/Ib ∫y dA Depending on the shape of the cross section (ie. If its an I beam, T-beam, hollow square/circle) , after integration we will end up with a different equation. I want to know the exact procedure to...

Preface to my question: I can assure you this is not a homework question of any kind. I simply have a pedagogical fascination with physics outside of my own studies in school. Also, I did a quick search through the forum and could not find a question similar enough to what I want to know, so i...

I know you can derive the double angle formulas for sin(2a) and cos(2a) from Euler's identity, but is there any way to derive the tan(2a) in a similar manner from an easier formula? What about the addition/subtraction formulas (i.e. sin(a+b), etc.)

Deriving Probability Density Functions from Partial Differential Equations? Hiyas, I have been told that it is quite normal to get PDFs (Probability Density Functions) from PDEs (Partial Differential Equations). That in PDEs that the function can be a PDF and you can get this by solving the...

I hope I can make sense out of this question. Suppose I have an image of the sky and know on that image say the RA/Dec and x,y position of 20 stars, and the time the image was taken. The zenith is somewhere in the middle. Now suppose one hour later I have another image of the sky, and would like...

So I'm having problems being able to derive the MGF for Y = Z^2 where Z ~ N(0,1).I was able to obtain the density function: [y-1/2 / (2pi)1/2] e-y/2 now to get the MGF of this I know I have to integrate from -∞ to ∞: [y-1/2 / (2pi)1/2] e-y/2 etYthis is where my issue is, I'm having...

Hey all, making my way through Landau and Lifgarbagez classical theory of fields and i had a specific question on the Einstein equations. Following the palatini approach, we assume that the connection and metric are independent variables and are not related a priori. In the footnote, they say...

Hi, Bernoulli's/Newton's classic elastica equation is of the form: 1) curvature = dθ/ds The RHS reforms to the well known elastica equation: 2) d2y/d2x/(1+(dy/dx)2)3/2 How do I get from 1) to 2)? Regards,

Homework Statement Hey all, I am encountering a problem with a derivation of the formula K_{ineticEnergy}=mc^2-m_{0}c^2 as it is described by my textbook. I need someone to explain to me how the author changes the integral and the upper limit of it in the final part. I'll now give you the...

Pls does anyone know how to derive for Vout1 and Vout3 in terms of Va and Vb for an inverting operational amplifier. Thank you.

I am trying to understand the meaning of the Ricci Tensor. I tried to work it out in a way that was meaningful to me based on ideas from Baez and Loveridge. Unfortumately, the forum tool won't allow me to include the URLs to those documents in this post. Anyway, I get the wrong answer. Can...

A straight wire clamped vertically at its lower end stands vertically if it is short, but bends under its own weight if it is long. It can be shown that the greatest length for vertical equilibrium is l, where kl(3/2) is the first zero of J-1/3 and k=4/3r2*√(ρg/∏Y) where r is the radius, ρ is...

Since Ac = Dv/Dt (Ac being constant acceleration) I can isolate Dv and integrate both sides...did I derived the final equation correctly?http://img685.imageshack.us/img685/211/ssvvssvv.jpg Is that right?

Since the issue of deriving the Born rule comes up from time to time in the forum and I'm always a little mystified by some of the opinions people have. I recently fleshed out the details about the derivation I'm about to present and realized it pretty much makes the Born rule a triviality, so I...

Homework Statement Hi I'm doing a physics lab about uniform circular motion to measure frequency and to compare it to mass,radius and force tension. (A & B) I did (C,D, E) I need help (a) What variables are being measured / manipulated in this lab? What type of relationship is being...

Hi, I'm having a problem with a MATLAB assignment in my probability class. It has to do with finding the joint and marginal PDFs of a pair of random variables. I understand this stuff on paper, but for some reason this assignment is giving me problems since I don't have a good idea of how the...

Hi guys, I derived an equation for determining orbital period, given an altitude, speed, and mass of the primary and the object orbiting it. I think it makes sense, but I'd welcome anyone who is willing to check it for conceptual error or nonsensical math. Here is the equation: P = \frac{2 \pi...

We're asked to derive the following equation: F=\triangledown(\vec{m}\cdot \vec{B}) by evaluating F=\int I(d\vec{l}\times \vec{B}) along a sqaure loop with sides of length ε, parralel to the yz plane. The square's bottom left corner is situated at the origin. so far I have, d\vec{l}...

Hi everyone, I am currently working on a program which involves stabilizing a man wearing a jetpack at some arbitrary point along the vertical axis. This program is part of an experiment my faculty mentor gave me. Basically, what I am trying to do is have the Jetpack man stabilize at a point...

Homework Statement Show that the exit intensity as a function of Io (intensity out of light source) and θ12 (angle of second polarizer compared to the first polarizer) is I = (Io/8) sin(2(θ12)))^2 Homework Equations Malus' Law I = Io (cosθ)^2 The Attempt at a Solution I1 =...

Hey all, I posted this in the Astrophysics sub-forum, but traffic here seems higher (if a mod sees this, can you close the other thread please?) Long story short, for my Modern Physics course, we have to do a research paper on a physics topic we didn't cover in class. Since I've always...

Hey all, Long story short, for my Modern Physics course, we have to do a research paper on a physics topic we didn't cover in class. Since I've always been interested in astronomy and the cosmos, I figured I'd do star formation / life cycle of stars. The paper has to have mathematical and...

Homework Statement Consider an electromagnetic wave hitting a metallic surface with conductivity σ at normal incidence. a) Derive the wave equation describing this situation. Hint: Use Ohm’s law, J = σE to eliminate the current. b) Solve the wave equation for the electric field to...

Homework Statement The rotation matrix below describes a beam element which is rotated around three axes x,y and z. Derive the rotation matrix. http://img194.imageshack.us/img194/3351/60039512.png http://img808.imageshack.us/img808/159/64794596.png Homework Equations -The Attempt at a...

Folks, Consider a 2d disk with 2 forces ( ie a bolt pattern) acting axially ie into the page. One can easily get the equivalent force and its point of application to represent the given force system. One can do the same with an annulus, get an equivalent force and its point of application...

Homework Statement A very long solenoid of circular cross section with radius a= 4.80 cm has n= 77.0 turns/cm of wire. An electron is sitting outside the solenoid, at a distance r= 5.30 cm from the solenoid axis. What is the magnitude of the force on the electron while the current in the...

Homework Statement Derive the equation for the potential energy of a system of 2 hydrogen atoms as a function of internuclear distance. Homework Equations For electron/electron and nucleus/nucleus repulsion: V_E=\frac{e^2}{4\pi\epsilon_0 R} For electron/nucleus attraction...

Short story: How does one go about to derive x = a cos(wt)? The way it is derived in my book is from the "SHM Diagram" file that I have uploaded but it seems that the diagram is incorrect as it does not correspond to the expression. Also, why is the Amplitude in the expression constant when the...

Homework Statement Figure 5-53 shows Atwood's machine, in which two containers are connected by a cord (of negligible mass) passing over a frictionless pulley (also of negligible mass). At time t = 0 container 1 has m1 and container 2 has mass m2 with m1 < m2, but container 1 is losing mass...

I am doing an undergraduate project on bars and I am trying to derive the bar instability mode given by Mo et al. It says "whether or not a disk is globally stable depends on the global properties of the disk... it is not possible to write down a universal dispersion relation or stability...

Homework Statement Determine the error in the calculated centripetal force, F (dynamic), for each value of r from the estimated error in the quantities m, r, and from the standard deviation from the mean of your three measurements of f. Derive the equation for the error using Rule # 2 for...

My classmate has already asked about this I think, but since I can't find the post I'll ask again.. Take a single atom with degenerate energy levels E1, E2 etc. We place the atom in a resevoir and want to find the probability of probability for finding the atom in the different energy states...

Homework Statement I am not fully sure where this is supposed to go, so forgive me if I get it wrong. I am just undertaking some private research and want to see if my work is correct. I wish to derive the Kinetic energy of something moving according to classical mechanics. Homework Equations...

(the following is Mathematica code) For the rice pdf... P(x)=(x/σ^2) BesselI[0, x (ν/σ^2)] Exp[-(x^2 + ν^2)/(2 σ^2)] ...the Second raw moment is given by doing the integral... Integrate[(x^3/σ^2) BesselI[0, x (ν/σ^2)] Exp[-(x^2 + ν^2)/(2 σ^2)], {x, 0, Infinity}] While the answer...

Deduce the formula giving the energy levels in terms of n for a free particle in a box of length l, using the fact that only stationary waves can be occupied by the particle. - considering stationary waves, λ = 2l/n. (1) 1) Using E=hv/λ= hvn (2) And P = h/λ, v = h/m*λ, v = hn/2ml (3)...

Hey ^^, new here but I already have a question haha Does anyone here know how the coefficient (x-μ)^2 was derived in the following equation: σ^3=(1/√2∏)∫(1/σ)*(x-μ)^2*exp((x-μ)^2)/(2σ^2)) I know the general equation for density probability is (1/σ)*exp((x-μ)^2)/(2σ^2)) but in this case...

Hello all I have a question about Markov chain I've obtained in an application. There is no need to mention the application or the details of markov chain because my question is simply: The transition probabilities are derived with equations that depend on the stationary probability, I know...

Homework Statement Why does lim( (1+(1/n))^n ) = e?Homework Equations If a_n convergent to a, and b_n converges to b, then (a_n * b_n) converges to (a * b)The Attempt at a Solution The lim(1 + (1/n)) = 1. If you multiply (1 + (1/n)) by itself n-times, you get the equation (1 + (1/n))^n, so...

Homework Statement A derivation of Instantaneous Velocity Arc length = s = θ * r ds/dt = d(θr)/dt = Instantaneous V Product rule: V_{t} = (dθ/dt)*r + (dr/dt)*θ V_{t} = (dθ/dt)*r + 0 V_{t} = ωr Question: Why does dr/dt*θ = 0 ?

Homework Statement Solve the logistic population model: dP/dt=rP(1-P/C); P(0)=P_{0} 2. The attempt at a solution First, I separated variables to get: \int \! \frac{1}{P(1-P/C)} \, \mathrm{d}P = \int \! r \, \mathrm{d}t Then, I took the left hand side and split into partial fractions: (1) -...

So this is my first quantum mechanics class and so far we have spent about a month (well 3 weeks) on just the mathematics. So in my book, the author explores the ideas presented by the stern gerlach experiment. It related the beam of silver atoms traveling through the separators to light...

Homework Statement Marian who is standing on her balcony is surprised by a pigeon, and throws a flowerpot up, in the air at 2.1 m/s. It takes a total of 3 s for the flowerpot to smash to the ground. The flowerpot experiences acceleration due to gravity of 9.8m/s a) How high is Marians...

Homework Statement Consider a rigid sphere of radius 1 and center at (0,0,0) that rotates about its center. The angular velocity is $\omega(t) = (\cos(t) , \sin(t), \sqrt(3))$. Does the path of the point starting at (0,0,1) ever reach this point at a later time? Homework Equations...

I have attached a PDF with some equations. (a) is essentially describing a pure state quantum system, with (b) and (c) statistical mixtures. I've managed to substitute (d) and (e) into (b) and (c) respectively, however I was wondering how to substitue (d) and (e) into (a). Apparently...

It might be difficult for you to read this integral in non latex form, but i'll try my best. As i don't know how to write this in latex form, assume "for this problem" that I(n) is pronounced as "I subscript n" or nth term of I. Homework Statement I(n)=∫ (sinx)^n dx [with...

Why in deriving invariant distance in space time we use Pythagorean Theorem with a negative sign?

Derivation of simple harmonic motion I'm looking at the wikipedia page for simple harmonic motion (http://en.wikipedia.org/wiki/Simple_harmonic_motion) and I'm confused by this line: c_1cos(\omega t) + c_2sin(\omega t)=A*cos(\omega t - \phi) How did they get from the left hand side to the right...