deriving Definition and 1000 Threads

I think I know how to derive conserved energy and momentum currents of a free EM field. Lagrangian is \mathcal{L}=-\frac{1}{4}F_{\mu\nu}F^{\mu\nu} I then substitute x^\mu\mapsto x^\mu + \lambda u^\mu, and take the derivative in respect to lambda. With some trickery I've got \partial_\mu...

Homework Statement Water is filled to a height H behind a dam of width w. Determine the resultant force exerted by the water on the dam. Homework Equations P=pgh = pg(H-y) (where p is density, greek rho) dF = PdA = pg(H-y)wdy (where dA is a narrow horizontal strip of the dam with...

Homework Statement n_1 moles of a monatomic gas and n_2 moles of a diatomic gas are mixed together in a container. Derive an expression for the molar specific heat at constant volume of the mixture. My answer can only use the variables n_1 and n_2, and I'm assuming constants. Homework...

Homework Statement Hello everyone, I'm in need of some assistance in regards to deriving an equation from a graph. I have been tasked to graph information which I've collected through experimentation and then write an equation to represent the graph. I'm stuck at steps 3 and 4 and I am not...

I am supposed to derive 4\,\arctan \left( 1/5 \right) -\arctan \left( {\frac {1}{239}} \right) from the complex product of \left( 1+i \right) \left( 5-i \right) ^{4} I do see how the argument of product of the complex expression is equal to pi/4 - 4 arctan(1/5) but I am totally lost. SO how...

Homework Statement I am trying to derive the mass of \Xi using the formula: M\left(baryon\right)=m_1 + m_2 + m_3 + A' \left[\frac{S_1 \cdot S_2}{m_1 m_2} +\frac{S_1 \cdot S_3}{m_1 m_3} + \frac{S_2 \cdot S_3}{m_2 m_2\3}\right] Homework Equations We have: S_1 \cdot S_2 + S_1 \cdot S_3 +...

Homework Statement Derive Bateman equation for a decay chain a->b->c->d where each decays with a given mean life let decay constant be L, where L=1/mean life Na(0)=No, Nb(0)=Nc(0)=Nd(0)=0 Homework Equations Want to derive Nb(t)={(No)(La)/(Lb-La)}*{exp[-La*t]-exp[-Lb*t]} extend for...

Hello everyone... can someone help me with this problem please: The rotation curve V(r) for a mass distribution characterizes the rotational velocity of a test particle in orbit in its gravitational field as a function of radius from its center. Suppose you have a spherically symmetric mass...

Suppose I had a random variable, X, that followed a Gamma distribution. A Gamma distribution can be defined as \Gamma(\alpha,\beta) , where \alpha and \beta are the 'scale' and 'shape' parameters. Now suppose if \alpha was a random variable, say following a binomial distribution, how would...

Hello again everyone Part of a problem I've been set is to show that the equation: B(r) = \frac{1}{2}\mu_0 (J x r) from Ampere's law: \nabla x B = \mu_0 J. The problem presents no... uh... problem thereafter, but I'm at a loss where to begin. I've been playing around with random...

Homework Statement I have solved the equation for the neutron density as a function of position and time. I need the boundary conditions to change my infinite number of solutions (the varying separation constant) into one value so that my answer for the critical radius does not contain a...

How are the Planck length, Planck time, and Planck mass "derived"? I know their values, but I don't understand where we get them from.

I am having trouble finishing this problem. I am supposed to first derive an equation for V_5 in this circuit: http://img292.imageshack.us/img292/599/picture3qy2.png I applied a Delta-Wye transformation to get here: http://img292.imageshack.us/img292/9672/workot8.jpg From there I am...

Could someone show me a derivation of the Weyl tensor or link me to a good site?

I am curious how you derive this law. It seems that you could derive coulomb ` s law from gauss ` s law, but are there are no similar analogy for Bio-Savart law.

Homework Statement Use the thermodynamic identity to derive the heat capacity formula C_V=T\frac{\partial{S}}{\partial{T}}_VHomework Equations C_V=\frac{\partial{U}}{\partial{T}} T=\frac{\partial{U}}{\partial{S}} dU=TdS-PdV+\mudN The Attempt at a Solution I used...

Homework Statement I have the following question to answer: Show that (X^2/h^2)*((1/2*y1) - y2 + (1/2*y3)) + (X/h)*((-1/2 y1)+(1/2 y3))+y2 (sorry about the format) is equal to (taylor expansion): y = y2+(x(dy/dx)¦0 + (x^2/2*((d^2)y)/(dx^2))¦0 Homework Equations also given in...

Homework Statement A uniform rod of mass M and length L is free to rotate about a horizontal axis perpendicular to the rod and through one end. A) Find the period of oscillation for small angular displacements. B) Find the period if the axis is a distance x from the center of massHomework...

I read somewhere that the whole of magnetism, and in particular the lorentz force, can be found merely by applying the lorentz transformation to transform the coordinates of the electric field of a charged particle from the frame in which the particle is at rest to a frame in which the particle...

Given the following formulaes prove that maximum speed (Vmax) of a mass on a spring is given by 2(pi)(frequency)(Amplitude) (constant k) A^2 = mv^2 + (constant k) x^2 ma = -(constant k)(x) f = 1/2(pi) sqrt (a/-x) and f = 1/2(pi) sqrt (constant k/m) i just don't...

A line charge of liner charge density lambda=4.5 nC/m lies on the x-axis and extends from x=-5cm to x=5cm. Derive an expression for E_y. I have started with this question and it seems that I have to sum the electric fields in the y direction caused by each dx along the line with a charge dq...

Hey... Could someone help me out with deriving the LaPlacian in spherical coordinates? I tried using the chain rule but it just isn't working out well.. any sort of hint would be appriciated. :) \nabla^2 = \frac{1}{r^2} [ \frac{\partial}{\partial r} ( r^2 \frac{\partial}{\partial r} ) +...

I'm in third year undergraduate physics, and more and more I'm seeing problems in homework and assignments that say "Prove that" and "Show that", basically just deriving equations. There's just one problem, I can't do it for the life of me. I had a thermodynamics test recently, and despite...

A body of mass m is in a gravitational field of strength g. The body is moved through a distance h at constant speed v in the opposite direction to the field. Derive an expression in terms of m, h and h, for the work done on the body. Im bad with derivations, I need to get better. So...

I could use some help with this question: Derive the geometric series representation of 1/(1-x) by finding a0, a1, a2,... such that (1-x)(a0+a1x+a2x^2+a3X^3+...)=1 Thank you.

So the problem I am working on is: In the figure, find an expression for the acceleration of (assume that the table is frictionless). I have attached the figure of reference. I have so far tried to solve by first looking at m2 to get: 2T-m_2*g=m_2*a so T= (m_2*(a+g))/2...

Yeah this one is good... Derive the following: int(1/(x^2 + a^2)dx = 1/a*arctan(x/a) + C any idea how I would derive this thing? Cause I'm totally lost...

Hi everyone, Right now, I am working on a homework problem asking me to derive the Compton effect, which is given by \lambda\prime-\lambda=\frac{h}{m_ec}(1-cos\theta) A diagram of the situation can be found here: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/compton.html#c1...

I've been given a small project to ease me into life as a PhD student and part of it involves working out Feynman rules for scalar bosons coupling to gauge bosons. I've been reading through Peskin and Schroder Chapter 9 and want to clarify if I've got my understanding right of how to do it...

Alright, I'm trying to derive the dopper shift using a spacetime diagram (see attached). If we model light pulses then we can derive the distance between the pulses in time, and hence the doppler shift... right? So, if we make some light pulses along some sort of time event in the x, cT frame...

Does anyone know how to derive the spherical unit vectors in the cartesian basis? Or a good link that might show how its done? I would also like to see it done for the cylindrical coordinates. I have tried to do it, especially for the spherical case, but i can only get r-hat. It would be...

I have a question from Strang's Linear Algebra on page 230. Does anyone know how to derive the attached statement?

Can anyone tell me how to derive the sin(x+y) and cos(x+y) expansions? The ones that are like cos x sin y or sin y cos x + other stuff? Preferrably, could this be derived with Euler's formula alone? Or something not too geometric? (All those OAs and OBs and XBs and XYs on geometric diagrams...

Newton's Law of Gravitation Derivative Hi, I was wondering if anyone could help me find the derivative of Newton's Law of gravitation [F=(GmM)/r^2] and what it means? What does the minus sign indicate? I'm kind of confused on the subject at hand and hopefully someone can help out. Thanks

y = ln[\sqrt(x^2+2)] I changed it to y = ln[(x^2+2)^{1/2}] I know the derivative of ln = \frac {1}{x} I'm not sure how to proceed.

I want to derive the theory of finite element using my own understanding. With this derivation i want to understand the fea theory of rod element I call the nodes as "points" in a structure. This scenario is for a simple one dimensional displacement of points(that is the single degree of...

A question asks for me to show that the minimum pressure of a star is given by: P_{min}=\frac{GM^2}{8\pi R^4} where M and R are the mass and radius of the star. My answer goes like this: Gravitational force towards center = \frac{GM(r)\delta M(r)}{r^2} Pressure force outwards =...

Well we start out with -\frac {d} {dt} \int_{V}^{} \sigma dV = \int_{\Pi}^{} \vec{J} \cdot d\vec{\Pi} Using the Gauss theorem \int_{V}^{} (\frac{ \partial {\sigma}}{ \partial {t}} + div \vec{J}) dV = 0 so \frac{ \partial {\sigma}}{ \partial {t}} + div \vec{J} = 0 and written in 4D...

I'm trying to linearize Klein-Gordon equation, following Dirac's nobel lecture: (E^2 - (pc)^2 - (mc^2)^2) \psi = 0 (E + \alpha pc + \beta mc^2) (E + \alpha pc - \beta mc^2) \psi = 0 Expanding the equations yields: -\alpha and \beta commutes with E and p -\alpha^2 = \beta^2 = 1 -\alpha...

I have to show that for a van der Waals gas the critical temperature, volume and pressure are given by: T_c= \frac{8a}{27bR} V_c= 3nb p_c= \frac{a}{27b^2} I started off this way: Van der Waals states that for a non ideal gas the pressure is: P = \frac{nRT}{V-nb} - a...

It's a really easy question, I know, but I must be doing something stupid. Can someone please spell out how to get the right hand side matrix form out of the individual equations? http://img234.imageshack.us/img234/8497/lorentz25wv.jpg

As a refresher exercise in modern physics, I want to derive Wien's displacement law: \lambda_{max}T=2.898x10^{-3}mK from Planck's formula: R(\lambda)=(\frac{c}{4})(\frac{8\pi}{\lambda^4})(\frac{hc}{\lambda})(\frac{1}{\exp^(\frac{hc}{\lambda\kT})-1}) by differentiating R(\lambda) and...

Hello. I need some help with the following problem. There is a cart on an incline and a pulley with a suspended block. Assuming that (the force of friction)= (mu)(N) symbolically show that the coefficient of rolling friction for the car moving down the incline plane with a constant...

I am trying to derive the geometric series for the following given identities, \begin{array}{l} \frac{1}{{0.99}} = 1.0101010101... \; \; \; {\rm{ (1)}} \\ \frac{1}{{0.98}} = 1.0204081632... \; \; \; {\rm{ (2)}} \\ \end{array} Here is my answer for (1), \sum\limits_{n = 1}^\infty...

For a van der Waals gas experiencing an adiabatic process derive the following expression: T(V-nb)^(R/Cv) = Constant I tried using PV^gamma = Constant with gamma = Cp/Cv and Cp - Cv = nR with PV = nRT but could not get it. Any hints? I would have to use Boyle's law to account for...

Using Newton's 2nd Law for a damped oscillator: ma = -kx - \alpha x which is a second order linear DE. To solve it we use the trial integrating factor e^{\lambda x} [/tex] to come to the root equation mx^2 + \alpha x + k = 0 where we can find our two solutions to be r_{1} \ and...

For some reason i can't post in the calculus and beyond section but i was hoping someone could help me with this question eq.1 du/dt - fv = g*(dn/dx) eq.2 dv/dt + fu = g*(dn/dg) eq.3 du/dx+dv/dg=(1/(H)*(dn/dt) manipulate the equations to derivate a single PDE in one variable n which is...

Ok these are the equations I am allowed to use. Ep=mg(delta)h w=fd v_av=(delta)d/(delta)t (delta)d=v1(delta)t^2 + 1/2a(delta)t^2 V2=V1^2 + 2a(delta)d w=work done(j) f=force(Newtons) d=distance(m) v_av=average velocity t=time(secs) v2=final velocity v1=initial velocity a=acceleration...

So, the average rate for a reaction of type A --> product is given by \text{rate} = -\frac{\Delta A}{\Delta t}. Also, \text{rate} = k \cdot \text{A}. The instantaneous rate for a reaction of that type is \lim_{\Delta t\rightarrow\0} -\frac{\Delta A}{\Delta t} = -\frac{dA}{dt}. Setting the...

Given the sum {_\lim {i} \rightarrow 0} \sum_{k=0}^{\frac{x}{i} - 1} i\sqrt{1 + i^{2n-2}((k+1)^{n} - k^{n})^{2}} I want to know how to derive to the value of this sum exactly. This is actually the value of the lenghts of a curve from a point to the origin of the form f(x) = x^n... I thought...