Derivation Definition and 1000 Threads

Homework Statement derive the angle of limitation sinθ=[(n2^2-n3^2)^1/2]/n1 n1 is the air out side of the fibre n2 is inside of the fibre n3 is the fibre wall Homework Equations Snells Law: n1sinθ1=n2sinθ2 The Attempt at a Solution I'm pretty stuck and don't really know...

Homework Statement Derive the 2 divergence equations from the 2 curl equations and the equation of continuity. Homework Equations ∇°D=ρ ∇°B = 0 ∇xE = -∂B/∂t ∇xH = J + ∂D/∂t ∇°J = -∂ρ/∂t (equation of continuity) The Attempt at a Solution 1)∇xE = -∂B/∂t ∇°(∇xE) = ∇°(-∂B/∂t)...

Homework Statement Prove for the canonical ensemble ##\overline{(E-U)(p-\overline{p})}=kT[(\frac{\partial U} {\partial V})_{N,T} + p]## Left hand side is covariance E is energy U is internal energy, average of E p is microstate pressure $$\overline{p}$$ is average pressure V is volume N is...

I have been trying to derive the Laplace in spherical co ordinates. I have attached a file which has basic equations. I am trying to get the following equation. d(phi)/dx= -sin(phi)/(r sin (theta)). I have also attached the materials I am referring to. Can someone please help me derive...

Homework Statement I just want to know how to get from this: ∂ø^/∂ø = -x^cosø - y^sinø to this: = -(r^sinθ+θ^cosθ) Homework Equations All the equations found here in the Spherical Coordinates section: http://en.wikipedia.org/wiki/Unit_vector The Attempt at a Solution I've...

Greetings! :biggrin: Homework Statement Starting from the Rodrigues formula, derive the orthonormality condition for the Legendre polynomials: \int^{+1}_{-1} P_l(x)P_{l'}(x)dx=(\frac{2}{2l + 1}) δ_{ll'} Hint: Use integration by parts Homework Equations P_l=...

Homework Statement Think of a fluid between two plates at a distance d from each other in the z-direction; then slide the top plate at a constant speed v_0 in the x-direction while holding the bottom plate still. The fluid pushes back, so you need to apply a force F in order to keep the plate...

Homework Statement Starting with the Lorentz transformation for the components of the velocity, derive the transformation for the components of acceleration.Homework Equations Lorentz Transformation for position and time : ##x'={\gamma}(x - vt)## ##t'={\gamma}(t - {\frac{vx}{c^2}})## Resulting...

hi everyone can anyone please give me a clue of how to derive this equation Hp= Q(gpm)* Δp(psi)/1714 Q is volumetric flow rate Δp is pressure

Hello, I've been looking at the derivation of the exponential function, here http://www.statlect.com/ucdexp1.htm amongst other places, but I don't get how, why or what the o(delta t) really does. How does it help? It's really confusing me, and all the literature I've looked at just...

I have been reading Lagrangian from Classical Mechanics by John R. Taylor. I have adoubt in a derivation which invloves differential calculus. I have attached snapshot of the equation , can someone please explain. Here y,η are functions of x but α is s acosntant. Please let me know if I...

Hi, Apologises if I have submitted this issue into the wrong Math forum. However, I was wondering if anybody could help me with 2 steps in a derivation of an equation. Simply by way of background, the derivation is linked to formation of a superposition wave subject to a Doppler effect [1]...

Hi, Can anyone give a derivation of the quadrupole moment in the TT gauge ( Equation metioned below ) of the gravitational wave ? QijTT(x) = ∫ρ(xixj-1/3δijr2)d3x Where ρ is the matter density Thanks In Advance

Greetings! Going throught Ballentine Ch.4 and the derivation of transmission/reflection coefficients. The math seems fairly straightforward: assuming a particle in a piecewise-constant potential, the solution of the correspondent time-independent SE is a piecewise-exponential wavefunction in...

In lectures I covered how a Schmitt trigger can be used in an RC circuit to determine the capacitance of the capacitor (Where the Schmitt trigger switches at 0.3V+ and 0.6V+). The equation given was that C = 1.2 R \ T (time period) Does anyone know how to derive this or where it comes from...

In a commentary thread DreamWeaver asked if anyone knew of a derivation of the multiplication formula for the Barnes-G function other than the almost impossible to follow derivation in Barnes' original paper. I suggested using the multiplication formula for the Hurwitz zeta function. In this...

I know I have seen this before a few time done a few different ways/starting points and I am always blown away when I see it worked out. Don't know why but I love seeing this derivation. Does anyone want to post the derivation for all to see, it being done a few different ways would be great.

$${\rho}({\lambda}) d{\lambda}=E({\lambda})*f({E(\lambda}))*D({\lambda})d{\lambda}$$ $${\rho}({\lambda}) d{\lambda}$$ is density of radiative energy, $$E({\lambda})= k_BT$$ is the energy of an atom vibrate in 3D, $$f({E(\lambda}))=1$$ is the probability distribution. Equals to 1 because we...

Homework Statement I am supposed to show equation 6.6 on page 97 of http://www.phys.lsu.edu/~jarrell/COURSES/ADV_SOLID_HTML/Other_online_texts/Many-body%20quantum%20theory%20in%0Acondensed%20matter%20physics%0AHenrik%20Bruus%20and%20Karsten%20Flensberg.pdf I have tried to plug A and the...

Would there be a direct proof of the energy-stress tensor of general relativity? My lecturer only provides me with a simplified proof - 1. Guess the form of the tensor in special relativity in co-moving frame (ρ+p)uμuv+pημv Note that the pη00 term cancels the p in u0u0, to simplify the...

Hi, Is it pure coincidence that if you put ##c=v_e=\sqrt{2GM/R}## in the escape velocity, you end up with the Schwarzschild radius ##R=2GM/c^2##? The derivation of the escape velocity is purely classical mechanics. It involves ##E_{kin}=mv^2/2## which is incorrect in special relativity...

Well I was going through class lecture notes and my professor wrote this When x = A(the maximum value), v=0: E=1/2kA^2 When v = wA, x=0: E=1/2mw^2A^2 where w = omega, A = amplitude, k = spring constant, m = mass, v = velocity and apparently both equations are equal, i would like to...

Homework Statement I need to know how to derive the equation for the moment of inertia of a rectangle rotated about an axis through its center. The rectangle has sides a and b. I know the equation to be (1/12)M(a2+b2), but I am having trouble deriving it. I have searched all over the...

Homework Statement You are a member of a research team studying magnetotactic bacteria. Magnetotactic bacteria from the southern hemisphere preferentially swim to the south along magnetic field lines, while similar bacteria from the northern hemisphere preferentially swim to the north along...

This could be seen as a rather "basic" math question, but it is a topic of curiosity for me. I'm currently a senior in high school, taking a pre-ap pre-cal/trig/AP-Calculus double blocked class. I'm absolutely fascinated by mathematics, and something of keen interest to me is the derivation of...

Homework Statement How to get equation 1 from the thumbnail? h1 h2 h3 doesn't have to be constant. The most I can try is equation 2 . Please guide thanks. Homework Equations The Attempt at a Solution

I am looking for a derivation of Friedman's equations from the Cosmological Principle and Einstein's field equations. The text from which I am teaching myself (Schutz) does it all in two massive leaps, whose reasoning are respectively "it is easy to show that ..." (it isn't) and "the Einstein...

Greetings, On page 7 of Landau and Lifschitz Vol. 1 3rd. Ed, it says L(v'^2)=L(v^2+2\bf{v}\cdot\bf{ε}+\bf{ε}^2). They then Taylor expand in powers of ε, getting (ignoring second order terms and higher) L(v'^2)=L(v^2)+\frac{\partial L}{\partial v^2}2\bf{v}\cdot\bf{ε}. The...

Homework Statement I'm trying to work out the derivation of the the Rutherford scattering trajectory. I understand the conservation of linear momentum, and that the only force acting is the coulomb force between the incoming particle and the target nucleus. Early on in the derivation I'm...

Homework Statement Show that \frac{dp}{p} =\frac{\gamma}{\gamma-1}\frac{dT}{T} if the decrease in pressure is due to an adiabatic expansion.Homework Equations Poisson equations: Pv^{\gamma} Tv^{\gamma - 1} Ideal Gas Law: Pv=R_{d}T, where R_{d} is the dry air gas constant. Hydrostatic...

In statistical mechanics the macro-state of a system corresponds to a whole region in the microscopical phase-space of that same system, classically, that means that an infinity of micro-states relate to a single macro-state. Similarly, given a hamiltonian, a whole surface in the microscopical...

I have been reading about the derivation of Clausius' Inequality and there are a few things I do not understand. I have attached an image of the cycles. B) shows one carnot engine performing work ##d W_i## per cycle and delivering heat ##d Q_i## per cycle. For ##T'## to remain unchanged, it...

Does anyone know where this forumula comes from? http://iopscience.iop.org/0067-0049/134/1/151/fulltext/ I don't quite understand the resonance widths, it's probably a naive question but what is 'resonating' in this context? Thanks!

Hey everyone, I'm currently doing research at a University, I've been working on a problem for a few hours and wrote up a quick paper that shows my derivation of a certain height based on an angle. Basically the experiment is looking at optical properties of graphene, but for this to happen we...

I have attempted a derivation of the Students t-distribution probability distribution function in the attached pdf. I defined T to be Z/sqrt(W/v) where Z has standard normal distrubution and W has chi squared distribution with v degrees of freedom. I know that Z and W need to be independent, but...

In my textbook there is a derivation of relativistic kinetic energy starting from an integral of the force applied over the distance required to take the particle's speed from 0 to v. There's one stage of the derivation I don't understand on mathematical grounds, which is going from: $$E_k =...

This is driving me crazy. The derivation of the current distribution in a long cylindrical wire is extremely straightforward, giving J(r) = J(a) \frac{J_0(k r)}{J_0(k a)} where J is the current density, a is the radius of the wire, and k is the complex wave vector, which in a metal (with...

In Griffith's derivation of the quantum SHO, he uses some funny math: first he considers asymptotic behavior to get ψ=Ae-(ε^2/2) then he 'peels off the exponential part' to say that ψ=h(ε)e-(ε^2/2) then he hopes that h(ε) will have simpler form than ψ(ε) I can kind of understand the first...

I am having trouble understanding part of the derivation of Faraday's law given in this lecture at around 57:00 So the first goal is to calculate the change in magnetic flux through a changing closed loop in a dynamic magnetic field, and it's given by the following \phi(t+\Delta...

Hi guys, I have been trying to find the "floppy" resonant mode frequency of a simple oscillator. The displacement is in the order of nanometers, while the dimensions of the oscillator is in cm. I think small angle approximations apply here. I got to the point of the equation of motion, but I...

Can someone explain to me how the Prandtl stress function is derived? The book only briefly describes how the Airy stress function is derived.

S=kln(\frac{eq}{N})N --->= S=Nkln(\frac{q}{N}+1) i understand that the e goes away and the N exponent comes down but where does the +1 come from?

Let number of energy levels be e(subscribe 0), e(subscribe 1)...e(subscribe r) N be the total number of particles and n(subscribe i) be the number of particle in with energy level where i =0,1,2,...r Let Ω be the number of ways attaining a given microstate Ω=N!/[ n(subscribe 0)!*n(subscribe...

Homework Statement Using the trig product identity, cosαcosβ=\frac{1}{2}[cos(α+β)+cos(α-β)], show that the time-average power at the detector can be written as Pavg = 1+cos(δ) That = is supposed to be a proportional symbol. Homework Equations Other than the ones given in the problem...

How is the number of oscillations per unit volume in the frequency range of v and dv is (8v^2*dv)c^3 where c is the velocity of light

Appendix 1 - simple Lorentz transformation derivation found at - http://www.bartleby.com/173/a1.html Given in equation (3) (x'-ct') = Y(x-ct) [Y = const.] by rearrangement, it yields, (x'-ct')/(x-ct) = Y. But it is stated that both (x-ct) and (x'-ct') are zero, so...

Hello there! I'm trying to read a set of notes on the standard model and the author states the following equality without any explanation: -u^{-1}(\partial_\mu u)u^{-1} = \partial_\mu(u^{-1}), u is here a NxN representation of some continuous gauge group and is a function over spacetime...

Greetings, In Griffiths E&M, 3rd. Ed., on page 214, the following is part of the derivation of the continuity equation (the same derivation is shown on the Wikipedia article for the current density, under the continuity equation section: http://en.wikipedia.org/wiki/Current_density)...

Current Density = (I/A) I = (Q/t) = (nVq)/t where n is the number of charges, V is the volume, q is the average charge and t is time. nVq/t = n(Ax)q/t = nAvq where v is velocity. Current Density = (I/A) (nAvq)/A = nvq My question is on the step where it goes Q/t = nVq/t Why does...

I was reading the derivation on Wikipedia: http://en.wikipedia.org/wiki/Group_velocity#Derivation Why is the first part before the integral sign ignored when calculating the velocity? Surely it would also cause a phase shift in some time interval and make the waves move forward (or backward)?