deriving Definition and 1000 Threads

Hi, The origin of this question was contemplating how to express the impedance of an inductor as a function of frequency, for non sinusoidal voltage wave-forms such as triangle waves, but in particular rectangular pulse trains. So going back to basics, I watched this video: He derives the...

Hi, I was trying to see where the equation N = No e-λt came from and it is derived from dN/dt = -λN which is discussed very well in this thread in post #2 (https://www.physicsforums.com/threads/derivations-of-the-decay-constant-equation.213312/). I understand the steps except for the reason why...

Hi, I am trying to learn Geometric Algebra by going through the book "New Foundations for Classical Mechanics" by David Hestenes. I was reading the part about reduction formula (shown below) but couldn't get the result the shown in the book. Can someone show me how iterating (1.15) gives the...

Homework Statement The problem is taken from Morin's book on classical mechanics. I found out Lagrangian of motion. Now to solve, we need small angle and small x approximation. The small angle approximation is easy to treat. But how to solve small x approximation i.e how do I apply it...

Homework Statement I want to try to derive the rocket equation and then add additional effects like gravity, air resistance, etc. Here's the equation that I found online: Homework Equations p (momentum) = mass * velocity F (force) = Δp / Δt The Attempt at a Solution [/B] pi = mv Here is...

Homework Statement This post contains the answer to my thread of 10th August... [/B] in which I asked if anyone could point out how to derive ##\pi^{ij} = \sqrt {^{(4)}g} (^{(4)} \Gamma ^0 \,_{pq} - g_{pq} ^{(4)} \Gamma ^0\, _{rs} g^{rs}) g^{pq} g^{jq}## from ##\mathfrak {L}## = (4)R...

Homework Statement This isn't a request for assistance, I am just posting this to help anyone else in the future who wants to see how MTW's equation 21.90 can be developed from the simple Lagrangian. MTW's Equation 21.83 is simply ##16π\mathfrak{L}_{geom} = (-^{(4)}g)^{(4)}R## One page...

Homework Statement i don't understand where the 1.22 number comes from like in ## sin \theta = 1.22 \lambda /D ## so i tried to derive but to not much help Homework Equations electric field at distance R due to slit of length D is ## E = \frac{\epsilon_l D}{R} sinc(\frac{kD}{2}sin \theta)sin(wt...

Homework Statement [/B] The problem consists of deriving the matrix for a 3 dimensional rotation. My approach consisted of constructing an arbitrary vector and rewriting this vector in terms of its magnitude and the angles which define it. Then I increased the angles by some amount each. I...

Homework Statement Sorry for so many posts lately, hopefully this is allowed. What tangent points on ##g(x)=\frac {12} {x+1}## has an instantaneous rate of change of -3? Homework EquationsThe Attempt at a Solution [/B] I know that once I derive ##g(x)=\frac {12} {x+1}## I can set the...

Homework Statement Starting with the second order polarization in the time domain: (1) I am trying derive the frequency domain form: (2) Multiple sources give essentially the same formula with the same integral, I have obtained the particular ones in here from those lecture notes. My...

Homework Statement I've been working through a paper by Alexey Golovnev, title 'ADM and massive gravity' arXiv.1302.0687v4 [gr-qc] 26 March 2013. I am hoping to use his result for the Einstein-Hilbert density to achieve my aim of finding a way to derive Equation 21.90 in MTW. I have worked my...

Is it possible to derive the Lorentz transformation from time dilation and length contraction? If so, how should I start? I know how to derive it while considering 4 scenarios finding values of A, B,D,E in x'=Ax+Bt t'=Dx+Et and the transformation is: x'=(x-vt)/sqrt(1-v^2/c^2)...

How can we derive Lorentz Transformation ? I used one approach using the length contraction and time dilation and simultaneity but my prof wasnt much happy about it. Is there any other way to derive it ?

Homework Statement How can we derive Lorentz Transformation using the length contraction and time dilation equations of relativity ? Homework Equations ##γ = 1/ (\sqrt{1-u^2/c^2})## ##t = t_0γ## ##L = L_0/γ## The Attempt at a Solution [/B] In position Lorentz Transformation calculations...

Hi, If I have a massive particle constrained to the surface of a Riemannian manifold (the metric tensor is positive definite) with kinetic energy $$T=\dfrac 12mg_{\mu\nu} \dfrac{\text dx^{\mu}}{\text dt} \dfrac{\text dx^{\nu}}{\text dt}$$ then I believe I should be able to derive the geodesic...

Dear @ll, the central point (for the unitary gauge) in the higgs-mechanism is the equality Φ = (v + η + iξ) = (v + η)ei(ξ/v) (see for example Halzen, Martin: Quarks and Leptons, eq. 14.56) Φ = complex scalar Field v = vacuum that breaks the symmetry spontaneously η,ξ = shifted...

Hi there - it has been quite a long time since I took Calculus. I am trying to brush up and understand where to start with this question: Starting with the identity a^x = e^xlna, derive the relationships between (a) e^x and 10^x; (b) ln x and log x. Note: log x = log10 x unless otherwise...

Homework Statement If you look in Wikipedia for ADM formalism, you are given a Derivation, which starts from the Lagrangian: ##\mathfrak {L}## = (4)R ##\sqrt{^{(4)}g}## and moves rapidly to... The conjugate momenta can then be computed as ##\pi^{ij} = \sqrt {^{(4)}g} (^{(4)} \Gamma ^0...

Homework Statement The problem I have been working with recently has been deriving the speed of light using maxwells equations, however in order to do this I must make two assumptions; there is no net charge or displacement currents in the space in which I am attemptin to derive the speed of...

I am a retired High School teacher trying to use tensors in getting the Euler-Lagrange equations from the em lagrangian density. I attached a document in my post since I am not fluent in writing LaTex. Can anyone, please check my work. Thanks.

Where can I find a detailed derivation for GHZ theorem for 3 particles?

I'm trying to make sense of the derivation of the Klein-Gordon propagator in Peskin and Schroeder using contour integration. It seems the main step in the argument is that ## e^{-i p^0(x^0-y^0)} ## tends to zero (in the ##r\rightarrow\infty## limit) along a semicircular contour below (resp...

Hello, I was watching a video on the derivation of the Maxwell-Boltzmann distribution function which would eventually lead to: $$\frac{e^{-\beta \cdot \epsilon_i}}{\sum_{i=0}^n e^{-\beta \cdot \epsilon_i}}$$ To do this, initially, the number of possible permutations ##\Omega## of a total of...

Homework Statement This is from Griffith's Introduction to Electrodynamics, where the book is deriving the magnetic dipole moment from multipole expansion of the vector potential The vector potential of a current loop can be written as $$\mathbf{A(r)}=\frac{\mu_0 I}{4\pi} \left[ \frac{1}{r}...

Homework Statement Homework EquationsThe Attempt at a Solution I only need help on part c. I tried to add up t1 and t2 and differentiate it. However what variables should I differentiate with respect to? If I differentiate with respect to f I got f=root(2) * h, if i differentiate with respect...

I was reading the derivation of Boltzmann distribution using the reservoir model. lets call the reservoir by index R and the tiny system by index A. In the derivation they proposed that the probability for being at energy e (for A) is proportional to the number of states in reservoir. I didn't...

Homework Statement Hi I'm attempting to derive the gravitational potential energy of a point mass (##m##) that's moving from infinity to a point r' inside a gravitational field produced by a another mass ##M##. For simplicity I treated it as a one dimensional case. The problem I get is that the...

Hello,I am not sure if these types of problems are Intermediate or advanced. I am not sure too whether they have a certain name or not. I have a function inside a definite integral. The solution of this definite integral is known. What is the function that satisfy the known solution. In...

Homework Statement attached: I am stuck on question 2, and give my working to question 1 - the ##B(r) ## part I am fine with the ##A(r)## part which clearly is the same in both regions seen by looking at ##G_{rr}## , and attempt, however I assume I have gone wrong in 1 please see below for...

Homework Statement Hi, So I'm having some trouble deriving the biot savart Law. We have been given a derivation in the notes and I understand everything up until the last step which is labelled in the picture? Equating the two, How did the B vector turn into dB? It seems like he...

Homework Statement The actual question was deriving Bose-Einstein, but I got confused on the F-D example. I'm basically following the method given here. Homework Equations [All taken directly from the above link] Taylor series: The Attempt at a Solution So after that third equation...

Hi guys, thanks for helping with this! I'm a little stuck with this question about the derivation for relativistic mass. 1. Homework Statement By considering the inelastic collision of two balls as perceived in different reference frames show that the relativistic mass is equal to the rest...

Homework Statement I have to derive the Nodal and Principle points distance equations. Homework Equations Equations can be found here http://scienceworld.wolfram.com/physics/ThickLensFormula.html The Attempt at a Solution I have no clue about how to approach this problem. If...

Homework Statement Derive the equations for the thick lens and obtain, ##\frac {1} {f}=\frac {n_L-n'} {nR_2}-\frac {n_L-n} {nR_1}-\frac {(n_L-n)(n_L-n')} {nn_L}\frac {t} {R_1R_2}## Homework Equations ##n## is the medium where light ray enters, ##n_L## is the medium of the lens and...

1. the question is this: a projectile's speed at launch is four times its speed at the top of the trajectory. What is the launch angle? I am given no numerical values, but from my understanding gravity is a constant 9.8, and at the maximum height velocity should be equal to 0. 2.the equation...

I am studyng accretion process on "Astrophysics in a nutshell" by Dan Maoz and I have some doubts about the derivation of the formula for the eddington limit. I understand what the edding limit is. The accretion rate cannot be arbitrarly large. The starting point is to consider an electron at a...

Hi. I am working through " A Student's guide to waves " by Fleisch. In deriving the wave equation for a longitudinal wave it uses dψ = (∂ψ/∂x) dx where ψ is the displacement but ψ is a function of x and t ; so shouldn't this equation be dψ = (∂ψ/∂x)...

Hello Physics Forums, I am studying the equations related to analytical ultracentrifugation. The equation I am interested in describes centrifugation equilibrium, ie at the point in time when sedimentation is balanced with diffusion in the ultracentrifuge. Fortunately, unlike the Lamm equation...

Homework Statement Derive an equation for the velocity vx(t), vy(t) of the particle. - my teacher writes this oddly, that means the velocity in the x direction at any point in time, and the velocity in the y direction at any point in time. Calculate the initial velocity of the particle...

Hello PF, I was reading through “A First Course in General Relativity” by Schutz and I got to the part where he derives the divergence formula for a vector:$$V^α { } _{;α} = \frac {1} {\sqrt{-g}} ( \sqrt{-g} V^α )_{,α}$$I’m having trouble with a couple of the steps he made. So we start with the...

I am trying to find a paper which explains the derivation of the Cosmological Constant. I looked several books and sources and it only says " The cosmological constant ##Λ## appears in the Friedmann equation as an extra term" or etc. Sometimes It directly puts it in the Friedmann Equation which...

Homework Statement so i read morin's derivation of rocket equation propelled by photons now i want to try for relativistic mass ejection but i am having some problems let subscript e denote quantities of ejected material and subscript of r denote quantities of rocket Homework Equations ## P =...

i have been asked to show that the TGF acting on a 1kg mass, on the surface of the Moon is equal to: TGF = 2g.e^2.(a/r^3) Where; g = 9.81 e = radius of the Earth a = radius of the Moon r = distance between the centres of the Earth and Moon.

Homework Statement There is a picture attached showing the entire problem. Equation 2.78 is the Clausius Clapeyron equation. Homework Equations Clausius Clayperon equation. L = L'T (since there is a linear dependence on temperature) The Attempt at a Solution $$ \frac{de_s}{dT} =...

Two small blocks, each of mass m, are connected by a string of constant length 4h and negligible mass. Block A is placed on a very rough tabletop as shown below, and block B hangs over the edge of the table. The tabletop is a distance 2h above the floor. Block A is then released from rest at a...

So, while textbook was deriving Liouville eq, this is one of step the book uses. I don't understand this step at all. Why is this step true?

It seems that one can derive all the fundamental equations of QFT and, consequently, of non relativistic QM, by requiring ##U(1), SU(1),SU(2),SU(3)## symmetries. Also, it seems that one can succeed in doing so if one considers the irreducible representation of those groups. My question is, Do...

Homework Statement the calculation can be considerably simplified by using the so called method of images. In this method, the electric field and potential produced by the induced charge distributed on the sphere can be represented as an electric field and potential of a single point charge...

Homework Statement Taken from Purcell Problem 1.33 Consider the electric field of two protons a distance b apart. The potential energy of the system ought to be given by U=∫E2dv. Let E1 be the field of one particle alone and E2 that of the other. Evaluate ε0∫E1⋅E2dv. Set one of the protons...