Derive Definition and 591 Threads

I was thinking about doing KVL around the circuit at the right but I noticed when the switch opens, the current through the circuit at the right is not the same throughout -5 + Ic*2*1-^3 + Ic*10^3 = -Vc Ic is not the same around the right circuit so I am stuck....

I am following [this YouTube lecture by Schuller][1] where he finds the appropriate formalism for the quantum mechanics in the physical curved space. Everything makes sense to me but at the very end I see that we find the pull backed connection one-form on the base manifold. He says to the end...

If the distance between the centres of two molecules is σ, then imagining a a cylinder with radius σ the number of molecules can be given by πσ²cn where c = average velocity. So mean free path can be given by λ = c/πσ²cn = 1/nπσ². But do I derive it from exp(-x/λ)?

I know we're supposed to attempt a solution but I'm honestly super confused here. I think the second an third terms of the del equation can be cancelled out because there is only an E field in the r hat direction, so no e field in the theta and phi directions. That leaves us with ##\nabla \cdot...

I have been reading Wikipedia’s derivations of the Lorentz Transformations. Many of them start with the equation of a spherical wavefront and this reasoning: - We are asked to imagine two events: light is emitted at 1 and absorbed somewhere else at 2. For a given reference frame, the distance...

tried writing the x position as x = Acos(wt) (ignoring the phase) so that d2x / dt2 = -w2x Substituting that into the individual motion equations would get the required result for the individual masses, but I am not sure how to combine the equations to get the reduced mass

On page 52 in Becker, Becker, Schwarz, there is an equation (2.148) for the number of open string excitation modes. I tried to Tayler expand eq 2.145, but couldn't reproduce 2.148. Plus, one gets 2.145 by setting w close to 1; even if I use the 2.146 and try to analyze it around 0, I am still...

Here, it's shown how white light, after passing from air to another medium, gets broken down into its constituent coloured rays. Each has its own refractive index in the medium, but it's only shown here red, blue and yellow. The auther comments on this image and says that, for small angles of...

Proof: Observe that ## 42=6\cdot 7=2\cdot 3\cdot 7 ##. Applying the Fermat's theorem produces: ## a\equiv 1\pmod {2}, a^{2}\equiv 1\pmod {3} ## and ## a^{6}\equiv 1\pmod {7} ##. Thus \begin{align*} &a\equiv 1\pmod {2}\implies a^{6}\equiv 1\pmod {2}\implies a^{7}\equiv a\pmod {2}\\...

Proof: Observe that ## 15=3\cdot 5 ##. Applying the Fermat's theorem produces: ## a^{3}\equiv a\pmod {3} ## and ## a^{5}\equiv a\pmod {5} ##. Thus \begin{align*} &(a^{3})^{7}\equiv a^{7}\pmod {3}\implies a^{21}\equiv [(a^{3})^{2}\cdot a]\pmod {3}\implies a^{21}\equiv a\pmod {3}\\...

$r$

Hi, I have been given the attachment formula and asked to enter this into an excel spreadsheet. Although I am not entirely sure how the answer was derived. Is anyone able to explain step by step as I want to try and enter this into an excel spreadsheet. For reference N = Newtons

Advanced apologies for this format; I am posting my question as an the image b/c the Latex is being very buggy with me, and I lost a kind of lengthy post to it. Can anyone show me what I am doing wrong? I have attached a pdf version for easier reading if need be.

Assume that ##T## has an Erlang distribution: $$\displaystyle f \left(t \, | \, k \right)=\frac{\lambda ^{k }~t ^{k -1}~e^{-\lambda ~t }}{\left(k -1\right)!}$$ and ##K## has a geometric distribution $$\displaystyle P \left( K=k \right) \, = \, \left( 1-p \right) ^{k-1}p$$ Then the compound...

Hello everyone. I was watching the Walter Lewin lectures and I noticed in the talk he used something called dimension analysis to study the time it takes for an object to drop based on differing heights. I'm 22:07 minutes into the video. With some guess work on what's proportional to what...

##\frac{dx}{dt} = \frac{dx_i}{dt} + \frac{d^2x}{dt^2}t## Multiplying dt on both sides and integrating we have ##\int_{x_f}^{x_i} dx = \int_{0}^{v_i t} dx_i + \int_{0}^{at} dvt## so ##x_f - x_i = v_it + at^2##, which is not right Where did I go wrong? I understand that if we substitute a for...

From Dr. Leonard Susskind's Stanford Lecture: Quantum Entanglement, Lecture 4, he sets up a "given particle is spin up along n (arbitrary direction) and discusses : what is probability we measure up along another arbitrary m directionHe does all of the setup, - calculates the eigenvectors and...

I have a scatterplot that I'm trying to extract. I found 54 values out of 55. There is one "missing" value, probably because it is overlapped and I can't actually see. I have the MEAN and Stand Dev of the 55 values. Is there a way to reverse find the one that is missing? I mean, is there a...

When I try to derive Gauss's law with a straight line of charge with density ##\lambda## through a cylindrical surface of length L and radius R, $$\vec E = \frac{\lambda*L}{4\pi\epsilon*r^2}$$ $$A = 2\pi*r*L$$ $$\vec E*A = \frac{\lambda *L^2}{2\epsilon*r} \neq \frac{q_{enc}}{\epsilon}$$ What am...

I want to determine the normal flow depth in a perfectly horizontal circular conduit. The system characteristics are known (Internal pipe diameter, Mannings roughness, Discharge). However, I am not sure how to calculate the normal flow depth. When using Manning's equation one can find the normal...

I just found here(https://byjus.com/physics/relation-between-density-and-temperature/#:~:text=Density and Temperature Relationship 1 When density increases,,reduces. 4 When the temperature decrease, density increases.) that P=##rho##RT. So they just took ##\rho=\frac{n}{V}##...

##\mathbb{D}## is open. Let ##\mathbb{A}:=\{z:|z-i/2|=\frac{1}{9}\}##. ##\mathbb{A}## is closed and contained in ##\mathbb{D}##. ##f## is analytic in ##\mathbb{D}##, so ##f## is analytic on the interior to and on ##\mathbb{A}##. By the Cauchy integral formula, ##f^{(4)}## exists at every point...

Is there the simplest, direct, and easy-to-understand method that only needs to apply the most basic algebra and logic to completely and strictly derive the Lorentz transformation? Thanks for your help.

I've been trying to derive a formula for diffraction pattern formed by casting a plane-wave through a generic 1D aperture onto a screen distanced ##L## from the aperture. The aperture is described by an opacity function ##f:\mathbb{R} \rightarrow [0,1]## so it can be a single slit, multiple...

So we all know that the form of the momentum operator is: iħd/dx. And for energy it is iħd/dt. But how do we derive these operators? The only derivations of the i have seen is where the schrødinger equation was used, but that makes the logic circular, because the Schrødinger-Equation is derived...

Homework Statement:: Derive Schrodinger equation Relevant Equations:: Schrodinger Equation I want to find the derivation of Schrodinger Equation. Actually, I learned quantum mechanics already, but I think the proof that begins from the plane wave solution is quit ambiguous. Because I feel...

The only way I know of to derive special relativity is to start with the two postulates, derive the Lorentz transformations, and rewrite the laws of physics consistent with those transformations. Are there alternative ways to derive special relativity? Thank you.

Suppose the E-field is ##-E_y\hat y##, and B-field is ##B\hat z##. Mass is ##m##. z | |_____x / y ##m(\ddot x \hat x + \ddot y \hat y) = q(-E_y \hat y + (v_x \hat x + v_y \hat y) \times B \hat z)## By grouping terms with ##\hat x## and ##\hat y## together, ##m\ddot x = -qv_yB##...

This is the problem statement: We can start by writing ## (\star d \star d \xi)_a = - \nabla^b (d\xi)_{ab} = - \nabla^b \nabla_a \xi_b + \nabla^b \nabla_b \xi_a = 2\nabla^b \nabla_b \xi_a ##. Then with ##\nabla_a \nabla_b \xi_c = R_{cbad} \xi^d = -R_{bcad} \xi^d## we can contract over...

The following attempt gives the wrong answer, and I would like to know where it goes wrong. Let ##\theta## be the angle of the ball with the vertical passing through the centre of the bowl, and ##\phi## be the angle the ball rolls through. Let ##m## be the mass of the ball, ##r## be the radius...

We need to derive the Maxwell "with source" equation, of course, using the tensor equation $$\partial F^{\mu v}/ \partial x^{v} = j^{\mu}/c$$ D is the spacetime dimension To do this, it was said to us vary the action wrt the ##A^{\mu}## The first term just vanish, and I want to evaluate the...

I'm just confused, no idea really what to do. Since the time derivatives of the ##\bar{\gamma}_{\mu \nu}## are assumed to be zero, and the space-space components are also assumed negligible, we have $$\begin{align*} \nabla^2 \bar{\gamma}_{00} &= 16 \pi J_0 = -16\pi T_{a0} t^a \\ \nabla^2...

I am studying interacting scalar fields (from Osborn) using the path integral approach. We define the functional integral \begin{equation*} Z[J] := \int d[\phi] e^{iS[\phi] + i\int d^d x J(x) \phi(x)} \tag{1} \end{equation*} The idea is to differentiate ##Z[J]## with respect to ##J## and end...

Background While watching Does time cause gravity? from PBS Spacetime, i wondered if its possible to "derive" the geodesic equation not from GR alone, but by assuming each particle is described by an extended wave function and the time evolution of this wave is not constant but the rate varies...

For a nice cubic non-centrosymmetric crystal like quartz/##\mathrm{SiO_2}## we can imagine that on application of stress the tetrahedral coordination polyhedra become distorted, and the central ion is displaced by a fraction ##\lambda## of the cell parameter ##a##. The total polarisation...

Stress tensor for the fluid is ##T_{ab} = \rho u_a u_b + P(\eta_{ab} + u_a u_b)##, whilst the equation of motion (assuming the system is isolated) is given by ##\partial^a T_{ab} = 0##. So I tried$$\begin{align*} \partial^a T_{ab} &= \partial^a \rho u_a u_b + \partial^a P(\eta_{ab} + u_a u_b)...

So if i have a photon of some energy and i want to find the magnitude of the momentum, i can get the right answer but the units don't make sense. So i derive p = E/c since i know the energy of the photon and i used f=E/h and substituted this into p=hf/c This means for units of the equation p...

I'm trying to find the local truncation error of the autonomous ODE: fx/ft = f(x). I know that the error is |x(t1) − x1|, but I can't successfully figure out the Taylor expansion to get to the answer, which I believe is O(h^3). Any help would be greatly appreciated!

1. Newton's Second Law states F=ma and the formula for centripetal acceleration is v^2/r Therefore, F= mv^2/r Would this be complete, I just feel that I should need to do something further but I am not sure what? 2.F=mv^2/r Gravitational force = GMm/r^2 Gravity is the cause of centripetal...

I know that it will take 3 washings to reach the desired purity of sand, and that "N-1" is an exponent in the general expression, but I am stuck beyond that.

##(\nabla\times\vec B) \times \vec B=\nabla \cdot (\vec B\vec B -\frac 1 2B^2\mathcal I)-(\nabla \cdot \vec B)\vec B## ##\mathcal I## is the unit tensor

So the Legendre transforms are straightforward; define ##S_1=S-\beta E## and ##S_2= S-\beta E + \beta \mu n## then we get: ##dS_1 = -Ed\beta - \beta \mu dn + \beta PdV## ##dS_2 = -Ed\beta + nd(\beta \mu) + \beta PdV## And so by applying the equality of mixed partials of ##S_1## and ##S_2## we...

We take an arbitrary spacetime point ##(x,t)## in any observer's reference frame ##A##. Let ##(x(v),t(v))## be the co-ordinates of this same event as seen from a frame ##B## moving at a velocity ##v## wrt ##A##. As ##v## varies, the set of points ##(x(v),t(v))## constitute some curve ##C##. So...

Is it possible to derive laws of Newtonian gravity from some symmetries?

Several weeks ago I had considered the question as to how one can start from the Schroedinger Equation, and after several transformations, derive F=ma as a limiting case. At some point in my investigations of this derivation, it occurred to me that this is simply too much work. While in...

I was studying how to derive the cross-section formula in the CoM frame from Mandl & Shaw QFT's book, and they state the following formula for the relative velocity (I'm going to use Vanhees71's notation though) $$\omega_1 \omega_2 v_{rel} = [(p_1 p_2)^2 - m_1^2 m_2^2]^{1/2} \ \ \ \ (2)$$ Then...

Hi, when learnig about reflected waves, I keep coming up with this equation; to calculate the reflected mach number (Mr). I can't seem to find the derivation for this and would appreciate your help Thank you

We work in natural units. Let's assume in this post that the differential cross-section of two particles that, after collision, yield ##N## particles is given by the following formula: $$d \sigma = (2\pi)^4 \delta^{(4)} (\sum p'_f - \sum p_i) \frac{1}{4 E_1 E_2 v_{rel}} \Pi_l (2m_l) \Pi_f...

Please let me make questions after showing what I am studying. We first consider two particles (they may be either leptons or photons) with initial (i.e. before collision) four momentum ##p_i = (E_i, \mathbf p_i)##, ##i=1,2##. These two collide and produce ##N## final particles with momentum...

The dictators at physics.stackexchange want to close my post that I post here. I hope someone can help me with this question, I want to compute this by hand, without Computer algebra software, mainly because I don't know which syntax to use for Mathematica (if you know the syntax, can you give...