deriving Definition and 1000 Threads

Homework Statement For the magnetic circuit: Derive the circuit approximation. Compute all magnetic fluxes if the total solenoid current is I. Homework Equations Rm = L / μS The Attempt at a Solution [/B] Mostly, right now, I'm just trying to determine the magnetic circuit equivalent. From...

Homework Statement For a system of discrete point particles the energy momentum takes the form T_{\mu \nu} = \sum_a \frac{p_\mu^{(a)}p_\nu^{(a)}}{p^{0(a)}} \delta^{(3)}(\vec{x}-\vec{x}^{(a)}), where the index a labels the different particles. Show that, for a dense collection of particles...

Hi I am having trouble with the derivation of the Rayleigh-Jeans from the steps shown at the hyperphysics web site. I have emailed Dr. Rod Nave who is listed as the person-in-charge at the site but I have been able to get a reply. It would really be much appreciated if anyone can have a look at...

Homework Statement Homework Equations $$\frac{\omega}{v}=\frac{s}{r}$$ The Attempt at a Solution How to get the equation above? Cause $$\frac{s}{r}=\omega$$ & $$\frac{\omega}{v}=\frac{1}{r}$$ since v=rw. Source: http://www.relativitycalculator.com/Newton_Universal_Gravity_Law.shtml

Homework Statement [ For a system of discrete point particles the energy momentum takes the form T_{\mu \nu} = \sum_a \frac{p_\mu^{(a)}p_\nu^{(a)}}{p^{0(a)}} \delta^{(3)}(\vec{x}-\vec{x}^{(a)}), where the index a labels the different particles. Show that, for a dense collection of particles...

Homework Statement A straight circular plastic cylinder of length L and radius R (where R ≪ L) is irradiated with a beam of protons so that there is a total excess charge Q distributed uniformly throughout the cylinder. Find the electric field inside the cylinder, a distance r from the center...

Homework Statement A stream of water flows downward from a tap. Assume that the water is in free fall once it leaves the tap, at which point its speed is v1, and the initial diameter of the water stream is A1. (i) Find an expression for the speed v2 of the liquid as a function of the distance...

Homework Statement The plano-convex lens has a diameter of 200 mm and the central thickness of 20 mm. The edge thickness is zero and the refractive index of glass is 1.5. Find the following parameters of the lens: (i) the back focal length Homework Equations N/A The Attempt at a Solution I've...

Hello, I am having trouble deriving the equation of motion for the quintessence field. The equation of motion which I am meant to get at the end point is: (with ' denoting derivative w.r.t time) φ'' + 3Hφ' + dV/dφ = 0 Using the inflaton lagrangian: (although with a generic potential V(φ)...

Homework Statement Show that the isotropy and homogeneity of space-time and equivalence of different inertial frames (first postulate of relativity) require that the most general transformation between the space-time coordinates (x, y, z, t) and (x', y', z', t') is the linear transformation...

I've calculated the joint distribution, XY_PDF(x,y) of random variables X and Y (both coming from a distribution N(n) = C*e^(-K*n^2)). I use XY_PDF(x,y) to calculate the joint distribution AR_PDF(a,r) of the random variables A (angle) and R (radius), with the PDF method and the Jacobian. Since...

Homework Statement I'm trying to derive the voltage waveform across the capacitor for a discharging capacitor that has been fully charged by a DC power supply ##v_0##, i.e. ##v_c(t=0)=v_0## and then at ##t=0## the switch is flipped and the capacitor starts to discharge. Homework Equations The...

Hi, I have a question Given the function LzYilm(θ,ϕ) =mħYilm(θ,ϕ) What steps can I take to confirm that Lz=ħ,0,-ħ

Homework Statement I am trying to derive the equation for the charge of a capacitor as a function of time: Q (t) = Qmax (1-e^(-t/tau). Homework Equations Kirchhoff's loop law I (t) = dQ(t)/dt Delta Vbat= Epsilon Delta Vresistor= -I*R = [-dQ(t)/dt]*R Delta Vcapacitor= Q/C Qmax = C*Epsilon Tau =...

Homework Statement Prove that the diffusion constant D of an ideal gas can be expressed as D=1/3λv(v bar) where λ is the mean free pass of the gas molecule. And v bar is the average speed of the gas molecules obtained from the kinetic theory of gases.(Use the picture to setup the net flux...

Homework Statement Given that the potential of dipole is equal to: V(\vec{r})=\frac{\vec{p}\vec{r}}{4\pi\epsilon_0 r^3} show that the electric field is equal to: \vec{E}(\vec{r})=\frac{1}{4\pi\epsilon_0}(\frac{3(\vec{p}\vec{r})\vec{r}}{r^5}-\frac{\vec{p}}{r^3}) Homework Equations...

Homework Statement Homework Equations average speed = total distance/total time The Attempt at a Solution 24. [/B] The shortest road distance from Toronto City Hall to the Shaw festival theatre in Niagara-on-the-Lake is 131 km. a) First I will calculate the area of each rectangle using...

Hi everyone. I'm trying to derive an expression of the velocity of an object in free fall on Mars, and I am having trouble. Here is what I've done so far: Drag on Mars can be expressed as $$F_d = \frac{C_d A \rho_M v^2}{2}, $$ where C_d denotes the drag coefficient, A the reference area, and...

Homework Statement Derive the Lorentz Transformation using light cone coordinates defined by ##x^±=t±x## ##x^+ x^-~## is left invariant if we multiply ##~e^φ~## to ##~x^+~## and ##~e^{-φ}~## to ##~x^-~##, that is ##~x'^+ x'^-=x^+ x^-## Homework Equations ##t'^2 - x'^2 = t^2 - x^2...

I posted a question about this yesterday, but realized I had made a stupid mistake in my derivation. Orbital dynamics: "The familiar arc-cosine form" That error has been corrected. I still have a deeper question. I believe this expression can be developed using the geometry of an ellipse in...

Hi, friends! I have been able to understand, thanks to Hawkeye18, whom I thank again, that, if ##\mathbf{J}## is measurable according to the usual ##\mathbb{R}^3## Lebesgue measure ##\mu_{\mathbf{l}}## and bounded, a reasonable hypothesis if we consider it the density of current, if...

Good day to you all, I could be asking too much here. I’m someone who prefers to understand formulas by deriving them from own made scenarios. In this case I was trying to derive the time dilation Lorentz formula using my own made up example and I wanted to know if I'm on the right track here...

Hi, friends! I have been struggling to understand the only derivation of Ampère's law from the Biot-Savart law for a tridimensional distribution of current that I have been able to find, i.e. Wikipedia's outline of proof, for more than a month with no result. I have also been looking for a proof...

I am trying to derive the geodesic equation using variational principle. My Lagrangian is $$ L = \sqrt{g_{jk}(x(t)) \frac{dx^j}{dt} \frac{dx^k}{dt}}$$ Using the Euler-Lagrange equation, I have got this. $$ \frac{d^2 x^u}{dt^2} + \Gamma^u_{mk} \frac{dx^m}{dt} \frac{dx^k}{dt} =...

So I am teaching myself physics in "Physics 1 For Dummies" and I have come across a chapter dealing with deriving equations, this one being the distance through using the average velocity. I have never derived equations before, so be easy on me! So basically it starts off with s=vt (distance...

Homework Statement Homework EquationsThe Attempt at a Solution So I am tasked with answer #3 and #4. I have supplied the indicated parenthesis of 8 also with the image. Here is my thinking: Take the Fourier series for |sin(θ)|. Let θ = 0 and we see a perfect relationship. sin(0) = 0 and...

I'm going through Ray D'Iverno's "Introducing Einstein's Relativity", and there is a step he makes in deriving the Lorentz transformations that doesn't seem necessary to me. So I'm not sure what I'm missing. He derives them from Einsteins postulates of relativity. From the postulate that the...

How is E=mc^2 derived from relativistic doppler effect? I looked up on wikipedia but it seems to have some errors. https://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence#Alternative_version

So there was a really old thread about this, but I don't think the matter was ever really resolved, which is why I'm making this thread now. I'm trying to derive the equation τ = Fd but I've run into a bit of trouble. I started with x=θr where x is the arclength on a circle (since any point...

I'm trying to figure out the effect of a force applied to a rotating body in 4+1 dimensions. A good place to start would be deriving the effect of forces in 3+1 dimensions. I have been looking around the Internet and even went to the local community college and checked out texts in the library...

Homework Statement I am trying to obtain the hermite polynomial from the schrødinger equation for a har monic oscillator. My attempt is shown below. Thank you! The derivation is based on this site: http://www.physicspages.com/2011/02/08/harmonic-oscillator-series-solution/ The Attempt at a...

So if I'm given a coordinate plane that graphs the position of a particle, how do you get the s(t), in respect to time if given a table of time intervals. Given: f(x) = -x^2 Needed: s(t)? v(t)? a(t)?

Homework Statement I am trying to get the hamiltonain operator equality for a rigid rotor. But I don't get it. Please see the red text in the bottom for my direct problem. The rest is just the derivation I used from classical mechanics. Homework Equations By using algebra we obtain: By...

I'm sure the inductor model, i.e. vL(t) = iL'(t)*L follows without directly from Faraday's eq. But even there, with Faraday's equation we think of the changing magnetic field as inducing the voltage in the loop, where in the model it seems the other way around, that is, the voltage increases...

Homework Statement Derive the transformations ##x \rightarrow \frac{x+vt}{\sqrt{1-v^{2}}}## and ##t \rightarrow \frac{t+vx}{\sqrt{1-v^{2}}}## in perturbation theory. Start with the Galilean transformation ##x \rightarrow x+vt##. Add a transformation ##t \rightarrow t + \delta t## and solve for...

Homework Statement The step I am trying to follow is detailed here where I am trying to get from equation 6.26: t=\int_{r_1}^{r}(1+\frac{2M}{r}+\frac{b^2V(r)}{2}+\frac{Mb^2V(r)}{r})dr to equation 6.30 t=\sqrt{r^2-r_1^2}+2Mln(\frac{r+\sqrt{r^2-r_1^2}}{r_1})+M(\frac{r-r_1}{r+r_1})^{1/2} Homework...

Why is relative speed taken to be symmetrical i.e. speed of one frame of reference from a second frame is equal to that of the second frame of frame refrence from the first frame

Homework Statement The first order ramp unit response is shown in the graph below. Determine: 1. The transfer function. 2. Plot the error function e(t) then determine its maximum magnitude and the time http://s24.postimg.org/cdbhqm80j/Capture.png Homework Equations G(s)=(1/T)/(S+1/T) ... G(s)...

For three years now i have been attempting to find some fundamental properties of gravity from which the three relativistic variables of GR, time dilation and the radial and tangent length contractions, could be determined without incorporating the EFE's. There is no rule or reason that i know...

Homework Statement [/B] I have this system below. It is the schematic of a linear accelerometer moving horizontally, where m is the total mass of the slide, b denotes the viscous damping, and k represents the spring constant. The relative position between the moving mass and the case is...

The commutation relations for the ##\mathfrak{so(n)}## Lie algebra is:##([A_{ij},A_{mn}])_{st} = -i(A_{j[m}\delta_{n]i}-A_{i[m}\delta_{n]j})_{st}##.where the generators ##(A_{ab})_{st}## of the ##\mathfrak{so(n)}## Lie algebra are given by:##(A_{ab})_{st} =...

The generators ##(A_{ab})_{st}## of the ##so(n)## Lie algebra are given by: ##(A_{ab})_{st} = -i(\delta_{as}\delta_{bt}-\delta_{at}\delta_{bs}) = -i\delta_{s[a}\delta_{b]t}##, where ##a,b## label the number of the generator, and ##s,t## label the matrix element. Now, I need to prove the...

Homework Statement A (spherical) rubbery balloon of 20 cm in diameter is filed with helium. The rubber balloon wall has a thickness of 0.05 cm and diffusivity of 0.1x10-10 cm2 /s for helium. When the balloon is left in the air at 25°C, helium leaks into the air by diffusion through the rubbery...

Homework Statement I'm trying to derive the vector identity: $$\nabla(\vec{A} \cdot \vec{B})$$Homework Equations $$ \nabla(\vec{A} \cdot \vec{B})=(\vec{B} \cdot \nabla) \vec{A} + ( \vec{A} \cdot \nabla ) \vec{B} + \vec{B} \times (\nabla \times \vec{A})+ \vec{A} \times ( \nabla \times \vec{B})$$...

Homework Statement For an upcoming test on 2D Motion, my Physics Teacher recommended that, instead of memorizing close to a dozen equations, he suggested we derive what we can from the main equations he showed us. So people in my class decided to split up deriving equations to bring them...

Homework Statement I need to derive the equation related to the Compton Effect from the equations for momentum and energy conservation. Homework Equations (1) Compton Effect: λ' -λ = h/me(1-cosθ) (2) Conservation of Momentum (x-direction): h/λ= (h/λ')cosθ+γumeucosΦ (3) Conservation of Momentum...

Homework Statement Integrate: Homework Equations The Attempt at a Solution I tried to get rid of the velocity in the numerator on the left side to use the relevant equation but to no avail. Any tricks on how i can integrate this? Also, this a small part of a larger mechanics problem...

Dear all, I am investigating a Transient Optimal Heating Problem with distributed control and Dirichlet condition. The following are the mathematical expression of the problem: Where Ω is the domain, Γ is the boundary, y is the temperature distribution, u...

Hello there, I'm reading a section of my textbook that is deriving the virial theorm from the hydrostatic equilibrium equation. In part of the derivation it states that $$-\int_0^M\frac{Gm(r)}{r}dm(r)=E_{GR}=-\frac{GmM}{r}$$ When I perform this integral I get the wrong answer. Here's my...

Homework Statement Consider heat flow in a long circular cylinder where the temperature depends only on t and on the distance r to the axis of the cylinder. Here r=\sqrt{x^2+y^2} is the cylindrical coordinate. From the three-dimensional heat equation derive the equation U_t=k(U_{rr}+2U_r/r)...