deriving Definition and 962 Threads

Homework Statement Consider an electromagnetic wave hitting a metallic surface with conductivity σ at normal incidence. a) Derive the wave equation describing this situation. Hint: Use Ohm’s law, J = σE to eliminate the current. b) Solve the wave equation for the electric field to...

Homework Statement The rotation matrix below describes a beam element which is rotated around three axes x,y and z. Derive the rotation matrix. http://img194.imageshack.us/img194/3351/60039512.png http://img808.imageshack.us/img808/159/64794596.png Homework Equations -The Attempt at a...

Homework Statement A very long solenoid of circular cross section with radius a= 4.80 cm has n= 77.0 turns/cm of wire. An electron is sitting outside the solenoid, at a distance r= 5.30 cm from the solenoid axis. What is the magnitude of the force on the electron while the current in the...

Short story: How does one go about to derive x = a cos(wt)? The way it is derived in my book is from the "SHM Diagram" file that I have uploaded but it seems that the diagram is incorrect as it does not correspond to the expression. Also, why is the Amplitude in the expression constant when the...

Homework Statement Determine the error in the calculated centripetal force, F (dynamic), for each value of r from the estimated error in the quantities m, r, and from the standard deviation from the mean of your three measurements of f. Derive the equation for the error using Rule # 2 for...

Homework Statement I am not fully sure where this is supposed to go, so forgive me if I get it wrong. I am just undertaking some private research and want to see if my work is correct. I wish to derive the Kinetic energy of something moving according to classical mechanics. Homework Equations...

(the following is Mathematica code) For the rice pdf... P(x)=(x/σ^2) BesselI[0, x (ν/σ^2)] Exp[-(x^2 + ν^2)/(2 σ^2)] ...the Second raw moment is given by doing the integral... Integrate[(x^3/σ^2) BesselI[0, x (ν/σ^2)] Exp[-(x^2 + ν^2)/(2 σ^2)], {x, 0, Infinity}] While the answer...

Deduce the formula giving the energy levels in terms of n for a free particle in a box of length l, using the fact that only stationary waves can be occupied by the particle. - considering stationary waves, λ = 2l/n. (1) 1) Using E=hv/λ= hvn (2) And P = h/λ, v = h/m*λ, v = hn/2ml (3)...

Hey ^^, new here but I already have a question haha Does anyone here know how the coefficient (x-μ)^2 was derived in the following equation: σ^3=(1/√2∏)∫(1/σ)*(x-μ)^2*exp((x-μ)^2)/(2σ^2)) I know the general equation for density probability is (1/σ)*exp((x-μ)^2)/(2σ^2)) but in this case...

Hello all I have a question about Markov chain I've obtained in an application. There is no need to mention the application or the details of markov chain because my question is simply: The transition probabilities are derived with equations that depend on the stationary probability, I know...

Homework Statement Why does lim( (1+(1/n))^n ) = e?Homework Equations If a_n convergent to a, and b_n converges to b, then (a_n * b_n) converges to (a * b)The Attempt at a Solution The lim(1 + (1/n)) = 1. If you multiply (1 + (1/n)) by itself n-times, you get the equation (1 + (1/n))^n, so...

Homework Statement A derivation of Instantaneous Velocity Arc length = s = θ * r ds/dt = d(θr)/dt = Instantaneous V Product rule: V_{t} = (dθ/dt)*r + (dr/dt)*θ V_{t} = (dθ/dt)*r + 0 V_{t} = ωr Question: Why does dr/dt*θ = 0 ?

Homework Statement Solve the logistic population model: dP/dt=rP(1-P/C); P(0)=P_{0} 2. The attempt at a solution First, I separated variables to get: \int \! \frac{1}{P(1-P/C)} \, \mathrm{d}P = \int \! r \, \mathrm{d}t Then, I took the left hand side and split into partial fractions: (1) -...

So this is my first quantum mechanics class and so far we have spent about a month (well 3 weeks) on just the mathematics. So in my book, the author explores the ideas presented by the stern gerlach experiment. It related the beam of silver atoms traveling through the separators to light...

Homework Statement Marian who is standing on her balcony is surprised by a pigeon, and throws a flowerpot up, in the air at 2.1 m/s. It takes a total of 3 s for the flowerpot to smash to the ground. The flowerpot experiences acceleration due to gravity of 9.8m/s a) How high is Marians...

Homework Statement Consider a rigid sphere of radius 1 and center at (0,0,0) that rotates about its center. The angular velocity is $\omega(t) = (\cos(t) , \sin(t), \sqrt(3))$. Does the path of the point starting at (0,0,1) ever reach this point at a later time? Homework Equations...

I have attached a PDF with some equations. (a) is essentially describing a pure state quantum system, with (b) and (c) statistical mixtures. I've managed to substitute (d) and (e) into (b) and (c) respectively, however I was wondering how to substitue (d) and (e) into (a). Apparently...

It might be difficult for you to read this integral in non latex form, but i'll try my best. As i don't know how to write this in latex form, assume "for this problem" that I(n) is pronounced as "I subscript n" or nth term of I. Homework Statement I(n)=∫ (sinx)^n dx [with...

Why in deriving invariant distance in space time we use Pythagorean Theorem with a negative sign?

Derivation of simple harmonic motion I'm looking at the wikipedia page for simple harmonic motion (http://en.wikipedia.org/wiki/Simple_harmonic_motion) and I'm confused by this line: c_1cos(\omega t) + c_2sin(\omega t)=A*cos(\omega t - \phi) How did they get from the left hand side to the right...

Homework Statement Show that the energy-momentum relationship, E^2 = p^2 * c^2 + (m*c^2)^2, follows from the expressions E = (gamma)*m*c and p = (gamma)*m*u where (gamma) = 1 / sqrt(1 - (u^2)/(c^2)) the lorentz transformation factor. m is the rest mass. c is the speed of light u is the...

I'm a bit confused by the following: We can derive the equation of motion for a particle traveling on a timelike worldline by applying the Euler-Lagrange equations to the Lagrangian \mathcal{L}=- g_{\mu \nu}(x(\tau)) \frac{d x^\mu}{d \tau} \frac{d x^\nu}{d \tau} However, to derive the...

Homework Statement I want to derive the square of the total angular momentum as shown here: http://en.wikipedia.org/wiki/Angular_momentum_operator#Angular_momentum_computations_in_spherical_coordinates Homework Equations The x,y, and z components of angular momentum are shown in the...

The energy-momentum tensor for a perfect fluid is T^{ab}=(\rho_0+p)u^au^b-pg^{ab} (using the +--- Minkowski metric). Using the conservation law \partial_bT^{ab}=0, I'm coming up with (\rho+\gamma^2p) [\frac{\partial\mathbb{u}}{{\partial}t}+ (\mathbb{u}\cdot\mathbb{\nabla})\mathbb{u}]=...

I'm going through Landau/Lifgarbagez's book II of theoretical physics. In it they have a derivation of the equation of motion from the principle of least action, however I don't understand one step. Homework Statement Derive the equation of motion: \frac{d^2x^i}{ds^2}+\Gamma^i_{kj}...

Hi guys, I can't find my notes on Fresnel diffraction and I have my Optics exam on Monday... Does anyone know how to derive F=a2/λL where L=1/z+1/z' I've googled it to death, checked here and tried in Optics 4th edition by Hecht with no luck... I'd really appreciate any help...

Hello, I am reading this paper about quantum gravity, trying and failing to follow along in the derivation of this, eq (204) p. 72, expression for the scale factor: a(t) = a_1 \left( 1 + \frac 3 2 ( 1 + \omega ) H_1 (t - t_1) \right)^{\frac 2 {3(1+\omega)}} (I'm not sure what the...

Homework Statement Assuming that ∅ is a differentiable scalar valued function and F a differentiable vector field, derive the following identities. a)∇(dotted with)(∅F) = ∇∅(dotted with)F + ∅∇(dotted with)F b)∇(crossed with)(∅F) = ∇∅(crossed with)F + ∅∇(crossed with)F Homework Equations The...

A car can accelerate 0-60 mph in 8.6 seconds and 0-100 mph in 26.1 seconds. How far (in feet) would the car have to travel in order to accelerate from 0-81 mph?

hi guys i was wondering how the coordination numbers for the atomic positions of atoms in crystals such as NaCl are derived ...more specifically why is Na at (0,0,0) and Cl at (1/2,1/2,1/2) and not (0,0,0) and (1/4,1/4,1/4) of course this is in fractional coordinates

I'm trying to derive T= 2π√m/k to become k= 4π2m/T2 How is that happen? Can someone please explain it to me? Thanks in advance!

Homework Statement Derive the expressions for the i_r and i_θ components of velocity and acceleration. Homework Equations r=|r|i_r \omega=\frac{dr}{dt} \alpha=\frac{dω}{dt}=\frac{d^2r}{dt} The Attempt at a Solution r=|r|i_r \omega=\frac{dr}{dt}i_r+r\frac{di_r}{dt}...

Question: Derive the formula y = arcsinh(x), the inverse hyperbolic function. I thought the question was asking to find the derivative of the inverse function but my teacher marked it 0/10 points because he did not want the derivative... Can "derived" mean derivative? If so... Is there...

Hello all, I'm wanting to learn how to derive all of the trig identities (well, not all, but the most common) rather than memorizing them. Perhaps someone here could provide me with a list of "essentials" that are the framework for deriving others. For example, I know there are a few that can...

Homework Statement I've been given a series circuit with a .5H inductor .01F cap, .5H inductor and 10Ω resistor in series. This circuit is connected to a source i(t) = 10cos(10t) and I need to find v(t) across Z Homework Equations From the givens I've found the Z(s) to be s+100/s+10 and...

When you derive the time dilation equation, and you see the light move straight down in one frame and in the other frame you see it move on a diagonal because the object is moving. My question is in the moving frame when you use the horizontal distance to derive the distance that the...

Homework Statement Use a Free body diagram to show that :Tanθ=static friction, on an incline plane Homework Equations FF/FN= coeficiant of friction The Attempt at a Solution I know I must get an angle to have a tan of the Force of friction and a Normal force, but I don't...

Hi, I am struggling with the heat equation ut = kuxx with the boundary conditions u(0,t) = u'(L,t) = 0 and initial condition u(x,0) = f(x) 0 ≤ x ≤ L 0 ≤ t I want to derive it's eigenvalue using complex analysis. After separating the variables...

Homework Statement State the Maclaurin series for sinx and cosx. Hence derive the Maclaurin series for tanx. Homework Equations sin(x) = x - x3/3! + x5/5! - x7/7!... cos(x) = 1 - x2/2! + x4/4! - x6/6!... The Attempt at a Solution I know you divide the series for sinx by the...

Homework Statement A popular model for the mass distribution in a spheroid (such as a bulge) is the Hernquist model, with density ρ(r) = M(total)*a / 2πr(a+r)^3 M(total) is the total mass. a is constant with dimensions of length. Derive the enclosed mass M(r) The Attempt at a...

Homework Statement I am not sure that my work is correct, and some guidance would be much appreciated. An electric toy car has mass m and has a power source of constant power P. The power source converts electrical energy directly into kinetic energy. If the car is initially stationary and on...

How do I go about deriving the thermal conductivity of graphene (specifically, in the low temperature limit) when I'm given the phonon dispersion relation? I haven't been able to find anything explaining how the dispersion relation relates to the thermal conductivity in materials. (this is...

Homework Statement I should derive the Hubble law redshift from Maxwell equations in closed Universe. Homework Equations The metric of closed Universe is ds^2 = dt^2 - a^2(t)\left(d\chi^2 + \sin^2 \chi d\theta^2 + \sin^2 \chi \sin^2 \theta d\phi^2\right). The Hubble law redshift: \frac...

Folks, I was checking to see was it possible to determine the bending moment diagram from the shear force diagram. Seemingly one can do it for simply supported beams but if we consider a rigidly supported beam on either end its not possible to derive the bending moment diagram from the shear...

Homework Statement Derive y= \sqrt(2x^4) - \frac{5}{3x^2} The Attempt at a Solution I am still at the first part of the function (the root): First I tried to derive inside the root like this: \sqrt(2x^4) = \sqrt(8x^3) = 2 \sqrt(2) \times \sqrt(x^3) = \sqrt(2) \times x^2...

Homework Statement A curve has equation y=(x^2+1)^4 + 2(x^2+1)^3. Show that \frac{dy}{dx}=4x(x^2+1)^2(2x^2+5). Homework Equations \frac{dy}{dx}=(\frac{dy}{du}\times \frac{du}{dx})+(\frac{dy}{dv} \times \frac{dv}{dx}) The Attempt at a Solution y=(x^2+1)^4 + 2(x^2+1)^3 let u =...

Hey all. I am taking my second college physics course (electromagnetic physics) and am looking for some help deriving the equations. I found it very helpful to know how to derive many of the equations in my first physics course. So far we have studied e fields, guass's law, capacitors...

Homework Statement In a lab experiment about Gravity Waves and Dispersion, one of the preliminary questions is: Show that for gravity waves the group velocity is: C_{g} = \frac{C_{p}}{2}\sqrt{1 + \frac{2kh}{sinh(2kh)}} Homework Equations C_{g} = dω/dk ω = \sqrt{gktanh(kh)}...

Homework Statement This is from Exploring Black Holes, Query 1, page G-3. It involves a one dimensional creature on a two dimensional circle. Constant dl but different dx. Collect terms in equation [5]. Show that the result can be written dl^{2} = \frac{dx^{2}}{1 - x^{2}/r^{2}} Equation...

How can one derive the relationship for a cubic crystal: d= \frac{a}{\sqrt{h^2 + k^2 + l^2}} It is shown here. This is probably trivial but I am having trouble proving it as the Miller indices are reciprocals but the reciprocal is not distributive. This isn't for homework by the way - I...