Derive Definition and 591 Threads

Homework Statement Derive equation (1) from equation (2): (1) \nabla \cdot D = \rho_f (2) \nabla \times H = J + \frac{\partial D}{\partial t}Homework Equations [PLAIN]http://img198.imageshack.us/img198/4645/maxwell.png The Attempt at a Solution \nabla \times H = J + \frac{\partial...

because it seems the Lorentz transformations constitute special relativity itself

Hi! I am looking for some help using Derive. I have a differential equation, you can see it in the third image (I wanted to use LaTeX to render it but apparently I can't post LaTeX in this section of the forum). The value of lambda is given in the first image. I know the function...

?How to derive the equation of motion F=ma, given this info Homework Statement http://img861.imageshack.us/img861/1557/2009b5a.gif Homework Equations The Attempt at a Solution Is my attempted solution correct? [PLAIN][PLAIN]http://img42.imageshack.us/img42/2465/2009b5asol.gif

Hi I would appreciate some help on this question please. Derive the basic equation for the voltage across a capacitor as a function of time for a circuit that includes a resistor and capacitor connected in sereis to a battery through a switch. I know the formulas but haven't the slightest...

I know the derivative of arcsin and that I should use the chain rule, but I was wondering if I should use (1 - 2 e ^-t) for the chain rule portion?

Is it possible to derive a formula for the equivalent resistance of n such sections in cascade? Show your analysis. Series: Reqv = R1 + R2 +...Rn Parallel: Reqv = 1/{(1/R1) + (1/R2) + (1/R3) +...(1/Rn)}

r' = 4r - rf f' = -3f + rf In this question, there was three parts: a) find all the critical points of this system. b) Derive the linearised system about each critcal point... c) Use the chain rule to derive the path equation of the trajectories in the phase plane. I managed to get a...

Hi.everybody How do I derive viscosity equation F=6π*r*μ?

Could anyone derive an assertion found in "light and matter, a strange theory"? Feynman writes in his book that the propagator of the Klein Gordon photon is proportional to 1/(r2 - t2) Have you ever read the proof?

Putting together a spreadsheet to calculate the hydrogen spectrum, cannot seem to get the right mix of units to get the Rydberg constant of 13.605... eV also, what is the significance of R (1/n^2-1) converging to R as n gets large? can anyone put this together or refer me to a source that...

Homework Statement Using Fermat’s principle, derive the spherical mirror formula in paraxial approximation: \frac{1}{s_o} + \frac{1}{s_i} = \frac{-2}{R} where so and si are object and image distances, R is the radius of curvature of the sphere. Homework Equations As far as I know you...

This is a homework problem and I thought about putting it in the homework section bu since its very materials science specific I decided to put it here: For a transversely isotropic material, the “plane strain bulk modulus”, K23, is an engineering constant that is defined by the stress...

Homework Statement Imagine a narrow pipe, filled with fluid, in which the concentration of a certain type of molecule varies only along the length of the pipe (in the x direction). By considering the flux of these particles from both directions into a short segment \Deltax, derive Fick's...

Apparently one can deduce the form of divergence in polar (and spherical) coördinates using the theorem of Gauss and Ostrogradsky, namely that the volume integral over the divergence is equal to the flux integral over the surface. I can't see a way to do that, do you?

Homework Statement Derive an equation that relates the velocity of a freely falling particle to its altitude. Assume that the particle is released from rest at an altitude from the Earth's surface. Express your answer in terms of the variables and , constant gravitational acceleration at...

1. Using V(x)= -max, in the following equation: \int_{x_0}^x \frac{dx}{\pm \sqrt{{\frac{2}{m}\{E-V\left( x\right)\}}}} \ = t - t0 to get: x = x0 + v0 + at2/2 E is total energy and V(x) is potential energy. I have tried hard integrating it in various ways but do not seem to get the...

I'm in my second year of a physics degree and my QM lecturer showed us how to calculate the RMS around the expectation of an operator by considering the E of a system in equal superposition of two energy eigenstates u_1 and u_2. He then says "This gives some measure of how far off we would be...

Homework Statement For a downtime analysis the spectrum of motion has to be calculated with the wave spectrum and the RAOs (given) for several frequencies. Given is a wave scatter diagram with the significant wave height (Hs) and the peak period (Tp). How convert the significant wave height...

Homework Statement Needs to be in TODAY (yeah I know I am cutting it close!) Derive an expression for the moment of inertia of the masses at the ends of the arms in terms of l, θ and m Is the example question asking for the derivative or is it asking to use the terms above in an equation...

I am reading the H. A. Bethe's book ---quantum mechanics of one and two electron atoms. In section 39, it is shown how to go from general form to pauli approximation form through momentum space. who knows how to go directly in position space?

How do we come to the formula for Conservation of Mechanical Energy? [Initial Kinetic Energy + Initial Potential Energy = Final Kinetic Energy + Final Potential Energy] It's not a part of our syllabus, but I'm just curious how to derive that formula. Also, could you please clarify to me...

Ok, I am really stuck on this one. I tried using the first principles formula and everything, but I don't get two separate terms like I am supposed to in the actual derivative. I always end up with -1/(3x-1)^2 when I try. Can someone please help me out?

What is the trick to derive the ideal gas law and gas constant from the "combination" of Charles', Boyle's, and Avogado's laws? The general chemistry books I have seen tell me this is how they derived the ideal gas law and constant but they do not show how that is achieved. I tried to go about...

x^2 y'' + x y' + n^2 y = 0 \; Is Euler equation and solution is y=x^m I understand the three cases with different solution. But my question is if n=0. If I use y=x^m \;\Rightarrow\; m(m-1)+m=0 \;\Rightarrow m^2 = 0 \;\Rightarrow m=0 That would not work. I know the answer is y=C_1...

[/tex]1. Homework Statement [/b] Given: \phi(x)=\phi^+(x)+\phi^-(x) Where: \phi^+(x)=\sum_{\mathbf{k}} \sqrt{\frac{\hbar c^2}{2 V \omega_{\mathbf{k}}}} a(\mathbf{k}) \mathrm{e}^{-\mathrm{i}kx} and \phi^-(x)=\sum_{\mathbf{k}} \sqrt{\frac{\hbar c^2}{2 V \omega_{\mathbf{k}}}} a^\dagger...

I am trying to get the coeficient gamma=1/squareroot(1-(v/c)2) I am trying to do this by my own knowledge starting from scratch. Can someone give me the first step? I want to see if i can get there but i just need a hint i am not sure on where to start Thankyou very much, Fox

Homework Statement Can someone please derive tan(2x) using the definition of the derivative? Homework Equations The Attempt at a Solution I've tried to expand it but I couldn't get anywhere with it thank you,

Homework Statement Find \frac{d^2y}{dx^2} of the following equation: x^2-y^3=3Homework Equations Quotient Rule: \frac{d}{dx}(\frac{f(x)}{g(x)})=\frac{g(x)\cdot f^{'}(x)-f(x)\cdot g^{'}(x)}{g^2(x)} The Attempt at a Solution I solved for the first derivative: \frac{2x}{3y^2} But I'm stuck as...

Hey, can somebody show me how to derive that the lagrangian in classical phyics is L=T-V i have seen this formula so many times, but i have no idea where it really comes from?

Homework Statement \Delta f = \frac{1}{{r^2 }}\frac{\partial }{{\partial r}}\left( {r^2 \frac{{\partial f}}{{\partial r}}} \right) + \frac{1}{{r^2 \sin \phi }}\frac{\partial }{{\partial \phi }}\left( {\sin \phi \frac{{\partial f}}{{\partial \phi }}} \right) + \frac{1}{{r^2 \sin ^2 \phi...

hi, I am trying to derive the group velocity equation (actually its inverse): \frac{1}{v_g} = \frac{1}{c}(n(\lambda) - \lambda\frac{dn}{d\lambda}) where n is the refractive index and depends on the light's wavelength. I have started by saying that if v_g = \frac{\partial\omega}{\partial...

Homework Statement [PLAIN]http://img697.imageshack.us/img697/6702/bungee.png Derive the equations of the motion for the jumper. Consider only the vertical motion of the jumper. (g = 9.81 m/s^2) Homework Equations Straing = (Stated Above) Strain Rate = v / lo = v/25 F = -kx...

Homework Statement Homework Equations equation 37.23 37.30 are the following 37.23 x'=gama(x-vt) x= gamma(x'+vt') t=gamma(t-vx/c2) t'=gamma(t'+vx'/c2) 37.30 u'=(u-v)/(1-uv/c2) u=(u'+v)/(1+uv/c2) The Attempt at a Solution i tried the following... since d=vt... i...

Homework Statement Today I had a physics lab. It involved a hanging mass on a string that hung off the table. It went through a pulley and the string was then spooled around a rotating spool on the table. We first measure the radius of the spool. Then we figured out the mass it took to...

Homework Statement Using: particle velocity, beta particle momentum, p total energy, E Lorentz factor, gamma kinetic energy, KE Derive an equation for momentum as a function of kinetic energy. The functions have to depend either on the variable in the bracket, p(KE), or on a...

Hi, Through some searching and guessing with LogiSim I was able to see how to build a XOR gate from only NOR gates. I would like to know what the process for deriving this would look like. Right now I am lost as to how to proceed given that the NOR function is A'B' and XOR is AB' + A'B. How...

Homework Statement Derive an expression for the temperature of an ideal blackbody so that its radiated light at the peak intensity wavelength has exactly enough energy to excite the ground state to fourth excited state. Homework Equations I = σ*T4 λm*T = 2.9 * 10-3 m * K E = hf = hc/λ...

Homework Statement derive f(x)=x2+2x+1/ x2-3x+2The Attempt at a Solution (x2-3x+2)(d/dx)(x2+2x+1)-(x2+2x+1)(d/dx)(x2-3x+2)/(x2-3x+2)2 =(x2-3x+2)(2x+2)-(x2+2x+1)(2x-3) =(2x3-4x2-2x+4)-(2x3+x2-4x-3) =5x2+2x+7/(x2-3x+2)2 that's what I'm getting... but according to the online derivative...

Let \bar{z} = x+iy. We are given that x = \frac{z+\bar{z}}{2} & y = \frac{z-\bar{z}}{2i}. We are trying to derive \partial F/\partial\bar{z} = 1/2(\partial F/ \partial x + i \partial F/ \partial y), where F(x,y) is some function of two real variables. Using the chain rule I get \partial...

Homework Statement Integrate v_{y} = v_{t} (1 - e^{-(\frac{k}{m})t})) to get y as a function of time. Homework Equations y = v_{t}(t - \frac{m}{k} (1 - e^{-(\frac{k}{m})t}))) is the solution. v_{t}=\frac{mg}{k} The Attempt at a Solution Well, when I integrate I get the following: y =...

Is there a practical utility to derive the electric field produced by a charged rod (and the 1/r dependence at great distance)? I know it can be useful to derive the electric field produced by a large plate since you can then show that the field between close parallel plates that are oppositely...

1. An infinitely long cylinder of radius R contains a uniform charge density Rho. Calculate the electric field using Gauss' law for r> R and R>r 3. I attached a pdf with my attempt at r>R. My answer doesn't agree with those given...

Homework Statement I wanted to know how this equation is derived. Thanks. Homework Equations {v_{f}}^2 = {v_{i}}^2 + 2a\Delta d The Attempt at a Solution v_{f} - v_{i} = \frac {\Delta d a} {\Delta v}

Hello all, I am currently studying multivariable calculus, and I am interested in the Taylor series for two variable function. I am not sure where to begin; I cannot understand any of the proofs (which are apparently sparse) on the internet; they all just state it using a sigma sum; not...

Homework Statement Show that it follows from \frac{dV}{V} = \beta dT that, for small changes, density has a similar linear relationship to thermal expansion, namely \frac{d\rho }{\rho } = - \beta dTHomework Equations The Attempt at a Solution Well, at first glance this one seems ridiculously...

I know you need to use some spacetime geometry to solve some conservation equations but what is the simplest way you derive the following equation about energy and momentum: E2 = (pc)2 + (mc2)2

"Definition" of Curl. Can anyone derive the gradient operator? Can anyone prove why this equality is true? http://en.wikipedia.org/wiki/Curl_%28mathematics%29#Definition Wikipedia says it is defined, however that's BS since the gradient operator was already defined so this needs to be proven...

I'm programming a minesweeper game, and I'm trying to come up with an equation to determine the maximum number of mines a board can have dependent on the amount of rows and columns given. I pulled some numbers from the Windows 7 version, but I'm not sure how to derive an equation from them...

Does anyone know how to derive a fraction? I want to be able to differentiate f(x)=\frac{x(20-x)}{36} Ill show you what I've done but think I've just simplified it. f(x)=\frac{x(20-x)}{36} f(x)=\frac{(20-x-x)}{36} f(x)=\frac{(10-x)}{18} Is this correct?...although not sure what...