deriving Definition and 1000 Threads

This is in page 346 of Griffiths "Introduction to Electrodynamics". This is regarding to work done by electromagnetic forces dW acting on charges in the interval dt . dW = \vec F \cdot d \vec l =q( \vec E + \vec v X \vec B) \cdot d \vec l = q( \vec E + \vec v X \vec B) \cdot \vec v d t...

I have problem understanding why the surface integral disappear when taking the volume to very large in this equation: W_e = \frac 1 2 \int_{v'} \rho_v V dv' = \frac 1 2 \int_{v'} (\nabla \cdot \vec D)V dv' = \frac 1 2 \int_{s'} V \vec D \cdot \hat n ds' \;+\; \frac 1 2 \int_{v'} \vec E...

I'm attempting to derive speed in terms of potential difference (voltage), can anyone let me know if there are any errors? http://www.texify.com/img/%5CLARGE%5C%21E_k%3D%5Cfrac%7B1%7D%7B2%7D%5Ctext%7Bmv%7D%5E2.gif...

Homework Statement The specific Lagrangian for a cantilever beam is given by: \overline{L}=\frac{1}{2}m[\dot{u}^2(s,t)+\dot{v}^2(s,t)]-\frac{1}{2}EI[\psi ^{\prime}(s,t)]^2 where m,EI are mass and bending stifness, respectively. \dot{u},\dot{v} are velocities in u,v directions...

Homework Statement A 4 kg particle moves along the x-axis under the influence of a conservative force. The potential energy is given by U(x) = ax^2 + b, where a = 6J/m^2 and b = 2J. What is the x-component of the acceleration of the particle when it is at x = 1 mHomework Equations deltaU = -W...

The question: A particle in a cyclotron gaines energy q \Delta V from the alternating power supply each time it passes from one dee to the other. The time interval for each full orbit is T = \frac{2 \pi}{\omega} = \frac{2 \pi m}{q B} so the particle's average rate of increase in...

Homework Statement Derive 1/f = (n-1)*( (1/r1)-(1/r2)+(((n-1)t))/(nr1r2))) using the ray matrix method. Homework Equations Matrix for curved dielectric interface: M1 = [1, 0] [(1/r)(n1/n2 - 1), n1/n2 ] Matrix for translation through homogeneous medium: M2 = [1, d] [0...

Hi, I am trying to re-derive, or should I say modify, the existing theory of classical electromagnetism by postulating the existence of magnetic monopoles. Where should I begin?

Hello, i am trying to derive flexible energy, but i get a negative sign in front of a Work (A). Where did i miss? F is force of a spring. I don't know if i used Hooke's law correctly... Thank you for looking.

For some reason I can't derive the Hamiltonian from the Lagrangian for the E&M field. Here's what I have (using +--- metric): \begin{equation*} \begin{split} \mathcal L=\frac{-1}{4}F_{ \mu \nu}F^{ \mu \nu} \\ \Pi^\mu=\frac{\delta \mathcal L}{\delta \dot{A_\mu}}=-F^{0 \mu} \\...

Homework Statement See Explanation below for details of my confusion. Homework Equations The Attempt at a Solution Hello all, I've derived a transfer function, T(s) = \frac{\frac{-R_{2}}{R_{1}}}{1 + \frac{1}{sCR_{1}}}, but I can't seem to derive the corner frequency...

Homework Statement Beginning with the kinetic and potential energies of two objects with masses m1 and m2, show that the total energy of a binary system is given by: E=\frac{1}{2}\muv2 - G\frac{M\mu}{r} Homework Equations The one given K =\frac{1}{2}mv2 U = G\frac{Mm}{r} The...

Homework Statement Attached image please, sorry I tried LaTeXing and i failed super hard. Homework Equations Fundamental Theorem of Calculus Multivariate chain ruleThe Attempt at a Solution I'm basically at a loss of words on this question. I might be thinking of this incorrectly but what my...

I was just curious as to how I can show the following properties of the Gamma Function, they came up in some lecture notes but were just stated? Notation: G(z) = Gamma function 2^(z) = 2 to the power of z I = Integral from 0 to infinity (1) G(z)*G(1-z) =...

Homework Statement I'm going through Jackson a bit, reading on Magnetostatics, and I came into a bump. I'm looking at \nabla\times B=\frac{1}{c}\nabla\times\nabla\times\int\frac{j(r')}{|r-r'|}d^3r' I expand that using 'BAC-CAB' rule and I get: \nabla\times...

Homework Statement I need to derive the 2D N-S equations for steady, incompressible, constant viscosity flow in the xy-plane. I need to use a control volume approach (as opposed to system approach) on a differential control volume (CV) using the conseervation of linear momentum...

Homework Statement Derive a formula for the maximum speed V_max of a simple pendulum bob in terms of g, the length l and the maximum angle of swing Θ_max. (Hint: Use the fact that the same amount of energy at the top of the arc is the same as at the bottom of the arc.) The picture depicts...

Homework Statement This is not a homework problem. I'm trying to do this for research purposes. I have an energy potential (the Keating potential) of the following form (attached). In this form, A, B, and C are force constants, and r_ab is the vector along the bond between atoms a and b...

http://www.damtp.cam.ac.uk/user/tong/string/string.pdf In these notes, I am trying to derive the equation of motion (1.21) corresponding to the Nambu-Goto action: \partial_\alpha ( \sqrt{ - \text{det} \gamma} \gamma^{\alpha \beta} \partial_\beta X^\mu ) =0 I have found and proved all...

f(x)=(x^(2)+5x+2)^(4) f'(x)= 4(x^2 + 5x + 2)^3 (2x + 5) = 8x + 20(x^2 + 5x + 2)^3 is this right than my equation of the tangent turned out to be y=160x +16

I will be thankful if the following points are clarified. 1. While deriving the lens formula for a convex lens-say, 1/f= 1/v - 1/u where u and v are the object and image distances, the minus sign is obtained after applying sign conventions. But, I don't understand the logic behind taking the...

I wasn't sure if this counted as intro physics. Feel free to move if I have it in the wrong place. Homework Statement In class we learned some linear transformations where we have a stationary observer and another moving near the speed of light. Describing the reference frames: s' -> x'=u't'...

Homework Statement Starting from a general axisymmetric metric ds^2=g_tt dt^2 + 2g_tφ dtdφ +g_φφ dφ^2 + g_rr dr^2+g_θθ dθ^2 ...(0) where the metric components are functions of the coordinates r and θ only. I've managed to show (via Euler-Lagrange equations) that g_tt dt/dτ + g_tφ...

Homework Statement Derive length contraction using Lorentz invariants. Homework Equations ds^2 = dx^2 +dy^2 + dz^2 - c^2 dt^2 The Attempt at a Solution Consider a rod parallel to the x-axis and moving with velocity v in the x-direction. We can measure the length of the rod of...

someone please help not sure were to start. use the method of area-moments to derive an expression for the mid-span deflection of a simply-supported beam with the following properties: Span= L : second moment of area of section= I : modulus of elasticitiy= E which has a total UDL along...

I have PTV=R where P and T are square matrices (4x4) and V and R are non-square (4x3). P and V are known, T is unknown, and R is partially known (3 unknown elements). Seems impossible, but T is a transformation matrix (ie upperleft 3x3 is a rotation matrix) which gives me additional clues...

relationship of angular velocy and translational velocity in simple circular motion?? Like if something is going in a circle of radiues R at speed v with angular velocity w, then w=v/R. Where does this relation come from? I'm having trouble deriving it. Please help! EDIT: I think i got it...

Homework Statement I'm trying to derive the equation of motion of underdamped motion. Homework Equations From F = m\ddot{x} -kx - c\dot{x} = m\ddot{x} m\ddot{x} + c\dot{x} + kx = 0 x_{h}(t) = ae^{\lambda t} \dot{x}(t) = \lambda ae^{\lambda t} \ddot{x}(t) = \lambda^2 ae^{\lambda t}...

On page 14 in the notes attached in this thread: https://www.physicsforums.com/showthread.php?t=457609 (i)In the definition given just above eqn 22, it says "In other words, \phi_\alpha \cdot \lambda is a smooth map from I to \mathbb{R}^n for all charts \phi_\alpha. Where do they pull this...

Could somebody help me in deriving the following expressions? I can judge that the first equation is a common expression for finding Keq for a mass-spring system in series.. Can't do the rest :/ anybody please ? Thanks in advance.

I'm having some problems trying to figure out how to derive relativistic momentum. The way it was explained to me, classically, p=mv=m(dx/dt),but dx/dt is measured differently in different reference frames. So, if you look at time dilation, t=ɣt' where ɣ= 1/(1-(v/c)^2)^1/2 and t' is time in the...

Right so there's this part in my notes where we begin to derive the schwarzchild solution. There's a substitution part I don't understand fully (I think) but I'll start from the beginning...The Schwarzschild Solution. The solution corresponds to the metric corresponding to a static, spherically...

Homework Statement So, I'm working through a relativity book and I'm having trouble deriving the Lorentz transformation for an arbitrary direction v=(v_{x},v_{y},v_{z}): \[\begin{pmatrix} {ct}'\\ {x}'\\ {y}'\\ {z}' \end{pmatrix}=\begin{pmatrix} \gamma & -\gamma \beta _{x} &...

1.Homework Statement We know the derivation of the method of variation of parameters for second order scalar differential. The task is to derive the method of variation of parameters for scalar equations using this approach: first convert the scalar equation into the first order system and...

Homework Statement Using the definition of gravity, derive the mass of the Earth Homework Equations I am unsure if this is simply a plug n chug problem and I am over thinking it or there is some way to use calculus to derive the mass from the gravity equation. The Attempt at a...

Homework Statement A vertical cylindrical tank of cross-sectional area A_1 is open to the air at the top and contains water to a depth h_0. A worker accidentally pokes a hole of area A_2 in the bottom of the tank. Derive an equation for the depth of the water as a function of time t after...

Homework Statement The problem consists of a ball almost completely submerged. The exact question is: "An object with density ρO and mass m is floating in a pool of fluid with density ρF. Derive an expression for the volume of the object that is above the fluid." Homework Equations...

Homework Statement A lab we were recently given in AP Physics class contained an equation already derived. This lab was about determining the charge on a pith ball, using the static charge of a fur to charge the balls negatively, so they repel. Finding the angle and distance between the two...

1. I can't understand one step in the derivation of the Einstein tensor from the Bianchi identity.I have looked in a lot of books and all over the internet and everyone glosses over the same point as if its obvious, but it isn't obvious to me. 2. Below is the entire derivation. It seems...

Homework Statement Derive the pressure, density and temperature profiles of an adiabatically stratified plane-parallel atmosphere under constant gravitational acceleration g. Assume that the atmosphere consists of an ideal gas of mean molecular weight \mu. Given \mu=14u, g = 9.81m/s^2, z =...

Hi there, I originally posted this in the SR, GR section so sorry for the re-post. Can anyone point me in the direction of any papers that explicitly derive the equations of motion in f(T) gravity. I have seen the wikipedia derivation in f(R) gravity but can't find anything for f(T) where...

Homework Statement Deriving the formula for a partially filled sphere using spherical polars. Note this is not a homework problem , I have solved it using a cylindrical slice method, just been bugging me about how to obtain the same result using spherical polars.if the sphere has a radius a...

Use the Leibniz rule to derive the formula for the Lie derivative of a covector \omega valid in any coordinate basis: (L_X \omega)_\mu = X^\nu \partial_\nu \omega_\mu + \omega_\nu \partial_\mu X^\nu (Hint: consider (L_X \omega)(Y) for a vector field Y). Well I have the formula L_X(Y) =...

The problem Can anyone explain me a step given in my book? This is actually the derivation of the distance between orthocentre and circumcentre of a triangle using vectors. ABC is a triangle. S is the circumcentre and H is the orthocentre. \vec{SA} + \vec{SB} + \vec{SC} = \vec{SA} +...

We derived a formula to calculate the dielectric constant for some materials. It works well for gases and some liquids. But, water has a extraordinary dielectric constant of ~80. I tried googling it up but couldn't find any place which explains (mathematically) why it's so big. The professor...

Homework Statement When I try working out the example below from PlanetPhysics, I wind up with 2PI rather than 4PI in my answer. Should I be considering my result valid for only a hemisphere and double it for a sphere--or am I just making a mistake in my math? "As an example of the...

Homework Statement [PLAIN]http://img51.imageshack.us/img51/4562/mecj.jpg Homework Equations The Attempt at a Solution How do I go about showing LHS = RHS in each of these? (\wedge denotes cross product) What is \dot{r}=\dot{x_1}-\dot{x_2} and \dot{R} ?

In A. Zee "QFT in a nutshell" in chapter I.5 on page 31 how does equation (3) come about? Just the line above this equation, he gives an equation which needs to be rearranged to give (3). It must be embarrassing simply, but I can't see how. Something with the indices goes on. How does the...

Say you have the coefficients a_k of a Fourier series representation of some function x(t). You can easily then give x(t) as $$x(t) = \sum_{k = -\infty}^{\infty} a_k e^{i k \omega_0 t}$$ But this doesn't do much good in telling you what the actual function looks like. For example, if we have...

Homework Statement Derive the following general relation : \left(\frac{\partial T}{\partial V}\right)_{S} = - \frac{1}{C_{V}} T \left(\frac{\partial p}{\partial T}\right)_{V} Homework Equations Maxwell's Relation : \left(\frac{\partial T}{\partial V}\right)_{S} = - \left(\frac{\partial...