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58 views

Does a rotating plank only acquire rotational kinetic energy?

I have another doubt with a Kleppner problem :(. A thin plank of mass M and length l is pivoted at one end. The plank is released at 60$^{\circ}$ from the vertical. What is the magnitude and ...
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113 views

Derivation of (2.45) in Peskin and Schroeder

I'm having trouble understanding the step $$\left[\pi (\vec{x},t),\int d^{3}y ~(\frac{1}{2} \pi (\vec{y},t)^{2}+\frac{1}{2}\phi (\vec{y},t)(-\nabla^{2} +m^{2})\phi (\vec{y},t)) \right]$$ $$ =\int ...
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51 views

Finite Square Well Inside an Infinite Square Well

Ok here's a potential I invented and am trying to solve: $$ V(x) = \begin{cases} -V_0&0<x<b \\ 0&b<x<a \\ \infty&x>a \\ \end{cases}$$ and $V(-x) = V(x)$ (Even ...
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57 views

Finding the total space that an oscillating body has gone through via complex analysis

I was solving my homework and I got to an exercise that stated: An harmonic oscillating body has an equation of $$y(t) = A \sin(t)$$ Find the total space that the body has travelled during $t \in ...
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37 views

Torque per unit length on infinite rotating charged cylinder

For homework I have the following question, but I am stuck on finding the torque on the cylinder. An infinite cylinder of radius $R$ carries a uniform surface charge $\sigma$. We start rotating the ...
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61 views

How do I use the direction of a cross product?

The question is: An electron is projected at a speed of $3.70×10^6\text{ m/s}$ in the $u=\frac{(i+j+k)}{\sqrt3}$ direction into a uniform magnetic field $\vec {B} = 6.43 i + 3.43 j −8.29 k$. ...
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34 views

Plank stopping time

Problem: A plank of length $L$ and mass $m$ lies on a frictionless floor, if the plank has an initial velocity $v$, what is the stopping time of the block if it meets a floor with friction constant ...
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27 views

Bandpass of diffraction grating - exit slit width?

I'm supposed to derive a relation for the range of wavelengths that's being transmitted by a spectrometer (bandpass) in terms of the dispersion, focal length and exit slit width. Given grating is ...
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66 views

Calculation of energy eigenvalues of $\hat{x}^4$

I would appreciate help in calculating the energy eigenvalues associated with $\hat{x}^4$, with $\hat{x}$ expressed using the ladder operators for harmonic oscillators. $\hat{x} = ...
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165 views

Electric Potential due to conducting sphere and conducting shell

The problem statement, all variables and given/known data A solid conducting sphere having a charge Q is surrounded by an uncharged concentric conducting hollow spherical shell. Let the potential ...
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25 views

Any way to Find the Position Function of a body under gravitational force?

Here's the problem I am trying to find a solution to: Consider a heavy point particle of mass $m_2$ fixed at a point (preferably the origin) and another light point particle of mass $m_1$ at an ...
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34 views

Thermal Conduction through sphere

In general, a sphere with conductivity $\kappa$, heat capacity per unit volume $C$ and radius $R$ obeys the differential equation at time t: $$C\frac{\partial T}{\partial t} = \kappa \frac{\partial^2 ...
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34 views

Mutual Inductance of co-planar (but not concentric) loops

Two small wire loops, each with radius b, are placed a distance $d >> b$ apart. The loops are oriented as shown below; i.e., both loops lie in the x-y plane. Each loop carries the same current ...
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25 views

Particle in a box under harmonic driving

Is the particle in a box under harmonic driving electric field solvable analytically? Here is the Schrodinger equation: $$ i\frac{\partial \psi(x,t)}{\partial t}=\left[-\frac{1}{2} ...
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50 views

Conditions that the coordinate must satisfy in order to become local inertial

Consider the coordinate transformation $$ \tilde x^a=x^a+\frac{1}{2}\Gamma^a_{bc}x^bx^c $$ I have shown that at the origin $O=(0,0,0,0)$, $$ \frac{\partial\tilde g_{ab}}{\partial\tilde x^c}=0 $$ ...
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33 views

(Special Relativity) Points that can be seen by an observer

Let the metric be $$ ds^2=(1+gz)^2dt^2-dx^2-dy^2-dz^2 $$ where $g$ is a positive constant. Let an observer be stationary at $x=y=0$ on the surface $z=0$ and look upwards at an angle $\theta$, how ...
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45 views

Quick question on Perturbation theory - How do I evaluate this probability?

We know that hamiltonian for interaction between an electron and external field along $z$ is: $$\hat H = \frac{e\hbar B}{2m}\hat \sigma_z = \frac{\hbar \omega}{2} \hat \sigma_z $$ This has energy ...
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47 views

A question about sign in Euclidean path integral

I have a question about the sign in the Euclidean path integral in Polchinski's string theory vol I, p 337. In page 335, Polchinski introduced path integral in Euclidean space $$ \langle q_f, U| ...
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7 views

Determing what is differnece beetwen eigenvalues for attractive Coulomb Field (Hydrogen) calculated by exact method and WKB aproach

I have task to compare eignevalues gained by exact calculation on electron in Coulomb attractive field (hydrogen) and gained by WKB method.. As far as I get, eigenvalues gained with exact method are ...
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24 views

If maximal work is extracted, in what manner does the heat flow between bodies?

There are two bodies starting with different temperatures and specific heat capacities (for simplicity assume that the bodies are solid to the volumes are constant). Let the rate of heat flow from ...
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99 views

Laplacian and Dirac Delta function

Although I find it mathematically dubious, we said that $$\Delta \frac{1}{r} ~=~ -4\pi \delta^3({\bf r}).$$ Now, I was wondering is there a similar relation to the delta function if we look at ...
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40 views

Rotating and moving reference frame

I've looked through your forums and can't find exactly what I need. I have a two objects whos dynamics can be described in discrete time as follows: $x_A(k+1) = x_A(k) + ...
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18 views

ElectroMagnetism , charge on a conducting surface

Given the potential field in free space: $V = \frac{100xz}{x^2 + 4} $ Assume that the z = 0 surface is a conductor and find the total charge on that portion of the conductor defined by $0 < x ...
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147 views

1D Infinite Square Well: Box Suddenly Increases in Size. How treat this?

I am currently working my way through John S. Townsend book "A Fundamental Approach to Modern Physics" (ISBN: 978-1-891389-62-7). Exercise 3.12 (p.111) is about the 1D infinite square well. The box ...
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40 views

What are eigenfunctions in a box which includes two kinds of medium?

I have to solve a problem of mathematical physics. There is a simple case which can inspire me to solving a more complex case. Considering a metal box in 2D $0<x<a$ and $0<y<b$. And ...
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73 views

damped and undamped oscillation graph comparison

I have been trying to solve a problem which compares the two motion. If the undamped free harmonic oscillator motion is $ x=A\sin\omega_{o}t$. So the corresponding motion in case of damped motion will ...
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25 views

How to show that in 1D scalar potential well there isn't pairs production (Dirac particle)

Let's have the potential $U = -V_{0}$ for $|x| \leqslant a$ and $U = 0$ for $|x| > a$. The stationary Dirac equation for bound states gives $$ tg(\frac{p_{2}a}{\hbar}) = \frac{2\Gamma}{1 - ...
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64 views

Center of mass coordinates in Lagrangians and Laplacians

Is there a quick nice and easy way to write Lagrangian's and the classical/quantum Laplacian operator in terms of center of mass coordinates? The algebra is so involved and it has me confused about ...
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66 views

What is the eigenvalue of $J_z$?

In the calculation of the Zeeman Effect, the most important calculation is $$\langle J_z + S_z\rangle.$$ Suppose we want to find the Zeeman Effect for $(2p)^2$, meaning $l = 1$. In Sakurai's book, ...
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52 views

Can't work out how the following free body diagram was created

I've been asked to draw a free body diagram of the following stepped bar setup: $ P = 10kN \;and\; Q = 30kN$ The one shown in the answer is the following: Could someone explain to me how this ...
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23 views

Is this how I find the rate of change of internal energy for filling a vessel?

If I am filling a tank with something (lets say air) and both its volume and pressure are changing with time (It's not rigid), it it safe for me to say: $$u=h-Pv$$ ...
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38 views

Two-dimensional atomic trap--how to set up the problem?

It is possible to trap neutral atoms between two solid surfaces in a potential of the form $V (x, y, z) = ax^2 + by^2$ where a and b are parameters. The allowed space for the gas extends to ...
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12 views

Does transverse flow always assist in mixed convection?

I am dealing with both natural convection and transverse forced convection over a flat plate. There are 4 different situations: Upward-facing cold plate Downward facing cold plate Upward facing hot ...
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29 views

3D SHO state transition problem

In this 3D SHO problem, the mass m is perturbed by \begin{align} H_{1} = Ar^{2}e^{-|t|/t_0} \end{align} The initial states has $n = n$ and $l = 0$ at $t = -\infty$. The question is what are ...
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75 views

Trouble with proof about operators in QM

I would like to complete the following exercise: Prove that if the operators $P_i$ satisfy $P_i^{\dagger}$ = $P_i$ and $P_i^2$ = $P_i$, then $P_iP_j=0$ for all $i\neq j$. From $P_i^2 = P_i$ I ...
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8 views

Poseuille number for flat channel?

For a flat channel with fully developed flow, the Poseuille number when using the hydraulic diameter is $$Po=C_fRe_{D_{H}}=24$$ But when using 2b as the length scale, the Poseuille number is ...
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36 views

Number of bosonic states in a $n$ particle system

Lets assume we have a system of three particles in which three energy-levels labeled by $$E_1, E_2, E_3$$ are occupied. We want to write down all states that are symmetric (bosonic). One symmetric ...
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26 views

The velocity of sound in terms of Fermi velocity

Assume this question: In a simple model of a monovalent metal consisting of point positive ion cores embedded in a uniform jellium of electrons, a value for the average energy for electron is: $$E = ...
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83 views

Hydrogen Transition Rate from n',l to n',l'

I am trying to solve Problem 9.22 in Griffiths' Intro to Quantum Mechanics (2nd Ed.) that asks to show the spontaneous emission rate for a transition from n,l to n',l' in hydrogen is given by ...
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20 views

Flux, intensity, etc in ferromagnetic core by integral

Cheng, Field and Wave Electromagnetics (newest ed.), ex 6-10, page 252 Some of the examples in this book are kind of sloppily described. Having trouble with this one. We have a toroidal core with ...
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249 views

Visualizing Tension in FBD — Rope With Mass

Asked to find the tension of a point that is halfway up a rope (where the rope has mass), given the system: The solution of the problem (FBD included) is as follows. In this diagram (Tm = tension ...
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92 views

Truss Analysis with multiple moments creates linear combinations

So in my engineering statics course we have been doing a great deal of work with trusses and machines, and a part of the physics behind it has really been confusing me. Just as a note, I also have ...
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23 views

Breakdown voltage

Capacitor (Geiger counter) is made out of wire with radius $R_1 = 5 mm$ and coaxial tube with radius $R_2 = 5 cm$. What is the maximum voltage on the capacitor, given the breakdown voltage of air ...
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46 views

Ground state of spin in magnetic field

I am trying to solve a time dependent perturbation theory problem, and it involves the Hamiltonian $$H=-\mu B\sigma_z$$ And a perturbation $$V=-\mu B_1\sigma\cdot(\cos(\omega t)\hat x-\sin(\omega ...
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64 views

Force between two charges containing several dielectrics between them

The following question is quite similar to mine. Dielectric modification of electrostatic equations? However, the answer does not prove satisfactory to me. The formula given in the above problem ...
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45 views

Question on dielectric sphere

The question is: Suppose the field inside a large piece of dielectric is $E(0)$ so that $D(0) =$$\epsilon(0)E(0)$ + $P$. Now a small spherical cavity is hollowed out of the material. Find the ...
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51 views

Deduce magnetic field based on electric field

I'm learning Maxwell's electromagnetic equations and i can't wrap my head around this problem: Given the volume $x\in [0,1], y\in [0,1], z\in [0,1]$, electric field $\vec E(x,y,z,t)$ and material ...
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31 views

Self-inductance of a toroidal inductor

I am trying to determine the self-inductance of a toroidal coil of mean radius $R$ with $N$ loops of radius $a$ with a current $I$ flowing within them. I have calculated the magnetic field by noting ...
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19 views

Do I ever not account for temperature variation from wall temperature in pipe flow?

Let's say I have internal pipe flow with a constant wall temperature. If I evaluate the properties at either the mean inlet temperature of the average of the inlet and outlet, do I always have to ...
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48 views

Trace of Spin Products Using Rotation operators

So I am working on this problem involving the trace of spin matrices. I am trying to solve for $Tr(S_iS_j S_kS_l)$ using rotation operators. I know how to go about solving for $Tr(S_iS_jS_k)$. It is ...