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What does "curl E = const." on Ω say about E on ∂Ω?

Assume I have a simply connected domain Ω and a twice differentiable vector field E for which I know that "∇×E = const." (1) and "∇E = 0" (2) on Ω - I am interested in solving a BC Problem on ∏ = (Ʃ ⊃...

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Energy "formulation" of classical mechanics?

When discussing the different formulations of classical mechanics, those that are always mentioned are Newtonian, Lagrangian and Hamiltonian mechanics. However, it is my understanding that when dealing...

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Surface Charge Density - notation used

Surface charge density is denoted with a lower case sigma: σ Though sometimes I also see it denoted as σ with a subscript 0. What is the difference in these notations? Thank you.

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the harmonic oscillator

Hi all, this is my first time on PF. I do not know English but I have a problem of a harmonic oscillator. I have rather large head, help me please , I do not know what else to do ... I have this...

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Complex current density of sphere confusion

Hello, I am a bit confused on how to get this into the proper form, $$ \begin{eqnarray} \vec{J} &=& \vec{v}\rho \\ &=& (\vec{\omega} \times \vec{r}')\rho_o \Theta(R-r') \\ &=&...

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Recovering WWII magnetic amplifier technology

I have a continuing interest in recovering the schematic of a 2 stage DC magnetic amplifier that was used in my graduate school. I was in the physics lab at the University of New Orleans working with...

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Fokker-Planck P(y,t)?

I am Reading in a Book of Stochastic Processes. I understood the Derivation of the Fokker-Planck equation from the master equation. The Result is (the FPE): $$ \frac{\partial P(y,t)}{\partial t} = -...

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gravity effects in particle accelerators

Is the effect of gravity ever considered in particle accelerator experiments? I would think not with all the high energy, velocities, and stong electric fields in use. But I am interested if...

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Getting high current from AA batteries

I am trying to increase the strength of my electromagnet, at the moment by increasing the amperage. I have been using an old 12V motorcycle battery, but also tried with 10 AA batteries. I was wondering...

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What is the time constant to evaporate a liquid

I have a liquid that is stored at pressure. This liquid is then released to a lower pressure where it should become a gas. The problem is how long does it take for the liquid to turn to gas. There must...

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Energy conversion difference in permanent magnet vs. field coil motor

New here, hello all. My question is more about the field magnet in a running DC motor. First of all, does the current required to maintain a magnetic field change with the load on the motor? And if so,...

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Feynman's Lectures Refraction Angle question

Hey there, recently been studying Optics in Feynman's book vol.1 and came across his geometrical approach of Fermat's least time theorem and its application on refraction. So he illustrates refraction...

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Standing waves - Wave Equation

I don't completely understand how equation 4.4.4 was derived and determined. I understand the derivation behind the basic wave equation 4.3.4 but not what happened in 4.4.4. Why is there a need for all...

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S.H.M. of helical spring.

We've just begun studying oscillatory motion and recently derived the differential equation of motion for a helical using Hooke's law and Newton's second law of motion. The differential equation of...

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Sum of forces

I'm drawing a cone (black color) inside balls. Balls are pressured from external force, but the pressure is fixed. Balls repuls themselves and cone repuls balls too. The cut view of cone (bot) showing...

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Damped Harmonic Motion

So my professor was discussing the case of a mass suspended from a vertical massless spring in some viscous liquid. He arrives at the equation of motion which was : x: + [itex]\frac{b}{m}[/itex]x. +...

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How do you connect angular velocity vector with the positions?

I've been working out a question about rigid body rotations, and though I can grasp the basic math, I'm completely lost about the physical quantities. In particular, I'm trying to relate the three...

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Photon wavelength probability distribution for blackbody

Hey everyone, This is my first time posting on PF! I want to model the photons ejected from a blackbody source at temperature T. The question I want answered is: given a photon is detected, what is the...

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Modeling Atmospheric Re-entry & Determing Optimal Re-entry Parameters

I'm taking a course in adaptive neural networks and became interested in trying to see if I can use neural networks to find the optimum values for the control parameters in atmospheric re-entry in...

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Need help understanding this thermo. derivation

Im trying to understand this concept of deriving an expression for ([itex]\frac{\partial T}{\partial P}[/itex])s in terms of T, V, Cp, [itex]\alpha[/itex], and [itex]\kappa[/itex]T...

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