Helmholtz Definition and 158 Threads

Homework Statement Arfken & Weber 9.7.2 - Show that \frac{exp(ik|r_{1}-r_{2}|)}{4\pi |r_{1}-r_{2}|} satisfies the two appropriate criteria and therefore is a Green's function for the Helmholtz Equation. Homework Equations The Helmholtz operator is given by \nabla ^{2}A+k^{2}A...

Homework Statement The Helmholtz free energy of a certain system is given by F(T,V) = -\frac{VT^2}{3}. Calculate the energy U(S,V) with a Legendre transformation. Homework Equations F = U - TS S = -\left(\frac{\partial F}{\partial T}\right)_V The Attempt at a Solution We...

Hi guys, This may be a daft question (or set of questions), but I just want to bounce a few ideas off the wall once I understand some simple issues. Can anyone tell me why if you pass a current through a wire in a magnetic field, the wire will move perpendicular to the both the current...

For a thermodynamic process, what equations would be used to find the change in Gibbs and Helmholtz free energy when: a.)The process is adiabatic b.)The process is isothermic c.)The process is at constant volume d.)The process is at constant pressure I know ΔG=ΔH-TΔS and ΔA=ΔU-TΔS but do...

Homework Statement Find the Green's Function for the Helmholtz Eqn in the cube 0≤x,y,z≤L by solving the equation: \nabla 2 u+k 2 u=δ(x-x') with u=0 on the surface of the cube This is problem 9-4 in Mathews and Walker Mathematical Methods of Physics Homework Equations Sines, they have the...

Helmholtz resonator? Intake manifold design Hi guys, I'm doing a bit of research into engine intake manifolds. The information I've found so far looks staright forward, but it's given out by turners and cottage industry designers, rather than engineers or physicists, so it's basic. I...

Hello PFs, I need to build some Helmholtz coils, and I was wondering if anybody here had suggestions on what to make the actual rims that hold the wire in a coil are generally made out of? So far its been suggested that I use bicycle rims, but even that creates a question--aluminum or steel...

PDE : Can not solve Helmholtz equation (This is not a homework. I doing my research on numerical boundary integral. I need the analytical solution to compare the results with my computer program. I try to solve this equation, but it not success. I need urgent help.) I working on anti-plane...

How to get U(r) and W(r), why are them defined out of nowhere, is that the standard structure of that kind of functions ( what kind of functions are them??) ? T.Y

Homework Statement Hi there. I have this problem which I'm trying to solve. Its from callen, it says: Two ideal van der Walls fluids are contained in a cylinder, sparated by an internal moveable piston. There is one mole of each fluid, and the two fluids have the same values of the van der...

Hi I'm suppose to find the direction of the magnetic field and the current in the diagram below and I was just wondering if I did this correctly. (red is magnetic field and blue is the current) Diagram: http://i324.photobucket.com/albums/k327/ProtoGirlEXE/100_0702.jpg And I have a few...

Hi, I'm building a pair of helmholtz coils to do a variety of magnetism-related experiments. I've borrowed an old Avo Douglas coil winder and plan to do a couple of thousand turns on two sections of 50mm or 60mm diameter pipe. Some nylon threaded rod will pass through the middle of each coil...

Homework Statement Show that \epsilon(r)=\frac{A}{r}e^{ikr} is a solution to \nabla^{2}\epsilon(r)+k^{2}\epsilon(r)=0 Homework Equations The Attempt at a Solution Is \nabla^{2} in this case equal to \frac{\partial^2}{\partial r^2} or \frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial...

Hello physics enthusiasts! I was looking for resources, and stumbled upon these awesome forums. I am looking for how to solve the helmholtz equation / wave equation on a figure 8 type shape. I wanted to find the resonant frequencies of a classical guitar. Would this work? I am considering...

Homework Statement Let H(r) = x^{2}yi + y^{2}zj + z^{2}xk. Find an irrotational function F(r) and a solenoidal function G(r) such that H(r) = F(r) + G(r) Homework Equations From Helmholtz's theorem, any vector field H can be expressed as: H = -\nabla\Psi + \nablaxA So then: F...

Homework Statement We have 2 circular loops, each of radius R with current I in same direction. This is called a Helmholtz coil. The loop axes are along the z axis and the centers are at z=+/-s/2. Find the magnetic field along the z axis between the 2 loops. Homework Equations...

When it comes to thermal/statistical mechanics, I'm a little retarded... so bear with me please. I've used the helmholtz free energy (F) dozens of times, almost as many times as I've heard and read that F is a measure of the 'useful work attainable from a closed thermodynamic system,' at...

Homework Statement The diagram illustrates a Helmholtz coil, consisting of two identical circular coils of wire, each one having N loops and carrying the same current I. The radius of each coil is R, and the two coils are R meters apart. (a) What are the direction and strength of the...

Homework Statement To state the differential form of the Helmholtz thermodynamic potential and derive the corresponding Maxwell's relation. Homework Equations Stated within the solution attempt. The Attempt at a Solution Helmholtz function: F = U - TS Calculating the...

I have to show that a generic vector can be decomposed into an irrotational and solenoidal component: V(r) = -Grad[phi(r)] + Curl[A(r)] I'm not sure how to start. Do I need to take the curl or div of V and use a vector identity? Any help would be greatly appreciated!

Hello all, This is to do with forced longitudinal vibration of a rod (bar). It's basically a problem to do with the linearised plane wave equation (1d). The rod is fixed firmly at one end, and excited at the other by a harmonic force. The wave equation (with constant rho/E instead of...

Dear Sirs, I was asked to design a Helmholtz coil. Being an electronic engineer, I can design electronic circuits but I have no idea about designing Helmholtz coils. Can you help me by suggesting a paper or article that describes a straightforward, step-by-step method for designing these...

Hi, I have been trying to find the (causal) Green's function of \frac{\partial^2 \phi}{\partial t^2} + \frac{\partial^2 \phi}{\partial x^2} + \frac{\partial^2 \phi}{\partial y^2} + m^2 \phi = 0. What would be a good way to approach this? I have initial values for t=0, so I use...

Hi guys, We all know that Helmholtz free energy, Gibbs free energy and Enthalpy are defined by Legendre transformation. For Enthalpy H=E+PV, I can understand it as the energy required to "displace the atmosphere" plus "creating the internal energy of system". What about Gibb free energy...

Homework Statement The Helmholtz free energy is written as: dA=-SdT-pdV-VMdH when an incompressible liquid is placed in a magnetic field H. Thus, the free energy can be written as since -pdV=0: dA=-SdT-VMdH The two heat capacities can be defined as: C_H = T (dS/dT)_H and C_M = T...

hi guys.. I'm trying desperately to solve the following Helmholtz equation: *(all parameters are known) \frac{\partial^2 E_z}{\partial x^2}+ \frac{\partial^2 E_z}{\partial y^2} +j\omega\sigma E_z=0 (Ez is a scalar of course) in the boundaries -inf<x<inf, -inf<y<0 with the...

Homework Statement Show that the most probable energy minimises the Helmholtz free energy. Homework Equations F=E-TS(E) where S(E) is the entropy of te system of given energy E. The Attempt at a Solution Not sure how you would 'show' is ? P(E) = 1/Z *weight funciton*exp(-beta E)

I'm trying to find a divergenceless vector field based on its curl, and discovered that I could use a http://en.wikipedia.org/wiki/Helmholtz_decomposition" , and the article I found on this didn't make much sense to me. First, can someone confirm that the dimension referred to in the...

I'm trying to find a divergenceless vector field based on its curl, and discovered that I could use a http://en.wikipedia.org/wiki/Helmholtz_decomposition" , and the article I found on this didn't make much sense to me. First, can someone confirm that the dimension referred to in the...

Homework Statement Explain why the formula (dF/dV)=-P , where T and N are constant variables , makes intuitive sense, by discussing graphs of F vs. V with different slopes. Homework Equations The Attempt at a Solution dF=SdT-PdV+mu*dN dT and DN are zero since T and N are...

Homework Statement Use the definitions of Helmholtz free energy, F, and Gibbs free energy, H, together with the thermodynamic identity, to show that S = -(\frac{\partial F}{\partial T})_V and S = -(\frac{\partial F}{\partial T})_P Then use those definitions again, and the...

Hello guru's, I've been trying to figure out a way to incorporate an electric field source in the Helmholtz equation, and have been accumulating lots of question marks in my head. So in case of no static charge, \nabla^{2} E - \mu (\epsilon\frac{d^{2}}{dt^{2}} + \sigma\frac{d}{dt}) E = 0...

Homework Statement Hi all. Lets take a look at the Helmholtz free energy. It is defined as the amount of energy one has to put into create a system once the spontaneous energy transfer to the system from the environment is accounted for. Now let's look at it once we have created the...

Homework Statement The coils in a set of Helmholtz coils have 186 turns and a radius of 15.9 cm. The current is set at 2.2 A. Express your answers in units of "T" for Tesla. a) Calculate the magnetic field along the axis at the center of the two coils (x = 0). b) What is the magnetic...

What is the reasoning behind defining the helmholtz free energy as F = -kT ln Z? I always wanted to know why it was just defined as the above. Is it as a form of convenience because the macroscopic theromodynamic observables of a system at constant temperature (ie the canonical ensemble) are...

Homework Statement The picture shows (there's supposed to be a pic) a Helmholtz coil consisting of two circular coaxial coils, each of 200 turns and radius R = 25.0 cm, separated by a distance s = R. The two coils carry equal currents i = 12.2 mA in the same direction. Find the magnitude...

"Helmholtz equation" Neumann and divergence Hello, I'm trying to solve the following elliptic problem : S = B - \mu\nabla^2 B Where S(x,y) and B(x,y) are 3 component vectors. I have \nabla\cdot S = 0 and I want B such that \nabla\cdot B = 0 everywhere. I'm using finite differences on a...

Helmholtz free energy decreases... Hello... I'm having trouble getting my head around something. I'm not exactly sure what is meant by the Helmholtz free energy (F) decreasing in a system that's in thermal equilibrium with it's environment. Under what circumstances does it decrease...

Homework Statement The neutnral carbon atom has a 9-fold degeerate ground level and a 5-fold degenerate excited level at an energy 0.82 eV above the ground level. Spectroscopic measurements of a certain star show that 10% of the neutral carbon atoms are in the excited level, and that the...

Working in CGS units... hence i don't know if my answer is right or wrong anymore... It doesn't 'look' right Homework Statement Two coils are placed at l and -l on the Z axis as in the figure. They both carry a current I in the same direction (anticlockwise). Both have a radius of a. (Setup...

Hi everyone, new to this site and was wondering if anyone could help me out... I am trying to prove the following equation to be true but don't really know where to start. Supposedly, I should be finding the Laplacian first using spherical coordinates. ∇^2(1/|R|) = -4*pi*δ(R) where |R|=...

Homework Statement Determine the change in the entropy, Helmholtz free energy, and Gibbs free energy, when a mole of ideal gas is compressed from 1atm to 100atm at 20C. The Attempt at a Solution I am not entirely convinced by my attempt below -- can anyone spot something wrong? (I thought it...

I am currently working on a research project, and need an equation or method to find the magnetic field strength produced by any number of helmholtz coils, and not just on the central axis, but at any position in the space around them. Can anyone help me out? Thanks

Greetings, I have recently come across the Helmholtz differential equation. Is there already a thread here that discusses the mathematic techniques (differential equation techniques) used to solve it? If not can we discuss how one can solve the equation? I'm familiar but rusty with...

Possible Helmholtz equation? Homework Statement Heres my problem: In recent studies of migrating birds using the Earth's magnetic field for navigation, birds have been fitted with coils as "caps" and "collars". a. If the identical coils have radii of 1.2cm and are 2.2cm apart, with 50...

Homework Statement How do I take the first and second derivatives of the helmholtz equation? The equation is as follows: Bx= ((uR^2NI)/2) * ( [1/((x+a)^2+R^2)^(3/2) ] + [1/((x+a)^2+R^2)^(3/2) ] ) heres what I have to prove First Derivative...

Dear all, I know that I can create a uniform field using the design of a Helmholtz coil with an air-core. However, if I use a ferrous core like iron, will I still be able to create a uniform field under the same conditions? Also, how is the equation for the magnetic field, B, changed when...

Hi everyone! This question has me a little stumped.

" Classical and nonclassical symmetries for Helmholtz Equation " solitions help. Thank you.

what's the physical meaning of that equation? all i see is a jumble of numbers and equations...