Helmholtz Definition and 179 Threads

What would the behavior of an electromagnetic beam (transmission) be if directed through a Helmhotz coil? Is there a different result with a 4 or 6 coil configuration (all orthogonal)? Is there a direct response depending of frequency of the EM transmission (10kHz - 10 GHz) and current being...

So given the Helmholtz equation $$\nabla^2 u(x,y,z) + k^2u(x,y,z)=0$$ we do the separation of variables $$u=u_x(x)u_y(y)u_z(z)= u_xu_yu_z$$ and ##k^2 = k_x^2 + k_y^2 +k_z^2## giving three separate equations; $$\nabla^2_x u_x+ k_x^2 u_x=0$$ $$\nabla^2_y u_y+ k_y^2 u_y=0$$ $$\nabla^2_z u_z+ k_z^2...

As far as I can tell, the shape looks like a cuboid with 8 arms pointing in all directions.

I am trying to understand the Helmholtz equation, where the Helmholtz equation can be considered as the time-independent form of the wave equation. It seems to me that the Helmholtz equation can be derived from the Fourier transform, such that it is part of a larger set of equations of varying...

Question: Helmholtz as defined in text: My attempt so far

Hi, I have been reading a few literature regarding excess Helmholtz energy and I encountered this definition from the paper of Wong and Sandler (apparently, from the mixing rule used in a EOS): In particular, the ones in the red boxes. How did these equations come into being? I tried to look...

I am trying to solve a PDE (which I believe can be approximated as an ODE). I have tried to solve it using 4th Order Runge-Kutta in MATLAB, but have struggled with convergence, even at an extremely high number of steps (N=100,000,000). The PDE is: \frac{\partial^2 E(z)}{\partial z^2} +...

Plugging in the supposed ##G## into the delta function equation ##\nabla^2 G = -\frac{1}{4 \pi} \frac{1}{r^2} \frac{\partial}{\partial r} \left(\frac{r^2 \left(ikr e^{ikr} - e^{ikr} \right)}{r^2} \right)## ##= -\frac{1}{4 \pi} \frac{1}{r^2} \left[ike^{ikr} - rk^2 e^{ikr} - ike^{ikr} \right]##...

Hello, A generic vector field ##\bf {F} (r)## is fully specified over a finite region of space once we know both its divergence and the curl: $$\nabla \times \bf{F}= A$$ $$\nabla \cdot \bf{F}= B$$ where ##B## is a scalar field and ##\bf{A}## is a divergence free vector field. The divergence...

Attempt at a Solution: Heat Absorbed By The System By the first law of thermodynamics, dU = dQ + dW The system is of fixed volume and therefore mechanically isolated. dW = 0 Therefore dQ = dU The change of energy of the system equals the change of energy of the gas plus the change of energy...

What would be the formula to calculate the right spacing distance between the coils in order to get a uniform homogeneous B field in the middle of the coils and how to determine the B field strength? I can only find bits and pieces on google about these sort of formulas but their intended for...

Perhaps my question has to do with Helmholtz resonance, perhaps not. That's why I'm here. ;-) Here's my question: Say you have a large steel oil drum that is half full of water. If you bang on the side of the drum towards the top with another metallic object, what exactly is making the sound...

Hello all! Inspired by the Helmholtz synthesizer, I am experimenting with electromagnetic excitation and tuning forks. http://www.sites.hps.cam.ac.uk/whipple/explore/acoustics/hermanvonhelmholtz/helmholtzssynthesizer/ How can I determine the size and charge of an electromagnet in order to...

Does anybody happen to know the formula for resonant frequency of a Helmholtz resonator having N necks? Physics is not my field and I'm a bit over my head. I need the formula for a computer program related to musical instruments--this is the only thing holding me up. It seems like it would...

The Helmholtz function differential form for a reversible process is: dF = -SdT - PdV, as for a reversible process δW (by system/here an (ideal) gas) = PdV and dS = δQ/T. Therefore, for a reversible isothermal process, dT = 0 and hence dF = -PdV. Therefore, the work done by the system is W =...

Homework Statement Consider a harmonic wave given by $$\Psi (x, t) = U(x, y, z) e^{-i \omega t}$$ where ##U(x, y, z)## is called the complex amplitude. Show that ##U## satisfies the Helmholtz equation: $$ (\nabla + k^2) U (x, y, z) = 0 $$ Homework Equations Everything important already in...

Homework Statement Consider a harmonic wave given by $$\Psi (x, t) = U(x, y, z) e^{-i \omega t}$$ where ##U(x, y, z)## is called the complex amplitude. Show that ##U## satisfies the Helmholtz equation: $$ (\nabla + k^2) U (x, y, z) = 0 $$ Homework Equations Everything important already in...

The question is: Are acceleration independent forces that obey the Helmholtz condition necessary of the Lorentz form? ============================================================================== According to the "On Feynman’s proof of the Maxwell equations" (Hughes, R. J. (1992) American...

This is really basic,and I’m not seeing something obvious,but I’d appreciate help with this concept. In differential form dA= -tds-pdv. However s and v are the natural variables for this free energy and are held constant . As I understand it the Helmholtz free energy is the energy available to...

Hello guys, I read the other threads about HR, resonances and so on, but I couldn't find a clear explanation of what the practical implications of using a HR are. From one side, HR is described as a "reactive element", used in several contexts to attenuate a specific noise by means of...

So I am doing the charge to mass experiment and determining the relationship between: 1. accelerating voltage and radius formed by the electron beam 2. magnetic field strength and radius formed by electron beam Theoretically I should obtain an equation of the form: r = (1/B) *sqrt(2mV/e) where...

Hi. I'm studying fluid dynamics and in particular potential flows. I know that for an irrotational flow the velocity field is a conservative field and it can be rapresented by the gradient of a scalar field v=-∇Φ. In this case the explicit form of Φ is something like a line integral between a...

Homework Statement I've completed an experiment where the dependence of magnetic field strength ##B## on current ##I## is measured at the midpoint along the axis between two Helmholtz coils (separation distance = coil radius ##r##). I got the expected linear relationship from the data but am...

Homework Statement Show that $$ G(x,x') = \left\{ \begin{array}{ll} \frac{1}{2ik} e^{i k (x-x')} & x > x' \\ \frac{1}{2ik} e^{-i k (x-x')} & x < x' \end{array} \right. $$ is a Green's function for the 1D Helmholtz equation, i.e., $$ \left( \frac{\partial^2}{\partial x^2} + k^2 \right) G(x,x') =...

1. Robert Dehoff 4.12 A system is designed that permits continuous programmed control of the pressure and volume of the gas that it contains. The system is filled with 1 g atom of helium and brought to an initial condition of one atmosphere and 18 liters. It is then reversibly compressed to 12...

Sorry,i want to ask a question here the note said the volume is "fixed" here. if the volume if fixed,how comes the work done(because no change of volume) here i totally get lost here thank

Homework Statement This is a state ecuation of a gas: PV=AT+B/V, where A and B there are constants. First: Demonstrate that ##c_V## depends only of T Second: Find U(T,V) and S(T,V) Homework Equations ##\left(\frac{\partial U}{\partial S}\right)_V=T\text{ (1)}## ##\left(\frac{\partial...

First of all, hello to all of you. My question is, I want to simulate 3-axis Helholtz Coil in Maxwell 3d. I made some models of it, but I am not sure I got all right - especially ration of coils in x-y-z and their current excitation. Second, i'd like to see H field, or B field plot if some of...

Homework Statement Calculate changes in A and G of one mole of an ideal gas that undergoes the following processes respectively. 1. adiabatic expansion from (T1, P1) to (T2, P2) 2. isobaric expansion from (P, V1, T1) to (P, V2, T2) (if it is not isothermal) 3. isochoric expansion from (V, P1...

Homework Statement Hi, I've got a presentation on an experiment we did using the Helmholtz coil and I'm starting to run dry on material. As some additional applications I found that you can: - Use the coil set up to cancel external interference (Shield other experiments? Not sure about that...

Homework Statement Show that for a reaction occurring at constant T and V, F is minimized at equilibrium. Homework Equations ##F=U-TS## ##TdS=dU+pdV-\mu dN## The Attempt at a Solution ##dF=dU-d(TS)=dU-TdS-SdT=dU-dU -pdV+ \mu dN -S dT=-pdV - SdT + \mu dN##. At constant T and V this reduces to...

Hello! I read that the Helmholtz free energy is minimized at constant T and V at equilibrium. But I am not sure I understand why. So starting from ##F=U-TS## I got ##dF = \mu dN - pdV -SdT##. So at constant V and T we have ##dF = \mu dN##. Now I am not sure how does this implies that F is...

Hello Everyone, Helmholtz equations derives from the wave equation by using separation of variables and assuming that the solution is indeed separable ##g(x,y,z,t) = f(x,y,z) T(t)##. The solutions to Helmholtz equations are functions of space, like f(x,y,z), and do not depend on time t. the...

Can someone explain to me some of the key observations Helmholtz equation cannot explain and why that is so? Thanks!

The problem statement: I want to produce an LL-EMF of a specific amplitude and frequency in a pair of Helmholtz coils of pre determined radius. The frequency and amplitude are derived from the following equations from this publication...

Hi guys, I have been trying to solve the Helmholtz equation with no luck at all; I'm following the procedure found in "Engineering Optics with MATLAB" by Poon and Kim, it goes something like this: Homework Statement Homework Equations Let's start with Helmholtz eq. for the complex amplitude ##...

Hi everyone, I'm looking for a reference book that treats the theory behind the eigenfunctions solution of the so called vector Helmholtz equation and its Neumann and Dirichlet problems. I've already found a theory inside the last chapter of Morse & Feshbach's Methods of theoretical physics...

Homework Statement Use the fundamental eq for the helmholtz eq to find dA for 1 mole of ideal gas as it expands isothermally from 5L to 15L at 298 Kelvin Homework Equations dA = -PdV - SdT PV = nRT The Attempt at a Solution I tried to solve this the same way I did the problem on the previous...

Homework Statement Two subsystems within a 20 l cylinder are separated by an internal piston. Each of them is initially composed of 1 mole of component 1 and one mole of component 2, both of which will be treated as a monatomic ideal gas. The cylinder has diathermal walls and is in contact...

The complete Maxwell wave equation for electromagnetic field using the double curl operator "∇×∇×". Only when the transverse condition is hold, this operator can equal to the Laplace operator and form the helmholtz. My question is what's the condition can we use the helmoltz equation instead of...

Homework Statement [/B] The density of nitrogen molecules is larger at a sea level than at a higher elevation. Assuming thermal equilibrium, what is the altitude dependence of the (Helmholtz)free energy per particle? Homework Equations F=U-TS, not sure if anything else is relevant The Attempt...

Hi guys, I'm a typical nerd that wanted to do an at home science project but don't want to spend lots of money on this coil. I would love to borrow/rent one if someone could help me. Otherwise if someone new a cheap supplier that i could get one off? It looks like either of these pictures :)...

Homework Statement Homework Equations Maxwell relations The Attempt at a Solution I have an attempt at a solution, but I am not sure if I can replace the integral of dT in the helmholtz equation by the T I found using the internal energy. Does this make sense? Thanks

Homework Statement I've gotten myself mixed up here , appreciate some insights ... Using Fourier Transforms, shows that Greens function satisfying the nonhomogeneous Helmholtz eqtn $$ \left(\nabla ^2 +k_0^2 \right) G(\vec{r_1},\vec{r_2})= -\delta (\vec{r_1} -\vec{r_2}) \:is\...

I'm wondering if there's a simple relation between the specific heat capacity (at constant chemical potential) and the Helmholtz Free Energy? I can't seem to find a relation in the literature between these three quantities, specifically.

Hey, The helmholtz energy is supposed to have a minimum when the entropy has a maximum value. Does anyone knows the derivation for this statement?

Hello, I consider an ideal superconductor with the gibbs-energy $$ d G=-SdT + VdP - \mu_0 M V dH$$ and helmholtz energy $$ dF = -SdT -P dV + \mu_0 V H dM$$ Assuming, that in the normal state the magnetization is too small, so that G_n(H) = G_n(H=0) and at the transition point H_c the...

Firstly apologies for not typing this out - but I need the diagram. And I have no idea where to start. I 'think' most of it is correct. BUT - I have no idea what to do with the last part of c. I thought I could just double the energy. But I'm going to get a negative energy for the system...

I was reasoning about prandtl's lifting line theory. Now, a lot of books state that if the the circulation changes across the bound vortex filament a vortex sheet of the same intensity must be shed from the filament following the wake. Is this a consequence of the helmolzt theorem that forbids...

Homework Statement Show how a Legendre transformation is used to obtain the Helmholtz free energy A(T,V) from the internal energy and derive the general expression for the differential of A. Homework Equations Internal Energy is a function of Entropy and Volume. U Ξ (S, V) A Ξ (T,V) A = U...