What is Helmholtz: Definition and 179 Discussions

Hermann Ludwig Ferdinand von Helmholtz (31 August 1821 – 8 September 1894) was a German physicist and physician who made significant contributions in several scientific fields. The largest German association of research institutions, the Helmholtz Association, is named after him.In physiology and psychology, he is known for his mathematics of the eye, theories of vision, ideas on the visual perception of space, color vision research, and on the sensation of tone, perception of sound, and empiricism in the physiology of perception.
In physics, he is known for his theories on the conservation of energy, work in electrodynamics, chemical thermodynamics, and on a mechanical foundation of thermodynamics.
As a philosopher, he is known for his philosophy of science, ideas on the relation between the laws of perception and the laws of nature, the science of aesthetics, and ideas on the civilizing power of science.

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  1. A

    I How Do Helmholtz Coils Affect Electromagnetic Beam Transmission?

    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...
  2. bob012345

    I Helmholtz Equation in Cartesian Coordinates

    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...
  3. Sebobo

    Engineering Helmholtz pair, magnetic field in 3D

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

    I Derivation of the Helmholtz equation

    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...
  5. J

    Show that the Diffusion Eqn after substitution gives the Helmholtz Eqn

    Question: Helmholtz as defined in text: My attempt so far
  6. maistral

    Helmholtz free energy for mixing?

    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...
  7. J

    A Nonlinear Wave Equation (Nonlinear Helmholtz)

    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} +...
  8. P

    Confirming Green's function for homogeneous Helmholtz equation (3D)

    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]##...
  9. F

    I Vector field and Helmholtz Theorem

    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...
  10. P

    Entropy and the Helmholtz Free Energy of a Mass-Piston System

    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...
  11. A

    B Calculating the Uniform B Field in an AC Helmholtz Coil: What's the Formula?

    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...
  12. S

    A Question about Helmholtz resonance

    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...
  13. M

    Helmholtz synthesizer experiment

    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...
  14. E

    I Helmholtz resonator with multiple necks--formula?

    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...
  15. H

    Work done for isothermal process in terms of Helmholtz func

    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 =...
  16. Matt Chu

    Proving a complex wave satisfies Helmholtz equation

    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...
  17. Matt Chu

    Proving a wave satisfies the Helmholtz equation

    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...
  18. A

    Lorentz-like forces and the Helmholtz conditions

    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...
  19. G

    I How Does Helmholtz Free Energy Change During Constant Temperature and Volume?

    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...
  20. D

    A Helmholtz Resonator: attenuation vs. amplification

    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...
  21. K

    Error analysis E/M experiment -- help please

    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...
  22. P

    Potential flows and Helmholtz decomposition

    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...
  23. Ryaners

    Calculating B:I for Helmholtz coils

    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...
  24. DrClaude

    Green's function for the Helmholtz equation

    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') =...
  25. Z

    How do I solve this problem involving the Helmholtz and Gibbs Energy?

    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...
  26. tze liu

    Where is the work done coming from in Helmholtz free energy

    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
  27. D

    Free energy Helmholtz using only the equation of state

    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...
  28. P

    Help with 3axis Helmholtz Coil

    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...
  29. W

    Helmholtz and Gibbs free energy for an adiabatic process

    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...
  30. CricK0es

    Applications of the Helmholtz Coil: Shielding and Stabilizing Fields

    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...
  31. S

    Proving Minimization of Helmholtz Free Energy at Equilibrium

    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...
  32. S

    I Helmholtz Free Energy: Why is F Minimized?

    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...
  33. F

    I Wavevector k in Helmholtz Equation

    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...
  34. T

    A Observations Helmholtz equation is unable to explain

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

    Low Level EMF and Helmholtz coil design

    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...
  36. Vajhe

    Fourier transform of the Helmholtz equation

    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 ##...
  37. S

    Engineering Eigenfunctions of the vector Helmholtz equation

    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...
  38. grandpa2390

    How Is dA Calculated for an Isothermal Expansion of an Ideal Gas?

    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...
  39. O

    Helmholtz potential for mixture of simple ideal gases

    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...
  40. J

    When can I use Helmholtz equation for electromagnetics

    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...
  41. Y

    Is there an Altitude Dependence on Helmholtz Free Energy?

    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...
  42. W

    Wanted: Looking for a helmholtz coil in Brisbane, QLD AUS

    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 :)...
  43. wololo

    What is the solution for finding F in terms of T and V without integrating?

    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
  44. ognik

    Fourier Transforms, Green's function, Helmholtz

    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\...
  45. P

    Specific Heat and Helmholtz Free Energy?

    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.
  46. B

    Derivation of Helmholtz Energy Minimum in Thermodynamics

    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?
  47. B

    Gibbs and Helmholtz energies of a superconductor

    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...
  48. S

    Finding energy from dipole moment - Helmholtz pair?

    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...
  49. N

    Lifting Line Theory and Helmholtz theorems

    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...
  50. S

    Helmholtz Free Energy Legendre Transformation

    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...
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