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.
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...
Homework Statement
Given 3D Helmholtz eqn.
u_xx + U-yy + U_zz + Lamda*u = 0 ,Lamda > 0.
We are asked to "Calculate the fundamental solution directly (without using the Bessel identity for J_1/2 given)"
where:
Bessel identity given is w(r)=C_n*r^-(n-2)/2*J-(n-2)/2*(Lamda^1/2*r)...
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...
\tau = k_{B} T
a) Find the expression for the free energy as a function of the temperature of the system with two states - one iwth eneryg zero and one with energy \epsilon_{0}
b) From the free energy find the expressions for the energy and entropy of the system
c) Plot the average energy...
Im trying to solve Helmholtz equation
\nabla ^2u(r,\phi,z) + k^2u(r,\phi,z) = 0
in a hollow cylinder with length L and a < r < b
and the boundary conditions:
u(a,\phi,z) = F(\phi,z)
u(b,\phi,z) = G(\phi,z)
u(r,\phi,0) = P(\phi,z)
u(r,\phi,L) = Q(\phi,z)...
I'm trying to track down a quantitative proof that the most uniform magnetic field between two Helmholtz coils occurs for a separation equal to their radii.
So far I've just been playing around with the Biot-Savart law and proving that B is identical at several trial points along the axis...
Let’s say we have a 1 mol system in a state A (Pa,Va,Ta are given) and we take it to a state B(Pb,Vb are given) . We want to know what’s the maximum work we can give to a reversible work source. Considering the process is carried out attached to a 150 K heat source, the only data available is...
hey I am pretty sure that if the right amount of current passes through the pair of coils in a helmholtz arrangement, the magnetic field it produces can null out any magnetic fluctuation. but how can you calculate the magnetic field it generates?
thanks a lot
and correct me if there was any...
I'm solving a Helmholtz equation uxx+uyy+lambda*u=0 in a rectangle: 0<=x<=L, 0<=y<=H with the following boundary conditions:
u(x,0)=u(x,H)=0 and ux(0,y)=ux(L,y)=0
I found the eigenvalues to be:
lambda(nm)=(n Pi/L)^2+(m Pi/H)^2
and the eigenfunctions to be:
u(nm)=Cos(n Pi x/L)*Sin(m Pi...
hello,
here is my second message.(and my English is still very bad)
I don't understand these 3 little experiments(we need Helmholtz coils and a Hall Effect probe)
I know I have to draw a graph for each situation but I can't interpret the difference between the theory and the experiment...
Does anyone know anything about this?
I got a look at wolfram.com and I didnt get much.
I would like to prove that in fact, any divergenceless vector field can be decompose in a toroidal part and a poloidal part. And I think the proof of this is somehow related with this theorem...