Helmholtz Definition and 158 Threads

for the proof of the helmholtz free energy question, why is q smaller or equal to T(S2-S1)?

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...