Oh, I see. I believe you should still be able to use the cut-offs to get an answer. I think that for electrostatics of charges that continue to infinity, you need to use the more complicated equations, rather than the usual Gauss' law. Sorry I don't know much about it, so I can't give a better...
ooh, this is an interesting question. I believe the system you are talking about is called a "non-neutral Coulomb gas" in statistical physics. It is maybe quite a niche subject. I found a couple of papers talking about this problem in 2D...
I'm not 100% sure if I understood the question. But, in the magnet frame, the slab is moving, there is a force on the slab since it is moving in a magnetic field. In the slab frame, the magnet is moving, so there is a changing magnetic field that acts on the slab, so there is still a force on...
The more precise your question, the better the answer (in science, at least). Ultimately, the idea of scientific endeavour is to build a theory that has practical implications. To do this, precise (rigorous) definitions are needed.
I'm still not 100% sure what your concerns were. Taking the...
hm, as an example, the free energy of the 1D Ising model is $$f(\beta ,h)=-\lim _{L\to \infty }{\frac {1}{\beta L}}\ln(Z(\beta ))=-{\frac {1}{\beta }}\ln \left(e^{\beta J}\cosh \beta h+{\sqrt {e^{2\beta J}(\sinh \beta h)^{2}+e^{-2\beta J}}}\right)$$ I would prefer to say this macroscopic...
This wiki article https://en.wikipedia.org/wiki/Entropy_(information_theory) is the kind of entropy I'm thinking about when I say the amount of disorder, or lack of knowledge. They actually use the word 'surprisal' but it is maybe a bit intimidating for beginners, which is why people say...
On one hand, there is the idea of entropy as expressing our lack of knowledge of the system. On the other hand, we have the thermodynamics idea of entropy, which feature in the 3 laws of thermodynamics. They're related but maybe a little bit different.
If we had a system of particles in...
Hi,
your solution looks good to me !
It's true that the Normal force is a reaction to the mass being pushed into the cone, but there is no reason for the normal force to be less than the gravitational force on the block. The normal force will be whatever it needs to be, to stop the mass from...
yeah... I guess there will still be an interference pattern even if the slit width is not comparable to several hundred nanometers. There will still be diffraction from the edges of the slits, but there will also be light passing through the middle of the slit without being diffracted. So I...
I agree with Ray :) You used x=70,000, which is the current population. But you should be finding the long-term 'sustainable population'. Also, you were differentiating F(x) but that means you were trying to find the max value of rate of population change? that is not a relevant quantity for...
Hi lazystudent ! honest name :)
Yeah, I agree that your ##F(x)## function is important to this problem. But I don't think you should be differentiating it. First think of what that function means for this problem. ##G(x)## is a growth rate and ##H(x)## is the rate at which they are harvested, so...
I am not so familiar with this kind of stuff. But I think that usually, you must keep the condensate in the trap. Otherwise, the condensate would interact with the environment, which would destroy the condensate.
No, the thermometer is not only affected by translational kinetic energy because of the reason nasu gave. The molecules in the gas will collide with each other, and will transfer their energy to and from kinetic and rotational. Therefore, the rotational energy can also be passed to the...
yes, I think Khashishi is right to put some actual numbers down. Maybe this is the best way to explain. So, for a monoatomic gas, the average kinetic energy of the gas is 3kT/2 and the average rotational energy of the gas is zero, therefore the average total energy is 3kT/2. And for a diatomic...
uh... I think I see where we are getting mixed up. Each degree of freedom is independent of the others. And at a given temperature, each degree of freedom will contain the same energy as the others (due to equipartition of energy). So in this sense, temperature is proportional to the average...
I think the OP'er is saying that the energy stored in the rotational degrees of freedom contribute to the temperature. Which I guess is sort of true, since the temperature and average rotational energy are related in a simple way in this case. But I agree, generally it is not a good way to talk...
If we heat a polyatomic gas at constant volume, the heat capacity is greater than for monatomic gas. Therefore, for the polyatomic gas, it takes more energy to increase the same amount of temperature. This makes sense because the polyatomic gas has more degrees of freedom, i.e. more places to...
If there are rotational degrees of freedom, then the energy will be the sum of rotational and kinetic energies. So yes, I agree with what you are saying. We probably have to also assume that the polyatomic atoms only interact in brief collisions, and don't have extended interactions or correlations.
I feel like your professor is saying you can just simulate the physics on the computer. i.e. you don't need to calculate x(t). Instead, maybe the problem is to find difference equations which represent your problem, and get the computer to simulate it. Did your professor ever explicitly say to...
I was curious about this, so I looked it up. It seems there is a recurrence relation, for the n by n chess board sizes, given in the 2010 paper by M. Erickson et. al. "Enumerating rook and queen paths" in the journal "Bull. Inst. Combin. Appl." Which agrees with the answer 470010 for the 8by8...
that sounds like a good answer. Although, the magnetisation would not be close to zero, it is just less than the theoretical prediction. So, perhaps some of the domains get nudged out of place, and become non-aligned to the majority of domains which are pointing in the same direction. I think...
unfortunately, it is not possible to add up ##j = l + s##. It is slightly more complicated. Thinking about it intuitively, the orbital and spin angular momenta may be somewhat misaligned, therefore the measurement of the magnitude of angular momentum will have more than one possible value. On...
Hi, sorry slow reply. Yes, if we just consider magnetic field, it would seem the Curie temperature should be much lower. So there must be some other kind of interaction which causes the measured Curie temperature to be much higher. What kind of interaction could this be? hint: you have been...
We need to take the square of the coefficients to get the Probabilities. And as a sanity check, the probabilities of all possible outcomes should add up to 1.
You Have written it out correctly. But that is not necessary yet. Look at what the question is asking, it wants to know about eigenvalues. And the state you are given contains terms of spherical harmonics. What can you say about the spherical harmonics? (It makes the first question easier to...
that's ok! For the ferromagnet, when ##T<T_c## we have a nonzero net magnetisation (up or down). Therefore, if we add an external magnetic field (up or down), there would be some energy preference of one state over the other. i.e. the symmetry between the states is lost.
yes. those are the two...
Interesting. So, was the question statement the wrong way around? If we reverse it, we get: "Explain why determinate states for angular momentum are stationary states of the particle". But after reading your post, I guess this is not true either. We could have a state which is made up of...