Recent content by BruceW

  1. BruceW

    I Breakdown of Gauss' Law?

    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...
  2. BruceW

    I Breakdown of Gauss' Law?

    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...
  3. BruceW

    I Divergence of v x B = Divergence of E in the v=0 frame?

    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...
  4. BruceW

    B A Question about Entropy

    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...
  5. BruceW

    B A Question about Entropy

    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...
  6. BruceW

    B A Question about Entropy

    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...
  7. BruceW

    B A Question about Entropy

    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...
  8. BruceW

    I Circular motion in a cone

    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...
  9. BruceW

    Slit sizes needed for light diffraction

    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...
  10. BruceW

    Optimization growth rate Question

    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...
  11. BruceW

    Optimization growth rate Question

    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...
  12. BruceW

    Tan (a) = -1

    yes. The problem statement is essentially to find the solutions of arctan(-1)
  13. BruceW

    Question about harmonic poential trap

    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.
  14. BruceW

    Do rotational degrees of freedom contribute to temperature?

    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...
  15. BruceW

    Do rotational degrees of freedom contribute to temperature?

    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...
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