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For a classical Maxwell-Boltzmann gas, the partition function is given by $$Z=\sum_i g_i e^{-\beta \epsilon_i}$$ where $g_i$ is the degeneracy. And the probability for each level to be occupied by one particle is given by $$P_i=\frac{g_i e^{-\beta \epsilon_i}}{Z}$$ The partition function function in the above expression is essentially a normalization factor ...


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A trajectory or flight path is the path that a moving object follows through space as a function of time. The object might be a projectile or a satellite, for example. It thus includes the meaning of orbit—the path of a planet, an asteroid or a comet as it travels around a central mass. Read more here : http://en.wikipedia.org/wiki/Trajectory I believe that ...


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What a strange question. Is $x(t)$ the distance measured along the track? Without defining $x$, there is nothing else to say. And if it is the distance, then it's the distance. Along the track. And the car is traveling along the track. So x is the distance. Which is what is asked. I suggest you read ...


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Can we rigorously define force? Presumably this question is asked in the context of Newton's mechanics (not to be confused with Newtonian mechanics). I'll be unconventional and say the answer is "no". Newton's three laws and his first few corollaries do not define force. They instead describe what forces do and how they relate to mass (also undefined), ...


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Suppose you set the zero of potential so both conductors have zero charge at zero potential. If you then set them to potentials $V_A$ and $V_B$, you can prove that they will acquire charges \begin{align} Q_A=C_A V_A+C_{AB}V_B,\\ Q_B=C_{BA}V_A+C_B V_B, \end{align} respectively. This is the real definition of capacitance, and particularly of mutual ...


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In fact, global gauge transformations are a subset of local gauge transformation: changing the same amount everywhere is a special case (ie, more restricting) of changing the phase of each point independently. In the Dirac Lagrangian $$\mathcal{L} = \bar{\psi}(i\gamma^\mu\partial_\mu - m)\psi$$ you have to derive $\psi$. If you make a global transformation ...


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Multiplying by $e^{i\theta}$ is a rotation of $\theta$ in the complex plane. Physically it changes the phase of a plane wave by an angle $\theta$. This is a global symmetry because we arbitrarily choose a reference point for measuring the phase of plane waves. If we change the phase of all plane waves by an equal amount then this is equivalent to just moving ...


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Basically, the system is simply that which is studied in a problem in physics. It refers to that which we want to know more about, in this case the moving electric charge in the presence of the electric field. Be cautious with the terms 'electric potential' and 'potential energy', since they're two different things. Electric potential is defined as ...


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You are right that the charge gained potential energy. But this statement is only true because the charge is part of a system. We cannot talk about the electrical potential of a charge unless it is in an electric field - which means that there is "something else" that is essential for our definition of the potential. We say the "system" (the charge, plus ...


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Normal fluids at fixed pressure are liquid (or solid) at low temperature and gaseous at high temperature. At some temperature the phase transition from liquid to gas occurs. However, at sufficiently high pressure, there is no such phase transition. The critical point is the largest pressure and temperature where the phase transition can be (just barely) ...


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Characteristically, a critical point occurs somewhere anytime you have a continuous phase transistion. That is, if you have two phases of a substance that themselves share their intrinsic symmetries. The classic example is the critical point associated with the liquid gas transition, as you note. Liquids are isotropic and homogenous, gases are isotropic ...


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Momentum: The resistance of an object to a change in its state of motion. That sounds like a fishy definition of momentum to me. A slightly better definition, at least at your level, is that momentum represents the "amount of motion" an object has. Granted, "amount of motion" is a very vague term, but it stands to reason that if "amount of motion" were ...


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Inertia is an intrinsic characteristic of the object related to its mass. Inertia tells you how much force it will take to cause a particular acceleration on the object. Momentum is a function of an object's mass and velocity. Momentum is a measure of the kinetic energy of the object. A massive object can have any momentum (at least as long as its velocity ...



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