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7h
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Do conductors have bound charges? Let us continue this discussion in chat. |
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7h
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Do conductors have bound charges? By "displacement electric", do you mean electric displacement field $\mathbf D$? |
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15h
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Do conductors have bound charges? If we went with your definition consistently, a uniform dielectric in electrostatics with $\rho_b=0$ has no bound charges, and metal with $\rho_f = 0$ has no free charges. But of course, both dielectrics and metals are made of bound charges, and metals also have free charges inside, even when $\rho_f=0$. We know this because these free charges manifest via current and its effects, even when $\rho_f=0$. |
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15h
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Do conductors have bound charges? Yes it does. Using "bound charge" to refer to $\rho_b$ instead of to the bound charged particles themselves is a common metonym, a short-hand for shorter sentences about $\rho_b$. It does not actually mean $\rho_b$ is the charge that is bound. $\rho_b$ is volume density of electric charge of a particular kind, and the kind is - the charge that is bound to the rigid structure of nuclei. |
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17h
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Do conductors have bound charges? Even bound charges in dielectric do not arise as $\rho_b = -\nabla\cdot \vec{P}$. That is just a formula for density of net bound charge in terms of average dipole moment per unit volume. When $\rho_b = 0$ in a dielectric, this does not mean the charges there are not bound. Similar in metals. They are bound, and their net charge density vanishes. |
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1d
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Do conductors have bound charges? > In a typical conductor, like a metal, the charges are all considered free charges That isn't true. Protons and non-conducting electrons stuck in bonds in dielectrics are not called free charge, because they do not participate in DC current when it is present. So naturally the same definition is appropriate in metals. Conductivity is much smaller than if all electrons participated, only few of them do. So there is nothing free about the protons and stuck electrons. Only conduction electrons and electrons jumping between bonds in semiconductors to make holes move are free charges. |
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1d
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Stefan-Boltzmann's law independence of surface density The Stefan-Boltzmann law holds for emission from a black body, a theoretical construct which has no atoms or density of atoms. Real bodies are allowed to deviate from it, and have different emission, even correlated with density of atoms. However, making solids denser is not easy, and even if we could make them denser with immense pressure, the expected change of intensity of thermal emission is small if it was already close to the Stefan-Boltzmann value, because it should be always below or equal to that. |
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2d
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From what equations is magnetic field uniquely determined for a given current distribution? @LPZ The Dirichlet principle is a theorem that is relevant when the integral of field squared is meaningful, either due to field decaying fast enough in infinity, or due to finite domain. It does not seem to work for fields which have infinite Poynting energy on the domain considered. |
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2d
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From what equations is magnetic field uniquely determined for a given current distribution? @LPZ It is not a hack, but useful boundary condition, and I don't see why we need a "deep mathematical property" such as being $L^2$, when many well-known field examples in physics are not $L^2$, such as field of infinite charged line, or infinite straight current. Whether we consider electric field in finite space region or infinite space, boundary conditions are important and help make the solution unique. Field being $L^2$ does not. |
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2d
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Besides the 2nd law of thermodynamics, what laws of optics prevent the temperature of the focal point of lens from being hotter than the light source? added 142 characters in body |
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2d
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Besides the 2nd law of thermodynamics, what laws of optics prevent the temperature of the focal point of lens from being hotter than the light source? added 142 characters in body |
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2d
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Besides the 2nd law of thermodynamics, what laws of optics prevent the temperature of the focal point of lens from being hotter than the light source? added 77 characters in body |
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2d
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Besides the 2nd law of thermodynamics, what laws of optics prevent the temperature of the focal point of lens from being hotter than the light source? > Your hypothesis means that you have an heat engine system spontaneously converting the heat in the thermal reservoir to work and there's your perpetual motion machine (of the so-called second kind). This is not so, because we do have colder reservoir in all cases: the connected Carnot engine has colder reservoir in the Sun. The whole big system including the Sun also has colder reservoir, in the Earth and the outer space, and it uses that reservoir. See my answer. |
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2d
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answered | Besides the 2nd law of thermodynamics, what laws of optics prevent the temperature of the focal point of lens from being hotter than the light source? |
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Jul
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Physics of vacuum expectation values in QFT @FlatterMann Empty space in classical relativity is Lorentz-invariant (all fields are zero). But quantum vacuum is not such an empty space; it is allowed to have something going on, and to have non-zero Hamiltonian eigenvalue. |
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Jul
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Physics of vacuum expectation values in QFT Energy eigenvalues can't be measured, only their differences can. They are a theoretical device. That is, unless you add the constraint on the Hamiltonian that its eigenvalues have to comply with $E=mc^2$; then you can measure inertial mass $m$ and calculate $E$. But it is not at all clear that vacuum energy should obey this relation; already classical EM wave does not. Re stone, a stone at rest, or an electron at rest is an example of a ground state that is not Lorentz invariant. It looks differently in different frames. So why should vacuum be any different. |
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Jul
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Physics of vacuum expectation values in QFT @FlatterMann Energy in theoretical physics is not always ability to do work, that is one aspect of it valid in macroscopic theories. Energy in quantum theory is a quantity that gets only values that are eigenvalues of a particular Hamiltonian chosen for the purpose, and if this eigenvalue turns out to be non-zero in the ground state, then energy is non-zero in the ground state. Re relativity, I'm pointing out Lorentz invariance of laws does not require Lorentz invariance of solutions. The stone is in "ground state" only in one frame, not in all frames. |
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Jul
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From what equations is magnetic field uniquely determined for a given current distribution? Field being $L^2$ and Poynting energy being finite seems to be a red herring. There are examples of infinite sources with infinite Poynting energy, and unique field, like electric field of a charged line, or magnetic field of a straight wire. The sufficient condition for uniqueness seems to be that the source is not infinite in all directions, and in infinity, the field decays to zero. |
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Jul
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Physics of vacuum expectation values in QFT @FlatterMann We're discussing theory, and in theory, plane waves do not need to have source. The ground state is defined as the state of the lowest definite energy. It is detectable in the sense the system can get into it, and get out of it. I don't see why it has to be Lorentz invariant. In classical relativistic mechanics, is the lowest energy state of a stone Lorentz invariant? No, it isn't - the condition of "lowest energy" is frame-dependent, in frame where the state is lowest energy, the stone is at rest, and in other frames, it is not. |
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Jul
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Why Consider Only Triplet States for Spin in $2$-Electron Systems? @James total $\Psi$ of electrons in helium atom is believed to be always anti-symmetric. The coordinate factor in it may be symmetric or anti-symmetric, depending on the actual state. In experiments, we see both kind of states - singlets and triplets. |