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Without touching on electromagnetism, I'd like to bring up this construction from mechanics (it's in the Feynman lectures). Consider two equal particles approaching each other with equal speed. A----> <----B You can argue from first principles that if they stick together they will not be moving afterwards -- any argument you could make ...


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Let us make things clear. Protons and electrons are quantum mechanical entities and there is little meaning to project classical electrical attractive behavior to the micro framework of quantum mechanics, nor classical electric field calculations . Classically, a negative charge attracted to a positive charge will experience acceleration, and accelerating ...


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Nothing is problematic with it. As FraSchelle says above—and is also true in the development of many other physics theories, in that they are, over time, purified of the scaffolding that helped construct them*—the original motivation doesn't affect the content of the developed theory. *cf. the top of p. 90 (PDF p. 91) of Stefano Bordoni's When ...


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You are correct in asserting that unpolarized light contains a mixture of many polarizations. However, each of these polarizations can be expressed as a combination of horizontally and vertically polarized light. Diagonally polarized light can thus be seen as containing both horizontally as well as vertically polarized light. When a horizontal beam of ...


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In your final two paragraphs you have it backwards. At Brewster's angle the reflected light is totally polarized, but the total polarization of the transmitted light is usually rather weak. Compare reflection coefficients $r$ and transmission coefficients $t$ from the Fresnel equations: Reflected light is completely polarized at Brewster's angle because ...


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No, magnetic lines of force don't flow. They have a direction, which shows the direction of the magnetic field but there is nothing flowing. If you were to place a small magnetic dipole at the location of the magnetic field line its north pole would feel a force in the direction of the line of force. The phrase "line of force" was introduced by Michael ...


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The concept of "mediation" depending on a photon comes from the use of Feynman diagrams. Feynman diagrams are the calculational tool of quantum electrodynamics because they give a prescription of how to calculate the integrals in each order of the pertubation series expansion for proton proton or proton electron scattering. Lets make it simple, because the ...


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It's just that the sum of kinetic and potential energies are constant through all times. You can say that potential energy is zero when they are far away, so when they are approaching, the potential becomes more negative, as it is converted to kinetic. Or you can say that the potential energy is largely positive when they are far away, then reducing to zero ...


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Here is the simple high school level answer which knzhou's answer is better than. The electric potential energy of a system of two point charges a distance $r$ apart is given by $$ E_E=\frac{kQq}{r}$$ If the charges have opposite signs than the potential energy will be a small negative value when they are far apart. As they move closer together potential ...


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The simple 'first year physics' answer is that the potential energy goes negative. The negative potential energy cancels out the positive kinetic energy, leaving the total energy equal to zero. This might still feel unsatisfying, because it still looks like the kinetic energy is coming 'out of nowhere'. The real resolution is better. In this situation, '...


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I may be wrong, but I think Lenz's Law might provide an answer. The circuit with the straight wire takes in current i(suppose) once the switch is closed. The one with the looped wire, will having a changing flux through it once the switch is closed. Since any change is to be opposed, the current drawn this time will be less,(assuming the dimensions of the ...


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Okay I'll have a go at answering this, although it may be a make belief scenario. Looking at where you got your inspiration from, he stated using a magnet as a core for an electromagnet, so your curiosity must have piqued from the idea that the wire carrying electric could itself be magnetic. Because of polarization and magnetization, all the magnetic ...


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Just like in Gauss Law, is the integral B.dl due to any current NOT piercing the surface always zero? Correct The problem which you face using Ampere's law with a wire of finite length is not to do with the current going through the surface it is to do with the magnetic fields produced at point $X$ on the loop along which the integration is to be done ...


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you are basically trying to undergo a transition from a law which is valid for static charges(or non relativistic speeds) to one which is valid for steady currents. That is why, simple differentiation is erroneous and does not include any magnetic field term in dE/dt.


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Suppose, as you said, we have a thin solenoid pointing upward, going through the middle of a loop one light-year wide. Then the three equations $$\nabla \times E = - \frac{\partial B}{\partial t}, \quad \mathcal{E} = -\frac{d\Phi_B}{dt}, \quad B = \mu_0 n I$$ together imply violation of causality, as shown in your question. Maxwell's equations are already ...


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I'm don't know if you will find this answer satisfying, but suppose the EMF went the opposite way. Instead of opposing the current, it boosts the current. Then the higher current will produce a higher field and higher EMF which will boost the current, which will produce a higher field and higher EMF ... until the wire melts. Lenz's Law established ...


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A 2013 paper by Shtanov and Sahni (already mentioned by Ben Crowell in the comments) says that the modes grow exponentially in conformal coordinates, and Barrow et al overlooked the fact that the conformal time changes very little during and after inflation. A 2014 preprint by Tsagas, one of the authors of the original paper, cites Shtanov and Sahni and ...



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