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The reason is confinement. Yang Mills theories with $SU(2)$ and $SU(3)$ gauge groups exhibit confinement, while for example $U(1)$ electrodynamics does not. Whether a theory is confining or not can be found out by studying the properties of Wilson loops.


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1) Yes, the charge is truly and exactly conserved. What it is confusing you, I think, is that the current for a scalar field explicitly depends on 4-potential $A$, whereas that for a spin-1/2 does not. This is obviously related to the number of derivatives in the Lagrangian kinetic term and, likewise, to the number of derivatives in the current. It can help ...


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You are correct that the protons' linear charge density doesn't change because any Lorentz contraction happens perpendicular to the wire. You are also right that the relativistic velocity addition formula predicts that the total speed of the electrons isn't simply $\sqrt{v^2+v_0^2}$. It is actually $\sqrt{v_{(\parallel)}^2+\frac{v_{0,(\perp)}^2}{\gamma^2}}$, ...


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According to "Surface chemistry of gold nanoparticles produced by laser ablation in aqueous media." Sylvestre J-P, Poulin S, Kabashin AV, Sacher E, Meunier M, Luong JHT http://pubs.acs.org/doi/pdf/10.1021/jp047134%2B A detailed chemical analysis showed that the nanoparticles formed were partially oxidized by the oxygen present in solution. The ...


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I'm only beginning to study electromagnetism, so please jump on any mistakes I may have made. Coulomb's law only holds for electrostatic situations, so applying Coulomb's law in the observer's frame of reference is invalid, since the charges are moving from the observer's perspective. The electric and magnetic field of dynamic systems is instead given by ...


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Electric field is zero in that point because the sum of electric field vectors have same intensity and direction, but are opposite. That point is halfway between two like charges.


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Is it simply that the repulsion of the equidistant point charges creates a dead zone? It has nothing to do with repulsion or attraction. To find the electric field at some location due to a set of point charges, you have to add the electric field contribution due to each of the point charges. You also have to remember that the electric field is a ...


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An important point here is that you don't just convert from Coulombs to ESU. You also change the units of various constants that appear in the expressions of electromagnetism. The most obvious example is, Coulomb's Law $$\begin{align*} F_{SI} &= \left (8,99 \times 10^9 \,\mathrm{N \, m^2/C^2}\right) \frac{q_{1, C} \, q_{2, C}}{r^2} \\ F_{guass} &= ...


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I suppose that in this type of circuit the current and the voltage are in phase, This question is asking for a transient solution, not an ac steady-state solution. So we can't really talk about the phase of the voltage or the current. meaning that immediately after the switch is shut the current should be I=0? This conclusion is incorrect. ...



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