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I don't think there is an analogous statement for spacelike intervals. The statement "The centre of mass follows a geodesic" is an immediate consequence of global momentum conservation. This is in turn follows from local momentum conservation. $$\partial_\mu T^{\mu \alpha} = 0$$ where $T^{\alpha \beta}$ is the stress-energy ...

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For each distance $y$ from the wire, there is a segment of area of a certain width (narrow, then wider, then narrower again); this width is a function of $y$. The magnetic field through this infinitesimal slice of area is the same everywhere since it runs parallel to the wire. Once you realize this, you can simplify the double integral to a single ...

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In the first one notice that the loop is being moved and thus the charged particles in the loop. Hence there are electrons moving in a magnetic field, which is basically Lorentz force. Griffiths argues that the Emf created in this scenario is due to, or better yet can be explained by the Lorentz force. In the second and the third one there is no charged ...

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But it seems to me that the EM momentum it radiates in each direction is balanced by an equal amount of EM momentum radiated in the opposite direction. Is that true? It is true in the frame where the particle is at rest when it produces the retarded radiation. In other frames, particle moves and its angular pattern of Poynting intensity of radiation is ...

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In the context of ion beams, space charge is the tendency of the beam to expand transversely (perpendicular to the direction of the beam's travel) due to the mutual repulsion of the ions in the beam. All the ions have the same sign charge, so they repel. The name "space charge" comes from plasma physics where is is often computationally easier to treat the ...

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A stress tensor has nine components at every point in space. If you group them into three sets of three, you can imagine it as three vector fields. Do so. Each of those vector fields has a divergence, and that would be three scalar fields. You could combine those three scalar fields together to get one vector field. What if that vector field were the ...

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In relation to all this here is another issue: in an electrostatic field $\mathbf{g}=0$ while $\mathbf{T}\ne 0$ so we have flux of momentum while the density of momentum is zero. In my opinion $T$ should be interpreted as a combination of momentum flux plus stress just as in continuumm mechanics the anolog of $T$ is (using indicial notation)  ...

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is my interpretation of the dynamics of the self-force correct and is there a physical or intuitive explanation for this extremely pathological behavior in the presence of a Coulomb potential? Eliezer makes his argument based on the equation with the Lorentz-Abraham-Dirac term. This term was originally (Lorentz) devised as an approximate way to account ...

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