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- W2183688411 abstract "If we consider the case of a single spatial dimension as similar to that of three dimensions but with all charges and field lines somehow confined inside a narrow tube, we are led to suppose that the electric field strength is constant (in both space and time) away from charges, since a tube of field lines has constant field strength. Then, there are no waves of electric field away from charges, even if the charges are moving/accelerating. Furthermore, the magnetic field (in 3 spatial dimensions) of moving charges does not affect other charges moving along the same axis. In effect, there is no magnetic field in 1 + 1 electrodynamics (i.e., in 1 spatial dimension, with only electric charges). As there are no waves and no magnetic field in 1 spatial dimension, the speed of light, c, plays no role in “electrodynamics” here. It is natural to choose (Gaussian) units in which the (Coulomb) force between two charges q and q′, which is independent of their separation, is simply F = qq′, with the implication that the magnitude of the electric field strength E of charge q is just E = q for observers at x > xq. Then, the electric field strength at a point x0 is E = q+ − q−, where q+ is the total charge at x > x0 and q− is the total charge at x < x0, independent of the motion of these charges (unless they cross the point x0 so as to change q+ and q−). There is not much more content to classical electrodynamics in 1 + 1 dimensions, which seems too trivial to provide useful “toy models” to help in understanding electrodynamics in 3 + 1 dimensions." @default.
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- W2183688411 title "Electrodynamics in 1 and 2 Spatial Dimensions" @default.
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