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Fernbauer
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There's no electric field inside a conductor, a classic observation of electrostatics. Any field that "should" exist is compensated for by charge redistribution on the surface of the conductor. This produces classic results like shielding since in a hollow conductive shell, the field is still zero, regardless of the shell or hollow's shape.
https://www.physicsforums.com/showthread.php?t=459324" asked about the time it takes to establish the field.
Three unrelated questions on this common topic of electrostatics:
Does the induced surface charge change based on the presence of dielectrics, either inside or outside the shell? It seems like at least inside dielectrics must modify the charge distribution since the (induced) field inside should be affected by the dielectrics.
Is induced charge computation similar to the way point charges can be represented by charge distributions? (The classic behavior is that a shell of charge produces a field identical to a point charge outside the shell, regardless of the shell's size.) How would you calculate the "equivalent" charge density for a non-spherical shell? As a concrete example, is there some distribution of charge on the surface of the 0 centered unit cube that (to points outside the cube) behaves identically to a point charge at the origin? How would you compute that surface charge density which produces that behavior?
Last question. The http://en.wikipedia.org/wiki/Harmonic_function#Mean_value_property" means you can compute the potential at a point by integrating the surrounding potentials over a closed surface or volume. The Wikipedia link shows how you'd compute the trivial case of a sphere, but how about for a cube? (ie, what weighting of points on a cube surface would integrate to the same potential at the center of the cube?) Is this weighting the same as the charge density in the previous paragraph's question?
https://www.physicsforums.com/showthread.php?t=459324" asked about the time it takes to establish the field.
Three unrelated questions on this common topic of electrostatics:
Does the induced surface charge change based on the presence of dielectrics, either inside or outside the shell? It seems like at least inside dielectrics must modify the charge distribution since the (induced) field inside should be affected by the dielectrics.
Is induced charge computation similar to the way point charges can be represented by charge distributions? (The classic behavior is that a shell of charge produces a field identical to a point charge outside the shell, regardless of the shell's size.) How would you calculate the "equivalent" charge density for a non-spherical shell? As a concrete example, is there some distribution of charge on the surface of the 0 centered unit cube that (to points outside the cube) behaves identically to a point charge at the origin? How would you compute that surface charge density which produces that behavior?
Last question. The http://en.wikipedia.org/wiki/Harmonic_function#Mean_value_property" means you can compute the potential at a point by integrating the surrounding potentials over a closed surface or volume. The Wikipedia link shows how you'd compute the trivial case of a sphere, but how about for a cube? (ie, what weighting of points on a cube surface would integrate to the same potential at the center of the cube?) Is this weighting the same as the charge density in the previous paragraph's question?
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