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Why does the electric flux inside a cube remain unchanged when the charge is moved within the cube (not on vertices/faces/edges) but just in volume?

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closed as off-topic by stafusa, Jon Custer, M. Enns, Kyle Kanos, ZeroTheHero May 20 at 11:35

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    $\begingroup$ Gauss's law. The cube is a Gaussian surface. $\endgroup$ – John Rennie May 16 at 6:51
  • $\begingroup$ This is a consequence of that fact that solid angle at any point inside any surface is 4π. $\endgroup$ – thewitness May 16 at 9:34
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Gauss’s law states that the TOTAL electric flux out of a closed surface equals the amount of charge enclosed divided by the electrical permittivity.

Notice my emphasis on the word total. The law does not specify how the flux is distributed on the surface. Moving the charge around within the volume only changes the distribution of the flux on the surface, not the total.

To put it another way. The total electric flux is proportional to the total number of field lines crossing the surface. Moving a point charge around within the volume doesn’t change the total number of lines crossing the surfaces of a cube, or any closed surface for that matter (e.g. a sphere). It only changes the density ( and therefore the field strength) of the lines on different parts of the surface. See the diagram below

Hope this helps.

enter image description here

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