General Physics
Does Coulomb's Law, with Gauss's Law, imply the existence of only three spatial dimensions?
1 Answer
Saurabh Koranglekar
Yes, absolutely. In fact, Gauss's law is generally considered to be the fundamental law, and Coulomb's law is simply a consequence of it (and of the Lorentz force law).
You can actually simulate a 2D world by using a line charge instead of a point charge, and taking a cross section perpendicular to the line. In this case, you find that the force (or electric field) is proportional to 1/r, not 1/r^2, so Gauss's law is still perfectly valid.
I believe the same conclusion can be made from experiments performed in graphene sheets and the like, which are even better simulations of a true 2D universe, but I don't know of a specific reference to cite for that.
You can actually simulate a 2D world by using a line charge instead of a point charge, and taking a cross section perpendicular to the line. In this case, you find that the force (or electric field) is proportional to 1/r, not 1/r^2, so Gauss's law is still perfectly valid.
I believe the same conclusion can be made from experiments performed in graphene sheets and the like, which are even better simulations of a true 2D universe, but I don't know of a specific reference to cite for that.
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