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**1. The problem statement**

Consider an infinite spherical charge distribution with constant charge density. According to symmetry of the problem, I expect the electric field at any point to be zero. But if you construct a Gaussian sphere and apply Gauss theorem, it will give you some finite field at that point. Is it a paradox or I am missing something here?

## Homework Equations

[tex]\nabla E=\rho/\epsilon_0[/tex]

## The Attempt at a Solution

Is there any problem in the symmetry argument or an infinite charge distribution is the problem? I don't think that Earnshaw's theorem should be considered here as the charge distribution can be fixed using other forces (theoretically) and the Gauss' law will still hold.

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