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Lets say there is a uniform charge density throughout the entire space. At any point $P$, if I consider shells entered at $P$, the field at that point will be zero because according to Gauss Law, field inside a shell is zero.

But If I consider shells which are not centered at $P$, then the field is non zero. Why are the answers different?

Aditya Dev
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    If there is an uniform charge density everywhere then there will be an electric field. Every surface you will consider will contain some charge and thus you will have a non-zero flux on that surface. – FrodCube Jan 24 '17 at 20:48
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    The field inside an empty shell is zero. Your shells will have charge in them. – garyp Jan 24 '17 at 21:07
  • http://physics.stackexchange.com/q/39654/ – Raziman T V Jan 24 '17 at 21:51
  • An infinite uniformly charged universe is mathematically inconsistent with Coulomb's law. –  Jan 25 '17 at 02:28

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There no unique solution to the problem you pose. The field inside a "uniform" charge distribution depends on what is going on far far away on the distant surface.

mike stone
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