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As per the title, I'm thinking if it is possible to have a conducting metallic solid sphere with uniform charge distribution if the charges in a conductor tend to distribute themselves on the surface of the conductor.

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  • $\begingroup$ It could have a uniform (net) charge of 0. Normally when we have problems that assume a uniform charge in some region, we shouldn't assume that region is a conductor. $\endgroup$
    – The Photon
    Commented Jul 25, 2021 at 14:44

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No, that is not possible. This can be shown by applying the following equations inside the conductor: $$-\frac{\partial\rho}{\partial t} = \nabla\cdot\mathbf{J} \\ \mathbf{J}=\sigma\mathbf{E} \\ \nabla\cdot\mathbf{E}=\frac{\rho}{\epsilon_0}$$ so that $$\frac{\partial\rho}{\partial t} = -\frac{\sigma}{\epsilon_0} \rho.$$ Therefore all charge in a conductor will move to the surface (and in a short amount of time, since $\sigma/\epsilon_0 \sim 10^{19}\,\text{s}^{-1}$ for typical conductors).

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  • $\begingroup$ Do you mean $10^{-19}$ s? Because if not, that would be a couple of million millennia ;) $\endgroup$
    – Philip
    Commented Jul 29, 2021 at 14:20

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