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In E&M, it is common to represent the charge on a body with a continuous, scalar charge density function. In reality though, the body contains discrete charges. I understand why this approximation can be used to, say, calculate the electric field outside of a charged body -- averaging the charge over the body serves is a good approximation because actual charges are so close together.
However, I will often see problems that ask you to calculate the electric field inside of a charged body (say a solid sphere of charge). Why can we get away with using the continuous charge distribution here? For the solid sphere of charge, using the continuous charge distribution, we would find that the electric field is spherically symmetric. However, isn't this not true? On a spherical shell within the body, you could be extremely close to a charge (making your E-field infinite) or in between two charges (making your E-field finite). Why is this approximation acceptable?