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For obtaining the electric field for bodies at the macroscopic scale, the discontinuities in the charge distributions are ignored. A continuous function for the charge distribution is considered.

But what if we do not ignore this fact that charge distribution is discontinuous throughout the space of a body in which it is present. Then what kind of a result would we be ending up with? What are the necessary steps followed to analyse such a complicated situation?

If we compare the electric field in the case of assuming continuity in charge distribution with the case where we considered discontinuity, what will be the error step size? Say by taking an example of a sphere (radius R, total charge Q, electric field to be found at a distance r from its geometrical centre)

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  • $\begingroup$ If you want to do a classical calculation with a charge distribution made up of a set of point charges, you would use a $\delta$ function for each point charge. The total distribution would be the sum of the $\delta$ functions. This approach is useful for Green's functions. Green's functions: the genius way to solve DEs $\endgroup$
    – mmesser314
    Commented Jul 7 at 15:43

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