The divergence of an electric field is zero for any combination of stationary electric charges because electric fields produced by static charges are conservative in nature. For conservative fields, the divergence must be zero at any point other than the location of a charge, since there is no source or sink of the electric field except at the position of the charge itself.

1. Hi, can anyone explain to me why we can immediately deduce that the divergence of electric
field is zero for any combination of stationary electric charges given that the divergence of an
electric field for a single point charge, other that at the location itself is zero.
Solution
Divergence of any vector at any point gives us information that whether there is a source of flow
or a sink for that vector, as in case electric fields produced by static charges which are
conservative in nature, the divergence has to be zero at any point other than the location of
charge as we are not having a source or sink for electric field at any other place other than the
location of charge itself.