Where does the net charge on a hemisphere appear to act from? I was wondering if, like centre of mass, there is anything called "centre of charge".
 A: In general, no: the field of a charge distribution $\rho$ is not the same as the field of a point charge at some point therein, except for some very particular cases (the one that everyone should know is that any spherical shell of charge has an inner field of 0 but an outer field that looks exactly like all the charge is located at the center point.
A simple example is the capacitor: if there were a center of charge, it would surely be a charge of 0 right at the center of the capacitor, and there would be no electric fields: but there is an electric field of course.
With that said, in general if you get far enough away from the internal structure, the field lines do eventually space out roughly evenly and so the "far field" of a charge distribution always looks like it comes out of a point. The answer of "which point?" in this case is "It doesn't matter -- in this limit the whole object is essentially being shrunk to a point, including all of the parts inside of it." In other words, if you can measure electric fields precisely enough to tell the difference between "located here" and "located there" for where this internal charge is located, then your high precision will necessarily prove to you that the charge distribution is not actually a point charge in the first place; correspondingly if your precision is low enough that we can treat the field as a point charge field, then it makes no difference to that measurement apparatus which point inside the object is chosen as the "center of charge."
