Griffiths electrostatics definition Small question about something said in Griffiths:
In Chapter 5, first sentence of 5.2.1, he says, 

"Stationary charges produce electric fields that are constant in time; hence the term electrostatics."

But in a footnote immediately after, he says that

"Actually it is not necessary that the charges be stationary, only that the charge density at each point be constant."

He gives the example that a rotating uniformly charged solid sphere has an electrostatic field the same as a non-rotating solid sphere. 
My question is: why does the rotating sphere have the same electrostatic field? Why is it even considered electrostatics in the first place (related: why is an equivalent definition of electrostatics that the charge density is constant at each point?)
This kind of goes against my previous intuition about electrostatics being about stationary charges.
 A: 
This kind of goes against my previous intuition about electrostatics
  being about stationary charges.

I might be mistaken but as I read it, he's saying that the electrostatic case is necessarily the time independent electric field case but it doesn't go the other way.
That is, a time independent electric field time isn't necessarily the electrostatic case.
Note that the rotating charged sphere problem mentioned in the footnote isn't an electrostatic problem but a magnetostatic problem.

why does the rotating sphere have the same electrostatic field?

Since there is spherical symmetry, the electric field can only have a radial component.  If the radial component were time dependent, the total charge on the sphere must be changing with time.  Since the total charge on the sphere is constant with time, the electric field is constant with time.
A: Obviously Griffiths defines an electrostatic situation as one where the charge density $\rho (\vec r)$ is stationary, i.e., it doesn't change in time $$\frac {\partial \rho}{\partial t}=0$$ A stationary charge distribution can, however, consist of moving charges producing a stationary current density so that for the current density holds $div \vec J=0$. This means that the electric fields are completely determined by the charge density distribution according to the Coulomb law $$\vec E=\int \frac {\rho (\vec r')(\vec r -\vec r')d^3r'}{4 \pi \epsilon_0 |\vec r-\vec r'|^3}$$ This corresponds to the case of the rotating charged sphere where the charge density is constant but the rotating charges are producing a stationary current density distribution. Stationary currents associated with the stationary charge density distribution produce only stationary magnetic fields which do not interfere with the electrostatic problem.
