Changing Electric Field in a Capacitor

A capacitor has circular plates with radius $R$ and is being charged by a constant current $I$. The electric field $E$ between the plates is increasing, so the energy density is also increasing. This implies that there must be a flow of energy into the capacitor. Calculate the Poynting vector at radius r inside the capacitor (in terms of $r$ and $E$), and verify that its flux equals the rate of change of the energy stored in the region bounded by radius $r$.

Hi everybody, I don’t want the answer, because actually I already know what it is, but I would really appreciate that someone answer my doubt:

While trying to answer this question, I was tentative to use the Maxwell equation
$$operatorname{curl} E = frac{partial B}{partial t}$$
I would try to use this fact, and the fact that the electric field in this case is $$E = frac{q}{Aepsilon}$$
So basically I would take the curl of this and put it in the Maxwell Equation I cited. But, I am not sure if we can do that! I would go on the math but I hesitated and tried to figure out if this is right (In my head, this electric field I calculated is for static fields, but, I do not see any equation that say this is wrong, so I am stuck here). What do you think?