# 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 $$E = \frac{q}{A\epsilon}$$ 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?

1. Use the Ampère-Maxwell law in the global form( using Gauss theorem) $$\oint_{\gamma} \vec{B} \cdot d \vec{l}=\frac{d }{dt}\Phi(\vec{E})$$