Understanding Displacement Current in Charging a Capacitor

[frozenguy]

Homework Statement

A 0.1[A] current is charging a capacitor that has square plates 5cm on each side. The plate separation is 4mm. Find (a) the time rate of change of the electric flux between the plates and (b) the displacement current between the plates.

The Attempt at a Solution

So I had hints from the teacher, and got the answer but I'm a little confused as to what I did.. Could someone help me out?
Why does the 4mm not come into play? or the 5cm?
Is I=I_d always? Usually?
What was the point taking double integral of CurlB? And what equals muI+muI_d?

 

[Mindscrape]

All you really have to do is worry about the displacement current. The other stuff is extra information for what you actually have to solve. The double integrals come from the integral forms of the Maxwell equation, it's really just a starting point.

I don't see how you got the right answer when your work is so funky.

$$\Phi_E = \int\int E \cdot da$$

gives the electric flux. Take the time derivative of that and multiply by epsilon for the displacement current.