Ampere/Maxwell law capacitor problem

[mcshadypl]

Homework Statement

A 0.200-A current is charging a capacitor that has circular plates 10.0 cm in radius. If the plate separation is 4.00 mm, (a) what is the time rate of increase of electric field between the plates? (b) What is the magnetic field between the plates 5.00 cm from the center?

Homework Equations

Ampere-Maxwell law:
integral(B*ds) = u0I + e0u0*d(fluxE)/dt

The Attempt at a Solution

I have found the solution to part A, but B is what is causing me trouble. I have really no clue how to go about finding the magnetic field.

 

[Hootenanny]

What does the Ampere-Maxwell law tell you? What do each of the terms represent?

 

[mcshadypl]

Well, it tells us what the magnetic field is that is created by a time-varying electric field as well as a conduction current. Since a capacitor is being considered, the latter part can be disregarded.

So I'm thinking that a cylinder can be constructed between the capacitors and we will assume that EA= u0e0*d(fluxE)/dt
I suppose that area, A, can represent the surface area of this cylinder such that A= pi(0.05m)²*(0.004m). So we want to find the magnetic field, which should be the "B" term of the integral portion of the equation. At this point I don't know how to proceed with the problem.