Circular Parallel Plate Capacitor

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Leitmotiv
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I haven't figured it out yet, I find it way above my understanding of phyiscs

Suppose we have two circular parallel plates or radii r, both the same radius. They have a Voltage difference of V and they are separated a distance d. What would be the Electric Field in the whole space? Actually, I'd be happy enough with the potential.
 
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You are given the potential difference V. Knowing that, you can say that, if the potential at the negatively charged plate is V0, the potential at the other plate is V+V0. Now what?

What does the electric field between the plates of a capacitor look like?