Consider a parallel-plate capacitor consisting of two circular plates with known radius R. The capacitors's gap is assumed to be vacuum. The capacitor's gap distance d is unknown, but it is known that the gap is small, d R (i.e., we can neglect fringing of the electric eld at the edges of the plates). It is also known that the capacitor's plates are charged with a manochromatic sinusoidal electric potential vc(t) = v0 sin(!0t), where both the maximum voltage v0 and the angular frequency !0 are known quantities. An experimenter measures the maximum value of the displacement current to be id (i.e., this is a known quantity). 1) Find d in terms of the known quantities. [15 points] 2) Find direction (providing suitable arguments, as shown in class!) and magnitude of the mag- netic eld ~B between the capacitor's plates at a distance r < R from the center. Note that this is a time-varying (i.e., dynamic) magnetic eld. Assume ~B is due to the displacement current. [10 points] 5