A battery with potential difference E charges an ideal circular parallel-plate capacitor of capacitance C, plate radius r0, and separation between the plates d, through a wire with resistance R. The total charge on each plate as a function of time is: Q(t) = CE(1-e^(-t/RC)). Consider the surface charge density uniform on the plates.
1. Find the electric flux between the plates as a function of time.
2. The rate of change of the electric flux between the plates as a function of time.
3. The magnetic field inside the capacitor at a distance r from the central axis.
4. The instantaneous energy of the magnetic field inside the capacitor.