Problem 2 We have two plates, so that the system has an axis of symmetry. The radius is o, the plate separation is h, and the material filling the space between the plates has a dielectric constant E. The capacitor is charged by being placed in a circuit that contains a battew of EMF V0 and a series resistor R. If the circuit is closed at time t = 0 (charging starts), nd the following quantities within the capacitor as functions oftime (neglect edge effects and assume RC >> a/c, where C is the capacitance of the plates and c is the speed of light). Each of the quantities below are functions of time and eitherrorz. a) the electric field At t=0, we close the switch and start charging the capacitor through the resistor R. Use circuit equations to calculate the time dependence of the charge on the capacitor, then calculate the electric field E(t). b) the magnetic field Using the result from part (a), calculate the magnitude and direction of B(t). Hint: Stokes theorem should be useful. c) the Poynting vector (time-dependent) Now calculate the Poynting vectors = E x H. Make a plot of 5(t), letting RC=1. d) the total field energy (timedependent) C53 e) the scalar potential