You might know already that it is possible to think of the energy stored in a charged capacitor as being stored in the electric field between the plates. We will explore this idea by considering the flow of energy into the space between the plates during the charging process. The capacitor is charged by a constant current i, which flows for a time T. At the beginning of this charging process (t = 0), there is no charge on the plates. The Poynting vector S gives the flow of electromagnetic energy per unit area per unit time and is defined in terms of the electric field vector E and the magnetic field vector B by the relation S = 1/mu_0 E times B. Find an expression for the magnitude of the Poynting vector |S(t)| on the surface that connects the edges of the two circular plates. Express the magnitude of the Poynting vector in terms of t, i, R, pi, and other variables and parameters of the problem. Ignore all fringing effects.
