The following calculation retraces the derivation of the Poynting vector, albeit for a specific simple geometry. Nevertheless, the underlying physics principles are the same. A long solenoid of length l, radius R, and a large number of turns N is made of wire with negligible resistance. (The negligible resistance is important because then we can neglect both the voltage drop along the solenoid due to Ohm's law, and the heat from I^2R, which will only complicate our analysis.) At a given instant, you know both the current in the solenoid, I, and it's derivative is dl/dt > 0. For that instant, we want to know the following quantities: What is the magnetic field in the solenoid? What is the energy of the magnetic field, U_B, stored in the volume of the solenoid? Is this energy increasing or decreasing? What is the rate of change of energy, dU_B/dt? Since the current is changing, an emf is being induced in the solenoid. What is this induced emf, epsilon? What is the magnitude of the induced electric field, E? Sketch the solenoid, and draw the induced electric field E in the wires as well as the magnetic field D inside the solenoid (reaching the wires). Draw the Poynting vector S. How is it oriented in the wires of the solenoid? What is the magnitude of the Poynting vector on the surface of the solenoid (in the wires)? What is the integral S dA, over the surface of the solenoid. What happens at the bases of the solenoid?