ELECTRIC FIELDS IN MATTER — Edward Purcell & David Morin
Physics — E&M · em-waves-poynting-vector
Problem
A capacitor is charged by having current flow in a thin straight wire from the middle of one circular plate to the middle of the other (as opposed to wires coming in from infinity, as in the example in Section 9.6.2). The electric field inside the capacitor increases, so the energy density also increases. This implies that there must be a flow of energy from somewhere. As in Problem 9.10, this ``somewhere'' is the wire. Verify that the flux of the Poynting vector away from the wire equals the rate of change of the energy stored in the field. (Of course, we would need to place a battery somewhere along the wire to produce the current flow, and this battery is where the energy flow originates. See Galili and Goihbarg (2005).)