ELECTRIC FIELDS IN MATTER — Edward Purcell & David Morin
Physics — E&M · em-waves-energy-density
Problem
Consider the capacitor example in Section 9.6.2, but now let the current change in a way that makes the electric field inside the capacitor take the form of E(t)=E0cosωt. The induced magnetic field is given in Eq. (9.46). Show that the energy density of the magnetic field is much smaller than the energy density of the electric field, provided that the time scale of ω (namely 2π/ω) is much longer than the time it takes light to travel across the diameter of the capacitor disks. (As in Problem 9.6, we are ignoring higher-order effects.)