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## Homework Statement

An infinitely long cylindrical capacitor with inner radius a and outer radius b carries a free charge per unit length of ##\lambda_{free}##. The region between the plates is filled with a nonmagnetic dielectric of conductivity ##\sigma##. Show that at every point inside the dielectric the conduction current is exactly compensated by the displacement current so that no magnetic field is produced in the interior. Find the rate of energy dissipation per unit volume at a point a distance ##\rho## from the axis. Show that the total rate of energy dissipation for a length l is equal to the rate of decrease of electrostatic energy of the capacitor.

## Homework Equations

Maxwell Equations, Ohm's Law, Energy of Capacitor = ##\frac{1}{2} CV^2##

## The Attempt at a Solution

Before getting far into the problem I am confused on two points. I can understand where the conduction current comes from, that's just applying Ohm's law inside the dielectric, but I cannot see where the displacement current comes from or how to evaluate the energy dissipation if the magnetic field is zero inside the dielectric.