An isolated spherical capacitor has charge + Q on its inner conductor (radius ra and charge -Q on its outer conductor (radius rb) Half of the volume between the two conductors is then filled with a liquid dielectric of constant K, as shown in cross section in Fig.
(a) Find the capacitance of the half-filled capacitor.
(b) Find the magnitude of it in the volume between the two conductors as a function of the distance r from the center of the capacitor. Give answers for both the upper and lower halves of this volume.
(c) Find the surface density of free charge on the upper and lower halves of the inner and outer conductors.
(d) Find the surface density of bound charge on the inner (r = ra) and outer (r = rb) surfaces of the dielectric.
(e) What is the surface density of bound charge on the flat surface of the dielectric? Explain.