A parallel-plate capacitor has circular plates of radius 5.0 cm separated by 1.0 mm. The space between the plates is completely filled with a solid dielectric of relative permittivity κ=4.0. The capacitor is charged until the free charge on the positive plate is Q=2.0μC and is then isolated from the charging source.
a. (i) Calculate the free surface charge density σf on the plates.
b. (ii) Determine the magnitude of the electric field E inside the dielectric after charging is complete.
c. (iii) Find the magnitude of the bound surface charge density σb that appears on each face of the dielectric.
d. (iv) Hence obtain the ratio σfσb and interpret its value physically.