The space between the plates of a capacitor is filled with a material of resistivity ρ = 10⁴ Ω · m and dielectric constant κ = 2.5. The parallel plates are circular with a radius of 20 cm and are separated by 1 mm. The voltage across the plates is given by V₀ cos ωt, with V₀ = 40 V and ω = 120π rad/s.

(a) What is the displacement current density?

(b) What is the conduction current between the plates?

(c) At what angular frequency is the total current 45^o out of phase with the applied voltage?