A parallel-plate capacitor is made using two circular plates of radius a, with the bottom plate on the xy plane, centered at the origin. The top plate is located at z = d, with its center on the z axis. Potential V₀ is on the top plate; the bottom plate is grounded. Dielectric having radially dependent permittivity fills the region between plates. The permittivity is given by (ρ) = 0(1 + ρ²/a²). Find

(a) V(z);

(b) E;

(c) Q;

(d) C. This is a reprise of Problem 6.8, but it starts with Laplace’s equation.