Conducting sphere surrounded by insulator with dielectric constant

[zhillyz]

Homework Statement

A conducting sphere of radius A has a charge +Q on it and is surrounded by an insulating material whose dielectric constant varies with radius according to ε_r = 2exp[-(r/a-1)]². The dielectric has a spherical outer boundary B. Find the values of D, E, P, ρ as a function of r.

Homework Equations

ε_r = 2exp[-(r/a-1)]²,

Gauss's Law?

The Attempt at a Solution

Outside conducting sphere:

D directed radially outward so using symmetrical surface integral form of Gauss law, D = q/4∏r².

E=D/ε₀ = q/4∏ε₀r².

Inside sphere:
D=0, E=0.

Not sure if this is right or what next steps to take?

 

[SammyS]

Homework Statement

A conducting sphere of radius A has a charge +Q on it and is surrounded by an insulating material whose dielectric constant varies with radius according to ε_r = 2exp[-(r/a-1)]². The dielectric has a spherical outer boundary B. Find the values of D, E, P, ρ as a function of r.

Homework Equations

ε_r = 2exp[-(r/a-1)]²,

Gauss's Law?

The Attempt at a Solution

Outside conducting sphere:

D directed radially outward so using symmetrical surface integral form of Gauss law, D = q/4∏r².

E=D/ε₀ = q/4∏ε₀r².

Inside sphere:
D=0, E=0.

Not sure if this is right or what next steps to take?

Hello zhillyz. Welcome to PF!

I take it that the spherical shell has inner radius A, and outer radius, B.

E = D/ε₀ outside the dielectric shell; where r > B .

For A < r < B, E = D/ε_r .