How Does Charge Distribution Affect Fields and Energy in Nested Conductors?

[DR33]

Here's the problem that I have been trying to solve:

A solid conducting sphere of radius 20cm is concentrically placed inside a spherical shell of inner radius 30 cm and outer radius 40cm. A Charge of 20uC is placed on the inner sphere, and a charge of -10uC is placed on the outer conductor. The dielectric constant of the medium between the 2 conductors is 5. Finc:
a) D, E and P at all points in space (all vectors)
b) the total energy in the system

Can anyone help me resolve this . Thakn you.

 

[CartoonKid]

What do you mean by D, E and P?
E = Electric field?
D, P = ?
Thanks

 

[DR33]

D = Electric Flux Density
P = Dipole Moment per unit Volume

 

[DR33]

..

Anyone?

 

[CartoonKid]

R_1 = 0.2m, R_2 = 0.3m, R_3 = 0.4m
For r < R_1,
Since the solid sphere is a conductor, the E field will be 0.
For R_1 < r < R_2,
\phi = \frac{q_{in}}{\varepsilon}
\phi = E\times 4\Pi r^2
So E = ...
For R_2 < r < R_3,
It's same with first one.
For r > R_3,
Use the method as for R_1 < r < R_2 with q_{in} being changed to -10\mu C (I don't know if the inner most charge has to be taken into account because it's bounded by the spherical conductor, correct me if I'm wrong)
As for the energy, would the inner charge contribute energy to the system?