Electromagnetism question: Current flowing between concentric spheres

[ka_reem13]

Homework Statement

The space between two concentric, perfectly conducting spheres (radii ra < rb) is filled with a medium of conductivity σ. At t = 0, a charge q suddenly appears on the inner sphere. This charge is subsequently free to move by conduction.
(a) Calculate the current density in the medium between the spheres as a function of time for t > 0.
(b) Calculate the total heat generated due to this current.
(c) Calculate the reduction in electric field energy due to the charge redistribution. Comment on your results.

Relevant Equations

maxwells equations?

I know that my solution is time dependent, and I initially tried to use a capacitor model of sorts, but I realised as it was filled with a conductive medium, I cannot use a capacitor model. So now I am very stuck on this

 

[berkeman]

Try working on a simpler version of the problem first, to start to get some intuition...

What if you have a flat plate capacitor with a resistor tied between the plates, and one of the plates gets a charge q placed on it? What is the equations for the current versus time through that resistor?

Then what kinds of changes should you make to account for the concentric sphere capacitor, and the varying resistance as a function of radial distance...?

 

[ka_reem13]

intuitively, it will be the same as discharging a regular capacitor through a resistor. However, instead of discharging to zero, it will discharge until both plates have equal and opposite charge? (Where this charge is q/2). Am I correct in saying this

 

[berkeman]

However, instead of discharging to zero, it will discharge until both plates have equal and opposite charge? (Where this charge is q/2). Am I correct in saying this

Discharging until q/2 is on each plate is not equal and opposite charges. What is the E field between the plates when they each have q/2 on them?