Radial flow of charge across cylinder?

[collectedsoul]

Hi

Please help me understand how charge flows in this case:

There are 2 concentric cylinders, the outer one is hollow but the inner one is solid. The space between them is filled with a material of high resistivity. Now an electric circuit with voltage V is connected to the cylinder's faces. +ve end of the circuit goes into the outer cylinder and -ve end to the inner cylinder. The cylinders themselves have negligible resistance. What will happen in terms of charge flow here?

 

[Termotanque]

Is there any symmetry? Use Gauss law to calculate the electric field.

 

[collectedsoul]

I tried using Gauss' Law, but I think there is charge flow from inner to outer cylinder through the resistive medium and Gauss' Law won't work in that case.

I am only given the voltage V of the battery, the resistivity of the in-between material $\rho$, the inner radius r1, outer radius r2, and the length L of the 2 cylinders.