Currents and charge between spheres

[omri3012]

Homework Statement

Consider two small conductive spheres in radius a and b located far from each other.
In t=0 "a" sphere charged with Q and "b" sphere neutral. We connect the spheres by wire with resistance R.
Find the charge on each sphere as a function of time.

Homework Equations

d$$\rho$$/dt+divJ=0

I=dQ/dt

J=$$\sigma$$E

R=$$\rho$$*(L/A)

The Attempt at a Solution

I'm assumed that the change in charge in one sphere is the same in the other sphere with opposite sign. I tried to understand what is the relevant electric field and where should I calculate it (outside the sphere? Inside the wire?). I think that capacitance
Required here but the two spheres connected so it more like capacitor discharge… I'm lost.

 

[nickjer]

It is the same thing as connecting two capacitors to each other. So treat sphere 1 with capacitance C1, and the other with capacitance C2. And the charges will move from 1 to 2 until both capacitors have equal charge.