# Currents and charge between spheres

1. May 15, 2009

### omri3012

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

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

I=dQ/dt

J=$$\sigma$$E

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

3. 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.

2. May 15, 2009

### 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.