# Equipotential Spheres

1. Oct 24, 2009

### nns91

1. The problem statement, all variables and given/known data
A spherical potential conductor of radius R1 is charged to 20kV. When it is connected by a long, fine wire to a second sphere faraway. its potential drops to 12kV. What is the radius of the second sphere.

2. Relevant equations

V=kq/r

3. The attempt at a solution

So I know that R2= R1* (q2/q1). Thus, I need to find the ratio q2/q1. I am kinda lost in what to use to figure out q2/q1 ratio.

k*q1/R1 = 2x10^4 and k*q2/R2= 4x10^3 (because 2 spheres are equipotential at 12kV and sphere 1 drops 8kV so sphere 2 has to gain 8kV so initially sphere 2 is at 4kV)

k*q1/R1 = k*q2/R2 = 12x10^3.

With these 3 equations, I am still unable to figure out what is q2/q1. Can you guys give me some hints and suggestions ?

2. Oct 24, 2009

### willem2

Sphere 2 only will gain the same amount of voltage if it has the same radius.
I think you are supposed to assume sphere 2 is initially uncharged. If it has an initial charge, you can't do the problem. Sphere 2 could be gigantic, with a potential slightly below 12 kv, or tiny with a very large negative potential.

the spheres act as capacitors with capacity r/k

3. Oct 24, 2009

### Fightfish

There is no need to consider them as capacitors.
Your equations are almost there, except for the part on sphere 2 being at 4kV initially of course, but do take care of the variables (why do i see q1 appear twice in different situations?)
Hint: Charge is conserved throughout the transfer process
That should allow you to simplify the expressions.

4. Oct 24, 2009

### nns91

So if I assume that sphere 2 is uncharged initially, then I should make its potential equal to 12kV right ? since 2 spheres are equipotential.

Oh, if charged is conserve then kq1/R1= 20kV = kq1/R1= 12kV ?

5. Oct 25, 2009

### Fightfish

Yes. Sphere 1 is at 20kV and Sphere 2 at 0V initially, with both becoming 12kV after charge flows between the two spheres

Er..no...that equation clearly doesn't make sense - 20 = 12??
Charge conservation in the sense that if Sphere 1 possesses Q coulombs of charge initially, and q2 coulombs of charge flow from Sphere 1 to 2, leaving sphere 1 with q1 coulombs remaining, then clearly q1 + q2 = Q.
Then your originally formulated equations can be written as:
k*(q1+q2)/R1 = 2x10^4
k*q1/R1 = k*q2/R2 = 12x10^3
I guess you can carry on?