Electric field problem -- Repulsive force between two charged spheres

[Dezzi]

Homework Statement

Two identical spheres have charges q1 and q2. When they are 20 cm apart, the replusive force between them is 1.35×10^‐4N. After they touched together and separated once again to 20cm, the replusive force between them is 1.406×10^-4N. FIND q1 and q2. (Ans 20nC; 30 nC)

Relevant Equations

F=kQ1Q2/r^2

I attempt to solve the problem in the picture below.

 

[PeroK]

Why is the force different the second time?

 

[Dezzi]

Why is the force different the second time?

The question say " they touched together and separated once again"

 

[PeroK]

The question say " they touched together and separated once again"

So, what changed?

 

[PeroK]

So, what changed?

I guess the charges get equalised. So, you've worked out that average charge: $2.5 nC$, which looks right.

The hard bit is to figure out what the original charges were. Any ideas?

 

[haruspex]

A quibble: since the spheres are evidently conductors, the question ought to specify that the spheres are much smaller than 20cm radius. Otherwise the charge distributions complicate matters.