Electrically connected charged balls

[Bashyboy]

Hello,

I am reading through the problem given in this link: http://physicstasks.eu/uloha.php?uloha=300

There is one sentence I am particularly unsure of, "Charged ball's potential is in direct proportion to the charge of the ball and in reciprocal proportion to the ball's radius."

Why is this true? Is there some derivation for this?

Also, here is a passage I have a question about:

"When the balls are connected by a conductive wire, the charge can move from one ball to other. The ball with higher potential will be partly discharged trough the wire while charging the other ball. At the end of this process, both balls' potentials will be the same."

When the two sphere's are at the same electric potential, does this mean that each ball has the same amount of charge?

 

[Simon Bridge]

The equation is Gausses Law.
The result for a ball of charge is that the potential at radius r ≥ R (where R is the radius of the ball) is the same as if all the charge in/on the ball were concentrated at the center.

If the two spheres are at the same electric potential, they will not have the same charge unless they have the same radius. This follows from the previous result.