What would happen to the two balls if one of them were kept positively charged and the charge on the other ball were slowly increased, making it more and more positive?

The force of repulsion between the two balls will increase

Explanation:

The electrostatic force between two charged objects is given by

where

k is the Coulomb's constant

q1 and q2 are the charges of the two objects

r is the distance between the centres of the two objects

We see that the magnitude of the force is directly proportional to the charges on the two objects. in this problem, we have two positively charged balls (so, there is a force of repulsion between them, since like charges repel each other and unlike charges attract each other), and the positive charge in one of them is slowly increased: this means that either or in the formula is increasing, and so the magnitude of the force is increasing.

where are the vectors ?