What happens if two small positively charged particles of equal magnitude are placed close to each other?

Two electrical charges exert an electrostatic force against each other, and this force is equal to:

where
is the Coulomb's constant
are the two charges
r is the separation between the two charges

The direction of the force is determined by the sign of the charges: when the charges have same sign, the force is repulsive, while when the charges have opposite sign, the force is attractive. In this problem, both charges are positive, so they exert a repulsive force against each other, therefore the two charges will start to move away from each other.