Two particles with charges are initially very far apart (effectively an infinite distance apart). They are then fixed at positions that are apart. What is which is the change in the electric potential energy?

potential energy increases.

Explanation:

The potential energy between the two charged particles is given by

U = k Q q / r

If they are very far apart then r tends to infinity and the potential energy is zero.

If they come closer then the potential energy between the two charged particles increases.

Thus, the potential energy increases.