There is a repulsive force between two charged objects when

When two electrically charged bodies come closer, appears a force that attracts or repels them, depending on the sign of the charges of this two bodies.

This is stated by Coulomb's Law:

"The electrostatic force between two point charges and is proportional to the product of the charges and inversely proportional to the square of the distance that separates them, and has the direction of the line that joins them"  

Mathematically this law is written as:  

Where is a proportionality constant.

Now, if and have the same sign charge (both positive or both negative), a repulsive force will act on these charges.

. west