Final answer:
A repulsive force between two charged objects occurs when the charges are of like sign, meaning both are either positive or negative. This follows Coulomb's Law, which dictates that like charges repel while unlike charges attract.
Step-by-step explanation:
There is a repulsive force between two charged objects when the charges are of like sign. According to Coulomb's Law, like charges repel and unlike charges attract. Consequently, two positively charged objects, or two negatively charged objects, will exert a repulsive force upon each other. This behavior is due to the electric field that is associated with charged particles. For example, two protons will repel each other since both carry a positive charge.
It's also important to note that the magnitude of charge of the proton and the electron are equal but opposite, with the proton carrying a positive charge and the electron carrying a negative charge. This means an electron and a proton will attract each other, demonstrating the principle that unlike charges attract.
The case where charges are of unlike sign results in an attractive force between the two charged objects, as opposed to the repulsion found when the charges are the same. The force between these charges also decreases with the square of the distance between them, illustrating an inverse square law in action.