When negative charges are applied to one end of a neutral copper rod, they quickly distribute evenly across the rod due to copper's conductivity and the principle that like charges repel.
When negative charges are applied to the right end of a short copper rod that initially had a neutral charge, due to the conductivity of copper, the charges will spread fairly quickly along the surface of the rod to distribute the charge evenly. Copper is a good conductor of electricity, which means it allows for free movement of charge carriers, such as electrons, throughout the material. Within seconds, the charges will redistribute themselves so that they are as far apart as possible, resulting in a more uniform distribution of negative charge along the entire rod.
The rods behavior can be understood with the principles of electrostatics. When excess charge is added to a conductor, it repels itself due to like-charges repelling, and this repulsive force causes the charges to move until they have reached a state where they are no longer experiencing any net force from the other charges, which generally means they are spread out evenly.