If I suddenly add a Tom to the original Tom, it will take at least a short time before Jerry is aware of the fact. There is another interesting fact that we discover experimentally or believe. Charge cannot be created, neither can it be destroyed. In order to increase the amount of charge in a region, it has to be moved in from outside. So if we are told all about all the currents, we should be able to calculate all the electrostatic forces.
Magnetism is closely related to electricity.
Circulating currents form little magnets. Then there is no net electrostatic force between the wires, but there is a magnetic force as soon as we move the mobile electrons. The stationary charge produces electrostatic forces on another stationary charge. The moving charge produces magnetic forces on another moving charge. These fields represent the forces that would be experienced by a unit test charge or unit magnetic pole, under the assumptions that these test items do not perturb the existing field distributions, and ignoring the fact that no-one has ever seen an isolated magnetic charge or pole.