How does a charged particle detect another particle at a distance?

[Cosmology2015]

Hello,
I have a question about the interaction between particles. Maybe it's a simple question, but it's bothering me.
Consider Coulomb's law. From Wikipedia we have a simple definition to illustrate:
"The magnitude of the electrostatic force of interaction between two point charges is directly proportional to the scalar multiplication of the magnitudes of charges and inversely proportional to the square of the distance between them. The force is along the straight line joining them. If the two charges have the same sign, the electrostatic force between them is repulsive; if they have different signs, the force between them is attractive."
So the Coulomb's law is describing a phenomenon: if we put two charges of the same sign, then there is a repulsion between them. However begs the question of how the first particle knows about the existence of the second particle in order to obey Coulomb's law? In general, how a particle knows about the existence of another particle? In classical physics and in modern physics?
I'm grateful for any response .

 

[phinds]

The electric field created by the charge.

 

[anorlunda]

If you want a deeper answer, it is called Quantum Electro Dynamics. Richard Feynman wrote a famous layman-accessible book about it called
QED: The Strange Theory of Light and Matter