The source charge causes an electric field which exerts a force on the victim charge. The net effect is that the source charge causes a force to be exerted on the victim. While we have much to discuss about the electric field, for now, we focus on the net effect, which we state simply (neglecting the "middle man", the electric field) as, "A charged particle exerts a force on another charged particle." This statement is Coulomb’s Law in its conceptual form. The force is called the Coulomb force, a.k.a. the electrostatic force.
Note that either charge can be viewed as the source charge and either can be viewed as the victim charge. Identifying one charge as the victim charge is equivalent to establishing a point of view, similar to identifying an object whose motion or equilibrium is under study for purposes of applying Newton's 2nd Law of motion, [formula].* In Coulomb's Law, the force exerted on one charged particle by another is directed along the line connecting the two particles, and, away from the other particle if both particles have the same kind of charge (both positive, or, both negative) but, toward the other particle if the kind of charge differs (one positive and the other negative). This fact is probably familiar to you as, "like charges repel and unlike attract.
The SI unit of charge is the coulomb, abbreviated C. One coulomb of charge is a lot of charge, so much that two particles, each having a charge of +1 C and separated by a distance of 1 meter, exert a force of 9x109N, that is, 9 billion newtons on each other.
This brings us to the equation form of Coulomb's Law which can be written to give the magnitude of the force exerted by one charged particle on another as [formula1(1-1)], where: k = [formula2], a universal constant called the Coulomb constant, q1 is the charge of particle 1, q2 is the charge of particle 2, and r is the distance between the two particles.
While Coulomb's Law in equation form is designed to be exact for point particles, it is also exact for spherically symmetric charge distributions (such as uniform balls of charge) as long as one uses the center-to-center distance for r.
Coulomb's Law is also a good approximation in the case of objects on which the charge is not spherically symmetric as long as the objects' dimensions are small compared to the separation of the objects (the truer this is, the better the approximation). Again, one uses the separation of the centers of the charge distributions in the Coulomb's Law equation.
Coulomb's Law can be written in vector form as [formula], where F12 is the force "of 1 on 2", that is, the force exerted by particle 1 on particle 2, r12 is a unit vector in the direction "from 1 to 2", and k, q1, and q2 are defined as before (the Coulomb constant, the charge on particle 1, and the charge on particle 2 respectively).
Note the absence of the absolute value signs around q1 and q2. A particle which has a certain amount, say, 5 coulombs of the negative kind of charge is said to have a charge of -5 coulombs and one with 5 coulombs of the positive kind of charge is said to have a charge of +5 coulombs and indeed the plus and minus signs designating the kind of charge have the usual arithmetic meaning when the charges enter into equations. For instance, if you create a composite object by combining an object that has a charge of q1=+3C with an object that has a charge of q2=-5C, then the composite object has a charge of q=q1+q2, q=+3C+(-5C), q=-2C.
We've been talking about the force of 1 on 2. Particle 2 exerts a force on particle 1 as well. It is given by [formula]. The unit vector r21, pointing from 2 to 1, is just the negative of the unit vector pointing from 1 to 2: r21= -r12. If we make this substitution into our expression for the force exerted by particle 2 on particle 1, we obtain: [formula1] [formula2].
So, according to Coulomb's Law, if particle 1 is exerting a force F12 on particle 2, then particle 2 is, at the same time, exerting an equal but opposite force F21 back on particle 2, which, as we know, by Newton's 3rd Law, it must.