 # Coulomb's Law

The electric charge of a material describes the net summation of positively and negatively charged ions. Like charges repel while opposite charges attract. They do so with a force that’s described by Coulomb’s Law. This law states that the magnitude of an electric force between two point charges is directly proportional to the positive product of the charges divided by the square of their distance. This equation can be better represented here: Remember, this force will be attractive if the signed magnitude of the charges (q) are opposite.

Now, you may be faced with multiple point charges suspended in three-space. If that’s the case, Don’t Panic. You have the law of superposition to save you. If you want to find the force on q1 from n point charges, simply convert everything to vector form and work Coulomb’s Law n times. Well, I guess that won’t be the easiest thing to do. However, if you are reading this there is a good chance you’re an engineer or scientist of some sort so maybe not.
Think of it this way. If a point charge is 10 units above your origin, it is at <0,0,10>. Any forces will be in the z direction. If it is 10 units to the right of your origin, it is <10,0,0>. Any force applied is going to be in the x direction. If it is 10 units above, 1 unit to the left, and 1 unit ahead, I would recommend converting to three-space polar form or spherical notation, depending on your math background. Hopefully you don’t run into problems that nasty. As a mere electrical engineering candidate, I only had to use superposition in 2d space. However, they are quite solvable in 3d if you have the time on your hands.
Anyway, if you discover that q2 causes 5 newtons of force in the x direction and q3 causes 6 newtons of force in the y direction, you can say that q1 experiences <5,6,0> newtons overall. Sling your Pythagorean theorem at it (x^2+y^2=h^2) and throw in an inverse tangent (remember, opposite/adjacent) calculation to get your magnitude and direction of force, respectively.
Oh, and to lead into a later lecture, the k value is equal to the reciprocal of (4 pi * permittivity of free space). This is equal to 9*10^9 N*m^2 / C^2

CGI Source: University of Alaska, Fairbanks