 So now let's introduce Coulomb forces, and these are the forces between electric charges. And we've got some general rules, which says that charges feel forces when they're near each other. As a basic introduction, we often learn that if I've got two positive charges near each other, they're pushed away from each other. If I had just two negative charges, they're also pushed away from each other. But if I have a negative and a positive, they actually get pulled together. So we'll paraphrase or shorten this up to tell us that same charges, sometimes called like charges, repel, while opposite charges attract. Now this general rule gives us just kind of a hint of what direction the forces should be in, but doesn't tell us how much force. Well, that's what Coulomb worked to figure out. Coulomb quantified the force, and again, Coulomb was the scientist who worked on a lot of this. And he determined that how much force we have is going to depend on the amount of charge, and it's also going to depend on the separation. Now these things make sense. The more charge I have, the more likely they are to affect each other. The more they're going to affect each other more greatly. So more charge means more force. Similarly, let's say the separation makes sense. If they're close together, they're going to affect each other more. If they're further apart, they'd affect each other less. So the relationship that he worked out here tells me my force in relationship to these charges and distances. Let's take this equation and break it down into the individual variables. Now again, f is my force. That's what I'm solving for. My q1 is going to be the charge on object one. And notice that it's in here in absolute value signs. That means for right now, I don't care if it's a negative or a positive charge. I just need to know how much charge. Similarly, for charge two, and yeah, I have to have two charges to have a Coulomb force. It's the force between those two charges. Now r is my separation between the charges. So if I look at how far is it measuring from q1 to q2, that's going to give me my r value. My k is the last thing in here. It's not actually a variable. It's Coulomb's constant. Well, that Coulomb constant, k, or you might see it in some books written out as k sub e, and that specifies this is the k used in those electrical equations, has a value of 8.99 times 10 to the ninth Newton meter squared per Coulomb squared. And it is a fundamental constant in nature. Now we're not going to use this right away, but to introduce it to you, our k is actually related to another fundamental physical quantity, epsilon, and we'll learn what that is a little bit later. Now let's take a look at the units. Since ultimately I'm solving for a force, everything over here on this side has somehow got to equal Newtons, so I have the right units for a force measurement. Let's take my equation and actually plug in those values. Well my k, remember, had units of Newton's meter squared per Coulomb squared. Each one of my two charges has units of Coulomb, and my r is in meters, but I've got r squared, so I've got meter squared on the bottom. Pretty obvious at this point the way it's written out that my Coulomb squared on the bottom and my Coulomb and Coulomb that came from the charges are going to cancel each other out. Similarly, my meter squared on my top and bottom are going to cancel each other out, and sure enough I'm left with a force in units of Newton's. Now remember, the equation that we've looked at so far is only telling us the magnitude how much force I have. It tells me absolutely nothing about the direction of those forces. I still have my general rules of repellent and tract, but I'm going to need to do a little bit more work to figure out my forces if I want to know the full magnitude and direction. So that introduces the Coulomb force to you so that you can start looking at problems and examples of this.