 So we know quantitatively where electric fields come from and what they do and we've talked about where magnetic fields come from quantitatively. Now we need to talk about what they do quantitatively. And first let's summarize what we've learned already. So we've learned about two kinds of things electric fields and magnetic fields. And we know that electric fields are made by charges. In Coulomb's law let's us be precise about that. So if we have a point charge q and we want to know the electric field a distance r away from that point charge, then it points away from q if q is positive and the strength of the electric field is given by kq on r squared. And for a negative charge where the sign on that q is opposite you just get the opposite vector same size by pointing the opposite direction. So that's what electric fields are made by. What do they actually do? Well electric fields affect charges. So again if I have a charge and this time it's in an electric field made by something else and put a bar under that symbol to denote that it's got direction as well, then there is a force on that charge. And the force is just proportional to the electric field and the charge. So Coulomb's law talks about the force between two charges and so it just kind of skips the electric field between here. So we can sort of put Coulomb's law in between the two. And if you have a charge q1 and a charge q2, a distance r apart, then the force between them is just given by this. And you see that's exactly the same as you get if you talk about the electric field, maybe a charge q1 and the effect of that electric field on a charge q2. So if you take this result and throw it into there, then you get exactly Coulomb's law. So Coulomb's law is not an extra law, it's just the effect of the electric field of one charge on a second charge.