 Now let's introduce the electric field. We're going to start with a conceptual picture of why we care about this. Imagine I've got an environment which has got a bunch of different charges distributed all over it. If I want to find the force on some small charge that's in this environment, I calculate the contributions to the force from each one of those charges in the environment. It takes a lot of work, but it can be done. The difficulty is that if I move my charge, I now have to repeat that entire set of calculations for the new position. And that's going to get tedious after a while. So instead, we want something where I can describe the environment. And I'm describing the environment independent of where I put my small little charge inside of it. Well, this description of the environment is what we call the electric field. It describes the electrical environment that a charge might go into. Formally, it's defined in terms of the force on a test charge, where the force on the test charge is going to be equal to the charge times the electric field, which means I could define the electric field in terms of the force divided by the amount of charge on that test charge. Now, this is for every position. So if I know the force at a position, I know the electric field at that position. But for another position, I'd have to find the new ones. What we're going to find, however, is that sometimes there's easier ways to find the electric field. And if there's an easier way to find the electric field, then I can use that electric field for any charge, not just the test charge, that goes into that environment. So once I have a description of the electric field, all I have to know is how much charge am I putting into that environment. And I know the force at any position where that charge could be. Looking at the units for a moment, we can start with our equation. Now, we can start with either the equation for force or electric field, since these are really just algebra versions of each other. Starting with the electric field equation, I see that my force should have newtons, and my charge should be coulombs. So that would imply that the electric field is newtons per coulomb. If I plug this into this upper equation, I see that charge should be coulombs. The electric field is newtons per coulombs. And as expected, those two coulombs cancel each other out, leaving me with my expected newtons for the force. We need to stress one thing about this electric field for you to really have a picture of it. It's what's called a vector field. And that means that every spot has a value for the electric field, but it also has a direction at each spot. Now, if I've got a uniform field, it might look something like this. And here, every single spot has a value in a direction, but they're all the same. It doesn't matter if I'm over here or over here or over here, I've got the same value for the electric field and the same direction. We don't have to have that. Here's another example of a vector field where I've got different directions and different values at different places inside that field. So that gives you an introduction to the electric field so that as we start working with our equations, you'll be able to picture what's going on.