 Now we're going to look at the specific equation for a parallel plate capacitor. Let's start by reminding ourselves of some of the diagrams for this parallel plate capacitor. And in particular, call your attention to this 3D view where we can clearly see the plate area and the distance between the plates, which are labeled with A and D on our diagram. Now on Make Note here that even though a capacitor could have a dielectric in the middle, it could also be empty space. We're going to start with the empty space category and come back to the dielectric later. So now we move to that general equation we had for any capacitor, which related the capacitance to the amount of charge that could be stored for a particular voltage. For our parallel plate capacitors, what we're going to see is that voltage or the potential difference is going to be equal to the electric field times the distance. That was one of our equations we had back for figuring out potential difference. And if I substitute that into the equation, I have Q over Ed. Well, the electric field from Gauss's law, I could figure that out as being sigma over epsilon naught, where sigma was the surface charge density. Combining those two equations, I'd see that for this case the electric field inside that capacitor is going to be Q over epsilon naught A. I can now substitute that back in to my E up here in my equation to give me this complicated form. Now all I have to do at this point is some simplification. Because I've got a fraction over a fraction, those are going to move up to the tops and the Q's are going to cancel, leaving me with this general equation. But it's not a general equation anymore. It's specific to the parallel plate capacitor because I use Gauss's law for the parallel plates to help find it. So just again to reinforce this equation for a parallel plate capacitor, C is our capacitance, our electrostatic constant epsilon naught, the plate area, and the distance between the plates. So we now have something which describes the capacitance, not in terms of the general properties of the charge stored and the voltage on it, but of the particular properties that were manufactured into the device. What area of the plates, what's the distance between the plates, etc. So again, that electrostatic constant that we saw back when we were dealing with Gauss's law is the Greek letter epsilon, but its name is actually the permittivity of free space. And it has a standard value. Right now I just want you to take a real quick notice of the units over here, Coulomb squared per Newton meter squared. Because we're going to look at the units for this entire equation. Remember that capacitance had a standard unit of Farad. My electrostatic constant I just saw was Coulomb squared per Newton meter squared. Area is going to have a standard unit of meter squared and the distance between the plates is going to be meters. Taking all these and putting them together, what I see is over here on the right hand side, I've got Coulomb squared per Newton meter squared times a meter squared per meter. Well, those meter squares are going to cancel, leaving me with a Coulomb squared per Newton meter equal to a Farad. I can take this a step further because I recognize that a Newton meter is a joule. So Farad is also equal to a Coulomb squared per joule. So that's your parallel plate capacitor equation.