Now we look at the calculus-based version of Faraday's Law. As a quick reminder of what we've already seen with Faraday's Law, a changing magnetic flux creates an induced EMF, and how much EMF depends on the rate. When I had the average formula, I used the delta symbol to represent my change, and so it was the delta phi per delta t, where the change in flux divided by the change in time. When I shift over to a calculus view, that means I'm taking the continuous limit as that delta t goes to zero, and it becomes d phi dt. Now let's look at this equation a little bit more carefully. So again, over here on my left, I've got the symbol epsilon, and that represents my induced EMF. It's not the average EMF anymore, it's the actual induced EMF at a particular moment in time. I still have my minus sign referring to the direction, and the n representing the number of loops. But now I want to take this whole quantity and represent it as one thing, d phi dt, which is the rate of flux change. Now another way you could write this equation to kind of emphasize this, is to look at the derivative with respect to time of the magnetic flux, emphasizing again that I'm looking at the magnetic flux, and I have to take the derivative with respect to time. This is one mathematical operation that operates on my flux. So there's no dividing by time or anything like that on this. You're simply looking at the rate of change of flux. So that's our Faraday's law in our calculus-based version.