Alright, guys. So we've seen a lot of stuff so far. We've seen electric forces. We've seen electric fields, potential energies, and potentials. And now we're basically going to put it all together in an awesome formula sheet that's going to be really helpful for your tests. Let's go ahead and check it out. So far, we've seen these four related things, and often it's really hard to keep track of all of them. Which one's which? Which one involves what variables? So this table is going to be really awesome at putting all of these things in perspective together. Let's go ahead and take a look at it.

We've got r2. We've got some equations involving r squared. Some that involve single r's. Some that involve multiple charges, and some that involve single charges. So basically, let's take it from the bottom. We know that this electric field here is a force field. And the best way that we can think about this is that it is a charge that sets up a field that another charge will feel and experience a force from. Now, I just want to point out really quickly that I know I'm using little q's here when I've used big Q's, and I know that's potentially might be confusing. But the thing is that it won't matter. You just have to be sure that on tests force. Because the reality is that some of your professors might use q1q2, force. Because the reality is that some of your professors might use q1, q2. Some of your professors might use big Q's and little q's. It's up to you to decide and figure out which one is the producing charge and which one's the feeling charge.

In any case, we know that a charge that it produces a field that is e, has a resulting force on a feeling charge. The relationship between these two formulas is f=qe. So if one charge produces an electric field, and another charge, which is this little q right here, feels that electric field, it's going to have a force.

Similarly, we know that a charge will also produce something called a potential. And this potential is basically just an energy field. Instead of telling other charges how much force to feel, it's basically telling other charges how much energy to have. And we know that this relationship between these two formulas is given as u=qv.

Now, what we haven't seen yet is we haven't seen the relationships between these two formulas, f and u. So basically, the negative of the potential energy difference is going to be f∇r. Most of the time, you won't see this as delta r. A lot of the times you'll see this as delta x instead. But I want to point out that I'm using this delta r because it sort of helps reinforce the relationship between these r's right here. But ultimately, these are distance variables.

And we have a similar relationship between the electric field and the electric potential, and that's that the negative of the potential difference here is just going to be equal to e∇r, or sometimes, most of the time, you'll see this as delta x. Again, just reinforcing the fact that it's just a distance variable.

The last thing I want to do is point out that these two quantities, these deltas, actually have special names. Remember that this delta v is defined as the voltage. It's the potential difference between these two points. That's delta v right here. That's the voltage. And this delta u over here, the negative in the change of the potential energy seen so far. Work, potential energy, electric force, electric field, all of those things. Alright?

So basically, that's it for this video. Go ahead and print out this page, take it to your exam, and you'll be good to go. Alright?