25. Electric Potential
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Hey, guys. So in the last couple videos, we talked about electric potentials, and we've talked about electric potential energies. So in this video, we're gonna cover a specific unit that you might run across when talking about these things called the Electron Volt. Let's check it out. So imagine we have these two plates and they're charged, and we have a potential difference of one volts across them. So now imagine that we have an electron that starting left plate moves to the right. So I'm gonna drop this little electron right here and after The charge on the electron is negative. E. And this electron wants to move towards the right. Why? Because it wants to go towards higher potentials, and it also wants to be attracted towards the positive end of the plate. So as this electron is moving between the plates, it is moving through a potential difference. And that potential difference is Delta V. And that's just equal to one volts. That's just the difference that we were told. So we have a charge that is moving through a potential difference in any time that a charge moved through potential difference. There is a change in potential energy. Remember that those two things are related by the equation. Delta U is equal to Q times Delta V So that means that we have a charge, which is that negative e moving through a potential difference, which is one volts. And that's just, you know, equal negative one e. Times V. Now all I have to do to flow, to plug in or to figure out the change potential energy in jewels is just use the relationship, that he is the elementary charge, which is 1.6 times 10 to the minus 19. So that's in jewels now. What's happening to this potential energy? What's happening is that is changing from potential to kinetic. So any time remember, we have a negative change in potential energy. The potential energy is getting smaller. That means that that's been converted to kinetic energy. So as the things moving across, it's basically speeding up. All right, so what if we were to actually have a positive charge? Someone you might be wondering what happens to a positive charge? So basically what happens is if you have a positive charge, it's going to do the exact same thing. But backwards. So this positive charge, it wants to go towards the left because it wants to go towards lower potentials and it's attracted to the negative plate that's over here. But now what happens is that the potential difference that's good that is going through is not one volt. We know from last couple videos that it's very important that we have positive and negative signs with our potential differences. So if we went to the right and it was positive one volt, if we're going to the left, that's actually negative. One volt, its final minus initial. So here this was the initial and the right side was the final. We're here. It is backwards. This was my initial, and this is my final. So everything gets sort of reverse like that. But in any case, we can figure out what the change of the potential energy is By using the equation. Delta U is equal to Q times Delta V. So in this case now we have a positive one electoral, one electron charge, because if this is a proton on the charge on this guy is equal to plus e and now the potential difference is negative. one volts. So that means that the change of the potential energy is negative. One, Evie, just as it was for the protons. We get the same exact thing, and the fact that it's negative means that it is basically accelerating as it's going and all the energy is being converted to kinetic energy. So I have this little this little variable here or these little units one e V and that's actually has a precise definition. This one EV, is actually called an electron volt. It's basically the change in the potential energy of one electron or really one Proton as it travels through one volt of potential difference. And basically, all this E V is it is basically just a unit of energy for a very, very small charges. So that's the whole entire thing. So basically, we're just gonna use all of our energy formulas, but we're just gonna have a different unit for it. It's just gonna be a conversion. All right, so let's go ahead and check out an example. So we're supposed to figure out what is the speed of an electron with 100 electron volts of kinetic energy. So we're looking for the speed and were given kinetic energy. So that means we're gonna use the relationship, that the kinetic energy is equal to one half m and this is gonna be the electron. So it's gonna be Emmy Times the final squared. So we're just gonna sort of, like, assume that this thing goes from rest, and it's now traveling at some speed. All right, so we gotta move everything over to the other side. One half goes over and the mass of the electron goes over as well. So now we have two times k divided by m e equals V final squared. So that means that the final is equal to the square root of two times the kinetic energy. Now, the kinetic energy I'm told is 150 electron volts. But that's not in the right units that I need. So 150 e. V. S is gonna be 150 times 1.6 times 10 to the minus 19 jewels, and that's gonna give me jewels because I need that in order to plug into this formula here for the velocity, I need to have these things in the right units. So when you work this out, 150 electron volts is actually equal to 2.4 times 10 to the minus 17 in jewels. So this is the number I'm gonna plug in for this formula. So I've got two times 2.4 times 10 to the minus 17. And now we're just divided by the mass of the electron, which, by the way, is gonna be given to you on a test. It's gonna be 9.11 times 10 to the minus 31 then you just have to square root that so you should get you should get 7.26 times 10 to the sixth meters per second. And that's it. So basically all of our equations for energy, you're gonna be working the exact same. It's just an electron volt. It's just a slightly different unit of energy. So basically we're just doing UNIX version here. Alright, guys, let me know if you have any questions