An electron moves from point A to point B. The potential difference between these two points is 100 V. What is a. the point of higher potential?b. the work done on the electron?c. the final speed of the electron if its initial speed is zero?

(a) B (b) 1.6 × $$10^{-17} J (c) 5.93$$ × $$10^{6} m/s$$

An electron moves from point A to point B. The potential difference between these two points is 100 V. What is a. the point of higher potential? b. the work done on the electron? c. the final speed of the electron if its initial speed is zero?

Hey, guys. Hopefully, you were to figure this one out on your own. I actually just provided the mass of the electron just in case that was the one constant that you were needing. Okay. So for this first part, we have an electron that is moving from point a to point b. We also have the potential difference, and those things are important important. So point a to point b and the the potential difference is 100 volts. So for this first part here, we're asked what is the point of higher potential. So what I want you guys to remember is that positive charges always wanna move towards low potentials, low v's. Whereas negative charges always wanna move towards higher potentials, higher voltage or sorry, higher volts. So that means that point b, which is the one that the electron is moving towards, has to be the point of higher potential. And that's basically the answer. So that's more of like a conceptual point. Alright. So part b says, what is the work that is done on the electron? So we just saw in the last couple in the last video that the work that's done, you might be thinking, okay. Well, I have to use k q q, and then you have to use 1 over r initial minus 1 over r final. The problem is that with this formula, you have to have 2 point charges. So in other words, we have to know what big q and little q are, and we also have to be told information about the final and initial distances. Now, in this case, we're not told any of that information, so we actually can't use this formula. Instead, we're gonna have to use something else about work. We know that work is equal to Well, it's both the change in kinetic energy, and it's also the negative change in the potential energy. Now, this potential energy, remember, inside of a potential difference, we know what this potential energy is equal to. That the change in potential energy is gonna be q, which is the feeling charge, which is the electron times the potential difference right here. So that's what we need to That's what basically we need to use for this, this this problem. We know that this q, the feeling charge, is equal to the negative electron, and that's actually gonna be really important. And we know this potential difference right here, delta v, is equal to a 100 volts. So if we put all of that stuff together and say that the work is equal to negative q times delta v, that means that the work is gonna be negative negative 1.6 times 10 to the minus 19. It's actually very important that you guys include that negative sign because these negatives are gonna cancel out. And then what happens is we have the potential difference, which is a 100 volts. So that means that the work that's done on this electron is 1.6 times 10 to the minus 17, and that's positive joules, and that's the amount of work that's done on the electron as it moves towards this higher potential. So now for this last part here, we just have to figure out that if this electron starts from rest, what is the final speed of this thing? So whenever we are talking about speeds and work, we use the work energy theorem. So we actually wrote it out over here. The work that's done is equal to the change in kinetic energy, which means that the work that's done is equal to 1 half m. So in this case, the mass of the electron. V final squared minus v initial squared. We're looking for what this final velocity is, but we're actually told that it starts from rest. So it means that we can cancel out this term because it's just equal to 0. So that means that we basically have to move over the one half and the mass of the electron over in order to solve for this. So I'm just gonna write it out over here. So this is just gonna continue. I've got that the final velocity is equal to the square root of 2 times the work divided by the mass. So one, the reason why that happens is because the one half goes over, becomes 2. You you divide over the mass, and then you have to square root both sides. So it means that the final velocity is the square root of 2 times 1.6 times 10 to the minus 17, and then we have tie divided by point Let's see. I have, the mass of the electron is 9.11 times 10 to the minus 31. And if you go ahead and work this all out and square root it, you're gonna get 5.93 times 10 to the 6th, and that's gonna be meters per second. Alright? So that is the final answer for all of these parts. Let me know if you guys have any questions, and I'll see you guys in the next

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An electron moves from point A to point B. The potential difference between these two points is 100 V. What is a. the point of higher potential?b. the work done on the electron?c. the final speed of the electron if its initial speed is zero?

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An electron moves from point A to point B. The potential difference between these two points is 100 V. What is
a. the point of higher potential?
b. the work done on the electron?
c. the final speed of the electron if its initial speed is zero?