11.4 Parallel Plates

Ok, today we're just doing a few add-on notes from what we did previously with voltage. First thing we're gonna talk about is what current is. So, you might have heard of current, we're going to be using this over the next little while, and what we're talking about is the flow of electric charge. So, if we have parallel plates that we've been talking about lately, let's suppose we have parallel plates, one plate is positive and the other plate is negative. If we put a positive charge in here, we know that it's gonna move across the plates due to repulsion and interaction. And so, we know that that's gonna have voltage, right? That's gonna have energy as that thing moves. We can calculate how much voltage there is in those plates. But anytime we have a moving charge, we say that there's also current. So, current instead of it just being one charge moving and figuring out the speed or things like that, what we're talking about is we're assuming that we have an infinite number of charges. So, in this case, if I had a whole bunch of positive charges one after the other and they're all gonna move, our current then is how many coulombs per second flow. So, it's sort of like a speed of the charges moving. A "might speed per charge" with sort of the rate or how fast they're moving across one after the other. For current, the formula we use is I for current, and it's just charge divided by time. So, it's a pretty easy formula. And our I is our current, and Q is our charge in coulombs. Time would be in seconds for a basic unit for a current, that is coulombs per second is the technical version. But, just like other units, we call current that you measure it in amps, named after ampere. So, amps is the exact same thing as coulombs per second. That's just a little key thing to remember. So, if we had positive charges like I have in the diagram, with positive charges moving one after the other, all we'd have to do is figure out what the charges are. So, our total number of coulombs divided by seconds, and that would be our current flow. So, a current of 2 amps means we have 2 coulombs per second flowing. And if positive charges move, so if you have positive charges like this diagram, we call that, obviously, flowing the positive charges. Or, another name for it is conventional current. Ok, and if we have normally what we would consider, because we don't normally have positives moving, so what we would do is typically we would call our negative charges, or electrons, what we consider moving in electricity, like in your plugins and so on. So, the negative, the electron charges move. Normally, this is kind of how we consider. Ok, so if we're talking about the flow of electrons, we'll usually say that's our current. But if you ever see the term "conventional current," that just means that we have positive charges that are flowing instead of negative charges. And that's pretty much it for current. So, pretty easy formula. You can solve any kinds of questions if they're dealing with current or time or anything along those lines. Ok, so what we're going to do is also now we're going to look at sort of how batteries work. So, if we have Let's suppose we have two plates. Okay, and we're going to have a positive charge. That's really, we have a proton or some sort of positive charge. And let's suppose it's going to move across the plates on its own. So based on that, we would know that this would have to be the negatively charged plate, and this would have to be the positively charged plate to get the proton to move across. So then the idea is, well, if we were to charge those plates, we have to hook up to some sort of power source like a battery. So then the idea is, what would the battery look like? So the symbol often used for batteries is just a wire connecting them, and then we put the symbol like that. So the longer line is to represent the positive connection, and the littler line is to show the negative part of the battery. And so in this case, if our proton is moving across on its own, it's going to be speeding up as it goes across. Then we have two positive plates and one negative plate, and our battery then has to hook up exactly like I've drawn. Okay? So if you see diagrams and the reverse would happen, so let's suppose I draw my battery this way, and we're going to hook it to two plates like this. Okay? And then let's suppose we put an electron this time in the plates. The question might say, "Is the electron going to move across? Is it going to speed up? Is it going to slow down?" Those types of things. So just based on this diagram, we know that this is our positive, so that means this has to be our positive plate. This is our negative, that is our negative plate. Therefore, the electron will be repelled from the negative and attracted to the positive, so we'd get our electron flowing upwards in this case. Okay? So when doing battery types of questions, just make sure you know which way positive and negative is, so you know which plate is positive and which plate is negative, okay? That's one quick example. So let's suppose that last example, or last battery registers, we have an electron moving between the two plates. Let's suppose the question then is, "How much kinetic energy is that electron going to change, or gain, if it moves through a battery that has charged the plates with a hundred volts?" So we're looking for energy, so we could use our formula, "Voltage equals energy over Q." So if we solve for energy, we would have voltage times Q. So we'd have a hundred volts, and the charge of an electron is 1.6 times ten to the power of negative nineteen. So we would get 1.6 times ten to the power of negative seventeen joules. Okay? It's a pretty easy calculation. But this is where electron volts are going to come in handy. So if we use the same formula, we have a hundred volts. Our charge is basically one electron. So then we just say it has a hundred electron volts of energy. So that's kind of why we use that term. We have an electron moving in voltage, so we end up with electron volts. So it's a pretty good situation to deal with these kinds of questions in terms of electron volts. Okay? Our last thing we're going to look at is what happens if we have electrons or protons or whatever moving through an electric field. They don't start or stop. So normally, we'd have, let's suppose we had an electron in the electric field. We know that it stopped and it's going to speed up, and we could calculate the speed when it gets to the other side of the plate. But in this case, what we want to do is we're not going to have that electron being stopped. So let's suppose the electron started outside the plates and we shot it through a hole into the Electric field. Let's suppose the original velocity of the electron was 3 times 10^6 meters per second. We're going to shoot that thing at a really fast speed. Then the question might be, what's its final velocity when it hits the other side of the plate? When we did these types of questions before, the shorter way was typically dealing with energy. So we used the change in kinetic energy to help us figure out the final velocity. We said our initial energy was zero. Then we could calculate that, just like we did. The trick with these kinds of questions is that we're going to have to calculate the energy that it has already escaped, and then we're going to have to add on the energy that it gains going through the electric field. Let's do this question. Suppose we have a voltage of 200 volts and a distance of 10 centimeters between the two plates. If we want to calculate the speed at which it's going to be, we know that originally it has a velocity of 3 x 10^6. We can actually calculate the initial kinetic energy by using the equation 1/2 * (electron mass) * (initial velocity)^2. Doing the math, we get 4.1 x 10^-18 joules. So it has that much energy before it even touches the plate. Now we have to figure out how much energy it's going to gain as it goes through the plates. We can use the equation energy = voltage * charge, where the charge is 2 x 10^6 x 1.6 x 10^-19. Doing the math, we get an answer of 3.2 x 10^-17 joules. So in this case, the electron has 4.1 x 10^-18 joules as it enters, and it's going to gain 3.2 x 10^-17 joules as it moves across. From there, we can now figure out the total energy. The easiest way to do this one is to add the initial energy and the gained energy, so our total change in energy by the time it hits the far plate would be 3.6 x 10^-17 joules. Now that we know the energy it has when it finally hits the plate, we can actually calculate its final speed. We can use the equation 1/2 * (mass) * (final velocity)^2, but in reverse. So we have 3.6 x 10^-17 = 1/2 * (mass) * (final velocity)^2. Solving for final velocity, we take our energy and divide it by 1/2 * (mass), and then......square root that answer. We get an answer of 8.9 times 10 to the 6. Okay, so the only thing that's different about this question is we have an initial velocity of this segment. So we just have to figure out what that energy is when it enters the plate, add the change of the energy that it's going to gain when it goes through the plate, and then just work backwards to calculate your velocity. We could calculate acceleration, time, any of these kinds of questions that we want. There's lots of different stuff that could be added on. But the key idea is you just got to remember that your velocity goes through. So one more time for the question. Let's kind of read/sketch this out. So let's suppose we have a plate like that. We have another one with a hole in it that we're going to shoot the electron through again. But now the question is, let's suppose we want to figure out the speed of the electron entering the plate. Actually, not the mess of the speed. So let's start easy. Let's suppose the electron, again, let's just make up a number here. Let's suppose it's moving at 3.2 times 10 to the 6 meters per second. So in the last example, we had our negative plate here and our positive plate there. So we knew that when it hit the plates, it gained more energy and it actually sped up. So my question then is, what happens if we reverse the charge of the plates? So what happens if the electron moves into the plates where the first one is positive and the second one is negative? So this electron is going to then, as it hits the gap, right, it's going to start slowing down because it's going to want to get attracted to the positive and it's going to get repelled from the negative. So if it's not going fast enough, like that's one super fast, it might just blast through and just slow down when it hits the negative plate. But let's assume that the voltage is going to be strong enough that the electrons can eventually come to a stop somewhere in between the plates. So the question is, can we calculate that? And the answer is yes, right? In the previous question, we added the energies to be able to fill up the total energy that would be at the end. So what we call this one now is we want to figure out how much energy or how much voltage, because the voltage is going to slow this thing down, is required to stop the electron. Okay, so we kind of do the question the same way. It's actually a little bit easier. So we still need to know the energy, so we still need to know how much energy the electron had when it hits the plates. So we know our kinetic energy of the electron is 3.2. Alright, we won't have them be squared. Let's write that in there f