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In the future people will only enjoy one sport: Electrodisc. Inthis sport you gain points when you cause metallic discs hoveringon a field to exchange charge. You a...

Question

In the future people will only enjoy one sport: Electrodisc. Inthis sport you gain points when you cause metallic discs hoveringon a field to exchange charge. You are an Electrodisc playerplaying the popular four disc variant. The disks have chargesof qA = −8.0 µC, qB = −2.0 µC, qC =+5.0 µC, and qD =+12.0 µC.(a) You bring two disks together and then separate them. Youmeasure the resulting charge of these two disks and find that itis +8.5 µC per disk. Which two disks did you bring togeth

In the future people will only enjoy one sport: Electrodisc. In this sport you gain points when you cause metallic discs hovering on a field to exchange charge. You are an Electrodisc player playing the popular four disc variant. The disks have charges of qA = −8.0 µC, qB = −2.0 µC, qC = +5.0 µC, and qD = +12.0 µC. (a) You bring two disks together and then separate them. You measure the resulting charge of these two disks and find that it is +8.5 µC per disk. Which two disks did you bring together? A and B A and C A and D B and C B and D C and D (b) You bring three disks together and then separate them. You measure the resulting charge of these three disks and find that it is +5.0 µC per disk. Which three disks did you bring together? A, B, and C A, B, and D A, C, and D B, C, and D (c) Given the resulting charge of each disk measured in (b) is +5.0 µC, how many electrons would you need to add to a disk of this charge to electrically neutralize it?



Answers

Two small spheres, each carrying a net positive charge, are separated by $0.400 m$. You have been asked to perform measurements that will allow you to determine the charge on each sphere. You set up a coordinate system with one sphere ($charge \space q_1$) at the origin and the other sphere ($charge \space q_2$) at $x = +$0.400 m. Available to you are a third sphere with net charge $q_3 = 4.00 \times 10^{-6}$ C and an apparatus that can accurately measure the location of this sphere and the net force on it. First you place the third sphere on the $x$-axis at $x =$ 0.200 m; you measure the net force on it to be 4.50 N in the $+ x$-direction. Then you move the third sphere to $x = +$0.600 m and measure the net force on it now to be 3.50 N in the $+ x$-direction. (a) Calculate $q_1$ and $q_2$. (b) What is the net force (magnitude and direction) on $q_3$ if it is placed on the $x$-axis at $x = -$0.200 m? (c) At what value of $x$ (other than $x = \pm \infty$) could $q_3$ be placed so that the net force on it is zero?

Preference. This is the problem based on first contribution of touch total charge of the system and will remain constant. And Fulham stop the force of interaction between two charges Escape if you want you to weigh rt Square. Yeah! No 1st 1st part put in charge of the system is Cuban prosecutor to prosecute tree my next spend my problem. But as for micro column, let's do my curriculum. So catastrophe minus six Microphone! Oh, yeah. After touching the spear, this charge will equally distribute Uh huh. Hey Mm. To trade Church, right? Yeah. Distributed equally. Yeah. Whoa! So Cuban escort Tokyo to escort to Q three. That is to fighter upon drip minus six. Micro pulling upon three. That is my next to my crapola. Okay, now force on Cuban. We have to calculate. See the diagram. Tired, but yeah, this is your nobody exist. This is the X axis here it is cute too. This is Cuba And this is guilty. Yeah, for sun Do you want to take you to be repulsive? Have fun too for sun cute one due to Q three. Been very repulsive Infantry So net force he will get on Cuba in this direction. Yeah. Mhm. Mhm. So net force F one baby our country minus I camp plus happen through minus Jacob. Okay. Do you want to treat upon urban Tree Square minus icap Keep Q two Q three Upon our 23 I squared minus G camp. So just do it KQ upon case gives square by our square minus I kept plus minus Jacob Mm. So Manny to love this is have fun and so have fun having the magnitude This is in vector form and have fun having the magnitude. Okay. She was square by our square root of my name is Bonnie Square plus minus Bonnie Square. We wrote to QE Square. By our respect, that is rude to eps here f is okay, you square by our script. No substitute the video. Go to K s 19 to 10 to the government charges Mhm mhm two and 2 10 to the power minus six to into 10 to the power minus six upon r and R is 3.5 and to turn to the palm industry who respect So it is to be 4.1561 Neutral that so Thanks for watching it

All right. So, uh, but this problem, we have this, uh, this set up so to threat, connected with two balls and, uh, angle between the thread and the vertical is data. So the mass of the boys and and the charges, Q one. So this is also an on the q two. The information we know Ah, about the state of it is that we know. Ah, the mess. Em is eight grand, and the CDA is 20 degrees and l l which is the lens of the threat, which is 200.5 meters. Ah. So, uh, part, eh? We want to show the free body diagram off the off the board, and we want to label the forces that down the hall. So we're just four simplicity. We just look at the right one. We just look at this one. A CZ. You can see that the club is bowl. We have the gravity queer de and we have the coon Falls because these two bowls, they carry the same, uh, listen, can this same kind of charge, So the colon forces upstate to each other, so it's pointing to right direction. And this is the force on the threat. So let's say this is ft. This is F C. And this is empty. Okay. And the four party, we want to find out the colon force. So if you're looking at this diagram, we see that the f t. It's basically office. It is opposite to the combination off F C plus F G. In that case, we know that I've see over FT Is tension pita So weird. This is the data. Okay, so we know that we can find out f c quote f g times tending beta and ft is simply the gravity. So this is m g times tended data. We already know where the mass and we know that data. So just plugging the two values and see that FC for their 20.28 54 nude is okay. And, uh, we also want to know on the fourth on the threat of tea, uh, again, we just look at this free body diagram. We know that f a g over ap ti equal course on data. Okay, so just the plug in the video full f g and the data second, see that t a quote point on 0834 new. It's okay. And for Parsi for here. A Parsi. Ah, we want to get some information about the Cuban. Que tu uh, I'll say that at this moment we can know determine the value for Kyu won And que tu However, we can steal some information, so we already have the magnitude of the cool and force over here. Right? So we know the expression for cool imposes. Have see, they call one over four pi Absolute knots times you want you to be. Bye bye. The separation. Here's the separation. So just utilize the strangler knowledge and you could see that separation. The call to L. A times son Peter with bread. Okay, so this value equal 0.28 54 as we found previously. Okay, So, uh, we can solve for Q one times Que tu by using this expression So we see that is equal to 3.71 times 10 to the negative. The thing Call him squared again Because this is a Q one dance, you two. So this is the only information we camped in for the time being and for party. Uh, so the thing is. We suppose we connected the two bowls with the with the metal with the metal wire so that the charge on the two bowls Ah, uh, now they're equal. Ah, and the we get in this case, we will obtain. Ah, I mean, if it were up to a new angle beta So they had a prime April 30 degrees. Yeah. So now that we have a new angle leader prime, however, the gravity stays as constant. So in that case, we can turn the new cool in Force FC Prime in this case, equal and G times 10. Jane's fleet of prime. Okay, so this sequel 0.0 fourty five 26 notice. And this equal to the expression for the colon force over here. One over four pi astronauts. You want you to worry it's not. Q on Q two. In the case, it's simply a Q quit because the two bulls in this kid's carried the same kind of charge the same amount of charge and the separation in this case is too. L sign made a prime. Quit. Okay, so in this expression Ah, the only all new variable is this Q. We know l we know Peter Prime. So just plugging the vetting for Aaron of Prime, we can find out Cube. So I saw I got q equal, Thio one point 12 times 10 to the negative six quotes. Okay, so remember that the charge is conserved on the two bowls. So in that case, Q, we go to half off Q one o'clock. You, too. Right. So, uh, we know that the committee we know where we know that some that some charge of Q and Q two by using this compression. And we also know that the product of Q one Q too, so we can solve for Q on q two. So the final solution I got is, uh, I like beer. So cute boy is 1.8 times 10 to the negative seven cools. And the cue to is, uh, it's the rested er, er I don't have much room here. I just square to label This is the final solution. And the other one, Q two is, uh, 2.6 times 10 to the native six homes. Okay, there's a six. So these or the funding solutions okay,

In this problem we are asked what happens when two identical metal spheres touch and actually also with more than two touch. First were asked about the nut charge that charges. Just very simply we just have to objects you want to ask you to never asked what happens to that value when the two charges touch and the answer is nothing charge is conserved. It does not. If there is no way for it to get away from those two objects then whatever is there is always going to be there. So Q is conserved constant, just like momentum is conserved. Charge is conserved. The next question asked what happens to the actual individual cues? I'll call Q one and Q two prime proprietors on those. Well, it turns out very simply when they're identical and I'll take you through a simple situation in a moment. Q one prime which is after touching secret acute to prime is equal to half of the net. Each one has half share. There's a sherry and let's try to make this possible with any type of motion. Not going to go through the actual what happens in terms of how the charges set up for the forest. Is just to understand that there is such a thing when there is motion. You have to have when there it wasn't motion before you have to have force net force. So let's just look at a simple example. Say I have minus eight micro columns on the left and I hear plus five micro columns on the right just before they touch. This gives me Q two and this gives me Q. What? So if I were to use my little formula minus eight plus five Is my three divided by two is -1.5 and that's what we should get in the end. Okay now let's look at what happens to a net charge, a negative charge in the interface, whatever forces a few. Well from the charge on its left, it's going to feel proposal for us to the right. From the charges on its right. It's going to feel attractive force it right? So that is the right. So now give charges are going to move from left too. Right. So sometimes later we're going to have to pick up the scene where maybe -5 columns and move from left to right. So this leaves me with -3 still excess negative charge on the left And uh -5 have moved from left to right. So that means I have no access On the right. zero. Does't mean there aren't charges there. Everything just bounced very pluses. And minus. And so now is this the end? Because I have uh neutral material? No, because the negative charge sitting here will be feeling a repulsive force to the right. Still. So they can charge is still going to be moving from left to right. So as each negative charge moves from the left to right, I'm gonna be getting a lesser negative minus three to minus 2.71 However you want to think about it. And as those negatives move to the formally neutral area, I'm picking up negative. So if point minus one moved, so I'm gonna mayes too. And I got -1 on the right. And this process of motion will end when they are exactly the same again, this is for identical cheers, it's different if they're not the same size. So let's see what happens here. Why is it stop here. Seems reasonable. But why is it stop? You think of a negative charge sitting here in a negative charge here is going to feel repulsive force to the right from what is on his left, is going to be feeling a repulsive force from what is on his right. And that's to the left. So I think they balance out. So that's it. There's no more emotion at this point. So this is Q one Primes equalize 1.5 and this is cute to prime. So like I said, as eight Plus five divided by two is -1.5. And there you have that's a you know what happens if you once this part and part far enough away that they don't really influence each other. The charge left on these years will be uniformly distributed, but that's after they parted uh far enough away, that really one does not really affect the other to any great degree what goes on during this process. In terms of location and things like that. That's that's a different process process. This is really the dynamic process as you head towards the equilibrium condition. So that can be very complicated in general. If you don't have nice shaped objects. Now, for the next few problems, we're going to use A Q. A. As much as eight michael columns, Q. B. As much as two Micro Combs. You see It's five Micro Cool. Rome's plus in cuba G Is equal to plus 12 michael Collins and were asked in the first case what were the original charges? So we're given here, we don't know which ones we want but were given that in the end, this process gives me plus five and plus five. Now what adds up Divided by 2, 2 Plus five. Well mm u minus two microcredit loan Plus 12 micro colon Over two. That's 10 over to that is five. So that that means I'm going to use, I'm going to use it be Andy Now the next case is three of them. Still the same idea. So instead of half each, each one is going to get a third. So we don't know which three and our end results. He's going to be plus three in each case. Then we asked what will give that? Well, let's see -8 Micro columns which is a Plus five Micro columns which is C Plus 12 microcredit loans which is deep divided by three. This might say plus five is is three plus trial. It's 9, 9 divided by three is 3. So that's what we have. So this means this means we're going to use Q A. You see. And cue deep for part C. Prepared to see they want to know what would, how many electrons would I have to add to one of these fears to neutralize it to give zero that charge. So I need to add -3 Michael problems. So the number of electrons is going to be fine. Here is my charge, my street 10 amount of six cool lumps charge. So one of that trod one of that tried Yeah, Is -1.6 Times 10 to -19 Cool loans. And this works out to be 1.9 times 10- 13. 13 electrons. Mhm. And that is the whole product.

For Problem 76. They have to particular skill in Kyoto hanging on history, and they make an angle of data the length off the stream, the length off the string is 0.5 m. The masses 8 g data is 20 degrees. So for a we need to find the free body diagram off Cuban and U two. Let's start First week, Q. One. No que in here. Reach tension. The electrostatic force Is this data? Yeah. Do you like component attention? Yeah, the X component of tension for a Kyoto. They have It's freed. You can detention in the electrostatic force. Yeah. And also you have the y component of detention in the X component off the tension. So for being very to determine the electrostatic force and attention. So first, we Mr Let's take a look at Cuba. So if you take the submission forces vertical, she goes to zero. We will get that attention. Why is it was too. Wait. So we have tension times, the cosine of data. She questo Muslims gravity so we can solve no detention, which is a question. My stems. Gravity divided by a cause. Enough data. So we have the Mass. Times 9.81 Divided by D of course, enough 20 degrees. So he is equals to it won 35 times. Then he's toe the negative toe. Newton's well for the electrostatic force. We take the submission forces horizontal, she close to zero. So we are t X c cost. Oh, the electrostatic force. So we have d sign of data. She questo Director static First way. So we have the forest. He said it was too. 8.35 times 10 degrees to the negative, too. Sign off the degrees. Yeah, the electrostatic forces in questo don't find 86. Thanks. Then resto the negative through your plans first see what I can say about Cuban n Kyoto? So we know that the electrostatic force she quest Okay, Q one Q two divided by the distance, which is l and screaming. So they have 8.29 times 10. They still the negative name Cuban Kyoto, derided by 0.5 Screwed. So this one is equals to 2.86 tense then, based on the negative eight point. Thank you Rain. So I'm Kyoto. Yeah, divided by 0.5 scripts. So solving for Q. One times Kyoto we would get. This came from 3.72 times 10 is to be 13 Gordon Square and Friday we connect the two particles with the wire. So now they make an angle of 30 degrees. So the total church on the pair off the spirits ease conserve so we can start display. Uh, I creating the new church with q one plus two divided by two. And we know that this is our equation one and our equation toe. Mr Pesto, you don't hear too. She wears store three points. I wanted to what? Time stand. Restore the negative Working. This would be the second equation, but first we need toe Saudi Q. Let's take the summation. Forces vertical. She was toe zero. So we have tea costs and data. She questo mustangs. Gravity cause enough. 30 She was toe 8, 10 centuries to the negative. Three multiplied by 9 2081 which is 9.6 times their face to the nearly 15 times. And we take the summation versus forests on type. We now get the sign off data she posed toe director static first. So we have nine when she was six times tennis to the negative. To sign off. 30 is supposed to. Cute screw. Divided by the distance 0.5. Screwed key is 8.99 Instant. Restore the negative on so we can start to you here. So I'm being for Q, We would get 1.3. Thanks. Staying way still the negative six column. So substitute hit here 1.5. So we have two equations. Equation, one equation. Thing way. Conserve our Cuban and cute. So that's solved it here. So we have Cuban overkill. Last 3.72. Okay, Thanks, Tyne. Restore the negative 13 when I talk to you one, she was 212 times 10 resto the negative six. So you can for me quadratic equation from this you have Q one square reading Plato the last 3.72 times in the restore The negative 13. You make it great to my husband. 0.12 times 10 Restore the negative six you are So so I've been 31. We will get 2.6 times 10 is to the negative six. Follow on our Kyoto US 1.81 times. Then restore the negative seven column This is dancer for D


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