5

Two identical conducting spheres _ fixed lace attract each other with an ectrostatic force of 0.140 N when thei center-[0 center separation 59.2 cm_ The spheres ar...

Question

Two identical conducting spheres _ fixed lace attract each other with an ectrostatic force of 0.140 N when thei center-[0 center separation 59.2 cm_ The spheres are then connected by thin conducting wire. When the wire is removed the spheres repel each other with an electrostatic force of 0.0321 N. Of the initia cnarges on the spheres, with positive net charge, what was (a) the negative charge on one of them and (b) the positive charge on the other? (Assume the negative charge has smaller magni

Two identical conducting spheres _ fixed lace attract each other with an ectrostatic force of 0.140 N when thei center-[0 center separation 59.2 cm_ The spheres are then connected by thin conducting wire. When the wire is removed the spheres repel each other with an electrostatic force of 0.0321 N. Of the initia cnarges on the spheres, with positive net charge, what was (a) the negative charge on one of them and (b) the positive charge on the other? (Assume the negative charge has smaller magnitude_



Answers

Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of 0.108 $\mathrm{N}$ when
their center-to-center separation is 50.0 $\mathrm{cm} .$ The spheres are then
connected by a thin conducting wire. When the wire is removed, the spheres repel each other with an electrostatic force of 0.0360 $\mathrm{N}$ .
Of the initial charges on the spheres, with a positive net charge,
what was (a) the negative charge on one of them and (b) the positive charge on the other?

Question 95 states that two identical conducting spheres are separate by fixed centre dissenter distance of 35 centimeters and have different charges. Initially, this fears trunk each other with the force of 0.99 Newtons. The spheres are not affected by it. Then conducting wire after the wires removed the series of positively charged and repel one another with the force of 0.31 Mutants find the A the final and be the initial charges on this for years, So that's a scenario. Q. One A sphere wanted you to a sphere to. They're initially different charges. When they're connected by this wire, we will share their charge and the violent removed and they have the same charge. So the final part of this question Army exits the first part of question. But the final part of the scenario where the charges have to be equal begin simply find that using force to so then we know they're both positive, and they both repel that already repel each other, I should say so you know F two after their parents separated. We know that we can just represent this as a cooling constant times. Q. Squared again because they must have the same charge off a D squared. We can rearranged us to sell for each charge f d squared over K Square root. And so, using this 0.31 Newtons for F two R distance of 20.35 meters and her cool constant, we can find that the charge for each sphere to two significant figures in 6.5 times 10 to the negative seven event Newton's. That's correct. It's cool. It's a charge, of course, Polities that part B going to find the initial charges in this fear. So, um, we know that finally, they're both positive. But because you know, initially that these forces tracked based on the information you do, it's one has to positive, and one has to be negative. So that's nearly I'm gonna soon Q one positive in Q two is negative. Doesn't really matter which is which we just want. One is positive once Negative, right? Okay. But we do know this final charge that they have capital que has to be equivalent to the sum of the two charges, right? So I know that if I see humans positive so say Q one U minus. This time I'm saying, because Q two is negative, so and it is up has the equipment to twice what the next? What I mean twice the charge of the end up with because you can't create charge out of nowhere has to be. It's it's conserved. So the total charge of one plus the total trudging to has to equal two times the final charge. And because I'm calling Q two negative, who has used this scenario so that I can represent my solution for Q two, then consent be just be here one minus two times. Cute, too sort of two times. Q. So my expression for cool and force F one is K few one times you too divided by D squared. I can use this expression now to remove que Tu as one of my unknowns, because two unknowns in one equation, which is not useful to me. Second, remove one que times Q one que two isn't the Q one minus two times the total charge. Get over D squared. This is cute story. Do a little bit algebra. The squared I confined that I'm expression here. K Q one square minus two K que q. One. And if I note this expression, of course. Quadratic formula looking to solve for Q one so by But I never met you choose to use the sulfur quadratic formula. My personal use excel, whichever you again, whichever you choose, we can find to ah solution for Q one. I believe you kind of positive native solution you you can use either. I mean, you can use both of them honestly because it should produce the same values. But if you just choose one at one point, I need times 10 the native six. Coombs By using this relation here, I can solve for cute too, therefore to be native 6.81 times 10 to the native seven Cologne's. I guess there's also this should be the other results that you get from the previous solution of quadratic formula. So either you choose one and get the value or use both of them. So ultimately, this should be rounded to six figures as well, which I forgot to do. Apologies to speak to Micro Coombs for Q one and cue to would be negative. 0.69 My group Coombs. There you have it. So again, I arbitrarily decided kichi was negative. Nothing in the question told me that was true. So little You could just mean one of the charges was to Micro Coombs and the other charters. Negative 0.69 Micro Coombs such that we can arbitrarily choose which one belongs to which, but yeah, so there you

And the super problem, based on columns force between two charges is given by Cuban cute away. Our respect here it is given to his fears, each having the charge to yeah, so force between them with a K Q square, by our respect. So you can tell us. Have our square by Cape Force is given quite 03 to Newton. Distance between them is 145 Okay, is nine into 10 to the power nine. So it is 8.5 10 to the power minus seven cooler. This is the answer of a park. Now be part Force Ju is given by route of, uh What, square by a kid. Yeah, yeah, yeah. Now the distance between them becomes 135 forces quite Jiro driven, right? Mhm. So charge must be 6.5 10 2 departments. Seven cooler, That's all. Thanks for watching it.

There is a two historical conducting charges right And over here and they're identical administrators of this I've seen. So basically initially they are a distance of 2% were. Okay, so this distance between their center is 2%. That is 0.5 minutes. Okay. And yourself force between them is nothing. But it is five in uh definition that is uh 0.10 ok 0.10 to Newton. Okay. And final force that is nothing. But It is 0.0360 Europe when he was 3, 6 years your countries. So what were the initial studies on this? So basically now finally it is connected by the conducting wide. Okay. So in final case we know that they feel is going to be a conductive force and then removed. Then the Tardis on the board, the board surface will be a revolution because potential should be same. So they are identical. That will take you by art and to cuba so that when skates constant are the same Cuban should be equal to that. Finally the arrest of water spare is equal. That was cute square upon the square. This source has given you know point you know 160. Okay, so from here you can get that. Mm hmm. Okay. It's nothing about 910 to the power of nine into cuba square upon this cardi European types of 25 into 10 to the power of -2 equal to You want to 2016. Okay. Do you want to go? So we can get you squared equals two. We can have 0.0760 into 25. Independent managed to Upon 19- 29. Okay, so it will become our 9 11 And if you remove these 273.6 13 So there's only 3.6 Us choir will be 3.6 in 225 upon 9 20 to minus 30 or you can say 36 in 25.9 minus 14 Okay so that you will be I think what Do that to people during this one's okay 36 have (360) 944 400 So 100 means this makes 10 to the power of -412 so this will be 10 to the -6. Okay. No we know that in itself force between them is given that you get you want to for the square that is also given And that is because to your .1 Okay so do you point 10 old Newton now is nine and the power of nine upon this but still here for 25 to 20 farmers to Into Cuba into Q two Equal to you don't .10. Right So this will be one into Q2 Equal to 25 into this will be 108 into 20 of our monastery. And this to develop manage to Upon nine into 25 out of nine. So it will be 25 And it's a bit 12 times of 12 And took the to do bar- Highland -14. Okay, So Q one Q 2 will be and this one 2512 into tentative out of minus 14 Or rather we can say that it will be four times 303 into 10 to devour of -12. So the silver we know that the finals are this that you both of them. Have you charged with two plus two equals or nothing. But if you want to ask you to write that when Stewart mosquito took you, We also know that you one plus two equals took. That was 225 16. That so we can replace any time just by this much that you can write Cuban. You can do this much when a student. So Cuban 224 -6. And the minus of Q. Two sorry cuba equals two three into the power of to help. Right so no this will do anything. What? 2? Interdependent Pharmaceutics Q one -1 squared equal 3-2012. Right so we conducted as a few square. You wanna square one is to enter tentative ar minus 6 to 1 and plus of things that are much too well what do you know? So how you can the government three so we can get the plus three. We need to we need our hair. That is first three. Yeah. Yeah. So Cuban over here that we don't think on minus B minus with two into 26 Palace minus mu squared. So this is quite as in for instance, there must well And Minour of Policy 12 In the past 12 upon to it, so the Cuban and does not have any real value.

So and this problem. We're told we have two identical conducting spheres, and we know they're repelling each other at a certain distance, and then we connect them, and they're gonna probably each other the different force. And we want to know what was the original charge on each, um, spear. So let's write down the givens, and then we can discuss how to do the problem. So was called F the original forests F one. So that's point no. 50 new ends in the original distances 0.25 meters. Okay. And the, um, second forest is 0.60 And we want to get the original charge on each, um, spear. So what's right down? Let's sort of take this approach. Um, let's approach this with a Newtonian perspective. So, um, Miss double track something, um, you okay? And they're identical, which I suppose is important. So if there are identical spheres, I think they must have the same charge. Initially, let me pause and check that. Oh, I see. No, I cannot be the case because, um, otherwise connecting them would would not change the charge distribution. So originally have these two chart two balls And then, um, I'll call this one A and B And then you can say that the forest between A and B that's what we know is F one. So I'll call that one. Um, that's going to be equal to the charge on a comes a charge on B times K over r squared. And so we don't know what we don't know what these two are. We have this and we have this and you have this. So what this equation gives us is the product of Q and Q B. So we can kind of keep that in mind. Um, now they distribute their charge. So, um, let's say that afterwards, um, there's, uh They redistributed their charge. And now you have a charge Que a prime. Here. Thank you. Be prime. Um, and then we know that we know the forest is equal to force to. And then that's que a prime q b prime over r squared times K. And our goal is to get the I guess there goes to get Q and Q B s. So I'm gonna just take off this cube. Doesn't matter. Um s o the main idea. We want to use is charge, um, conservation. And actually, before I dive into that, let me make one more simplification. Since Q A prime and Q B prime are equal. Let's just say that Q prime. So it's followed the charge on each sphere afterwards. Q. Prime. And so now, since it's the same charge Oh, yeah, and then it would be the same charge because once they're connected, the electron, the excess charge, will spread out as much as possible, equally distributing over each sphere. So so now this is our formula for the force. Between the two charges, Um, are the two balls given that they each have a charge? Q Prime, and then this is the original force. And now we want to use charge contribution. So we want to say that like, you know, this total amount of charge is equal to the total amount of charge here, So the total monitored originally is Q A Plus Q B. And then the total of my charge finally is to Q prime. So we have this formula, this formula and this formula. So it's kind of three unknowns, three equations so waken solve for, um so we should be able to solve for all of our unknowns, I think, um so where should we begin? Let's I'm tempted to just seven for Q prime here from from here on out. It's an algebra problem, by the way, so you don't have to follow exactly what I dio. I think it's sometimes more challenging to follow somebody else's algebra than to just do your own, so you find it difficult. Maybe just try it on your own. Um, so anyway, so I'm gonna sub in for Q prime. That's que a plus q b squared. And then we're gonna be also scoring this four. So four r squared and then you have this K. And, uh, I think our must a note on our I guess there's only one are there couldn't be multiple. Ours were. Also, I think this problem wouldn't make sense, so let's just assume our stays the same. Um, so now we have this equation in Lao. Let's sub for cute. A Let's say, um so que a from this equation is equal Teoh. But in terms of you being able summit in here, so cue a is equal. Teoh F one r squared, divided by you be times K. Um, maybe a little messy because it is squared. That's all right. Um okay, so now we'll stop this in here. Um, for Q A. So I'm gonna come over here just to continue this line. So cue A, we know is f one r squared plus Q b. It's over, Hubie Times K. And then that's plus Q b. This is looking messy into the units. I guess the units let me just check that they work out at first, word would be Okay, Well, hopefully get simply, This is are you looking a little messy? So at two is equal to this divided by four r squared. And then now we just have a nosh. The equation for Q B so we can solve it. Um, so let's bring this four r squared over so that we have four r squared up to divided by K is equal to this whole thing. And let's just take a square root while we're doing so. We're square rooting this square with this, and then we can say that's equal to F one r squared over Q b. Okay, plus cube be, um and yeah, so Let's see what's next up. I guess we can put, um, these under one denominator. So this I need to multiply by Q b k to keep it the original Q B. And now we can move the by both sides by q b. K. So then you have Q b k. Wow, what a mess this problem turned out to be. I really don't see any other way, But I am a little surprised It all the algebra All right, So bring not over there than f one r squared plus k q b squared. I'm just, like, really curious if the units work out here. So Forest Times this I guess that is gonna be cake, you square. Yeah, these two definitely have the same units. All right, I was really hoping something would cancel. Um, and we can bring this to the other side and we'll have a quadratic that we could just put in the quadratic formula. So f one r squared plus okay, Q B minus. Que que he be que screw of four r squared up to over. Okay, Um, okay, so now we have the quadratic formula. This is quadratic and Hubie. Oh, Yeah. Oops! And forgot this Q b squared. So those are these air are cowfish ships, books. This whole thing is a coefficient. So then we will get the Q b equals, Um, so we'll do negative Mrs are beat like for quadratic is a X squared plus B x plus c and then exes are Q b, you know, then B is gonna be the this coefficient. So, um so negative. This Yeah, I'm just using the quadratic formula. If it's not clear, so negative b, there's gonna be plus or minus the square root of B squared. So this thing squared so K squared for R squared F two over K. It's a little simplification minus four times a is K and then see is up one r squared. And then this whole thing is divided by two times a and in a, it's just K. Okay, let's simplify this a bit. So those K cancels with this K and, um Oh, that's nice. Then you can, um, then you just have to minus You can take out a four k. So let's go ahead and do that. Oops. And then why did I write Cavey here? So I should be negative BSO. It's just negative. Okay. Negative of this. Which at which I wrote, um And then, actually, So Kate of the first divided by Kato, the 1/2 is, uh, Kate of the 1/2 so that I can take this and simplify it and put a k here. Um, yeah, I'm to know yesterday and algebra. And now I'm seeing why it's so important to be able to do these manipulations. Um, some of these problems could be really thorny when it comes to doing them. Um, for R squared up to k or actually weaken. Yeah, whatever. I'm just gonna leave that. I think of doing too many simplifications. Might get confusing. Um, And then so the Adami of the Square root And then week again, we can take out a four r squared k from both terms, and then we have up to minus up one, and then that's divided by two K. Well, this from is really getting long. Um, yeah, I guess we can just Well, we can take out a k from both and then bring it down here and then make that square rooted square rooted K. And then we can take out, take the are and put it on the outside. Um, and that makes it are the first power. And then so we can multiply this whole thing by our and then I honest to I guess you can also dio So we have a two are No, This is really not that bad. I like it when these problems, like, really clean up. Um all right. And then this to cancels with this, too. So I'm cancelling. I'm just gonna castle it. So goodbye. This too good by this to and yeah, now we can plug everything into a calculator, so I pull out my calculator, so I want to do negative square root of two with prank. I go 60 Um, And then let's do the plus, um, first, plus the square root of f to myself one. So that's, um, 0.1 Now for that one. Yeah, that's why no one. All right, point of one. And then we want to take that whole paying in parentheses and multiply it by our It was just point to five, and then we wanted to buy that by the square root of of, um Que? Que is nine times 10 to the nine. So let's see what I get for that. I got, um, negative. 3.8 times 10 to the minus seven. And I'm just gonna write down both solutions and then think about which one to pick after. So that was the, um, plus solution. Let's do the minus the minuses. Negative. 9.9 Right? Right. Um and this isn't cruel ums. At least I'm getting numbers that are pretty similar to another numbers I've seen. I am. So I'm not using the right number six eggs. Three point. I'm just confused situation of threes with three pointing to okay with our Q b. And then is it okay and then let's go back to this formula here. Cuba is F one. You re right. It f one r squared, divided by Q b K. Um, and so we can get Q and either case so. So if we want to do like, 05 f one times 25.25 right, divided by Q b. So negative 3.2 times 10 B minus seven times nine times 10 to the nine. And then I get negative. 9.90 nice. So you can kind of see that the two results corresponds to, um, the fact that you can have, like, you can have ah thing. And the Q b can have Think the other thing and then or you can, like, swap the properties. I feel like that did not make sense. So I'm just going to write this out until it becomes clear. Um, s O 1.9 times two minus seven cools. Yeah, So you can see. And then I'm guessing, if I calculate by plug in this for Q B, they'll get this for Q A. So then this would be This is the original pair of charges. So Q and Q B is sort of general. So then I'll say that the two possible charges are this and this, and then I suppose they could be positive as well. I'm kind of wondering why I got negative charges. If there is some assumption that I made, um, I'm not sure, but I do stand by the math that I did. So I was already getting pretty long, so I think I'm just gonna end it here


Similar Solved Questions

5 answers
Forni rbrc rcmindcr An Wllustrative fgure, including coordinate 3y3cm orc i3 necded 3olution ornc problem Frcc body diagram DccdedTor thc problem Lawa incorcma wrrtcnIn gcncral forn labcked with thcir ramca thc timc / location thcir firat ua8 such staT of 3oluton Solution for unknown in symbola Numbcrs may orly appcar in minimum numbcr of linca aucn 93 9al onc linc rcagoning; Doxcd Adaucr with units
Forni rbrc rcmindcr An Wllustrative fgure, including coordinate 3y3cm orc i3 necded 3olution ornc problem Frcc body diagram DccdedTor thc problem Lawa incorcma wrrtcnIn gcncral forn labcked with thcir ramca thc timc / location thcir firat ua8 such staT of 3oluton Solution for unknown in symbola Numb...
5 answers
Point) Suppose g is a function which has continuous derivatives, and that g(7) = 4,g (7) = -3, g" (7) = 3,g" (7) = -5_(a) What is the Taylor polynomial of degree 2 for g near 72 Pz(x)(b) What is the Taylor polynomial of degree 3 for g near 7? P3(x)(c) Use the two polynomials that you found in parts (a) and (b) to approximate g(6.9) . With Pz, 8(6.9) With P3, 8(6.9)
point) Suppose g is a function which has continuous derivatives, and that g(7) = 4,g (7) = -3, g" (7) = 3,g" (7) = -5_ (a) What is the Taylor polynomial of degree 2 for g near 72 Pz(x) (b) What is the Taylor polynomial of degree 3 for g near 7? P3(x) (c) Use the two polynomials that you fo...
5 answers
2 3 ill 8 1 8 ; 1 1 U | 2 1 8 1 I 1 2 1 1 1 1 1 2 1 8 1 1 1 1 1 1 8 :
2 3 ill 8 1 8 ; 1 1 U | 2 1 8 1 I 1 2 1 1 1 1 1 2 1 8 1 1 1 1 1 1 8 :...
5 answers
What is the major organic product obtained from the following reaction?CHSHScOHpyridineCHs
What is the major organic product obtained from the following reaction? CHS HSc OH pyridine CHs...
5 answers
1 1scribes 2aimnalion 20 paral lelogramA 3
1 1 scribes 2 aimnalion 2 0 paral lelogramA 3...
5 answers
PolnuFind tha Ilmit . Use | Hospltal s Aule [ appropriato Iiz E+)
polnu Find tha Ilmit . Use | Hospltal s Aule [ appropriato Iiz E+)...
5 answers
Hcdicu dcviccs implintedthe bodyncrgy average injuced emtFtet)Winc @= Onuroeneclosciy Goucccemf i> gencrated Ailcana calvanes (roncoilinsiccvannnaoumcnt throuj ncunj Medini= Recal(roi TocitQUEdJcUt; producingmaqneltuz € alculaleTaelunnFanisulngenlIrmazimthat tne muonctic fieldcenter of the curennt-camanj extemul coilAGsume this mjanctic fieldconstuneofLrintcrior coil g Jre_orentcd penpendiculjrintemal coil )Hc
Hcdicu dcviccs implinted the body ncrgy average injuced emt Ftet) Winc @= Onuroene closciy Gouccc emf i> gencrated Ailcana calvanes (ron coilinsicc vannna oumcnt throuj ncunj Medini= Recal(roi Tocit QUEd JcUt; producing maqneltuz € alculale Taelunn Fanis ulngenlIr mazim that tne muonctic f...
5 answers
Problem 01 Integration by Parts [10 points] Use the technique of integration by parts to evaluate the following integrals. To gain full credit, you must define the individual parts [u; dut, dv, and vl; show the filled-in uv vdu; show your calculation steps to support your initial answer, and then your final answer reduced to lowest terms: x+1 8x ln3xdx b) a) eix-dx
Problem 01 Integration by Parts [10 points] Use the technique of integration by parts to evaluate the following integrals. To gain full credit, you must define the individual parts [u; dut, dv, and vl; show the filled-in uv vdu; show your calculation steps to support your initial answer, and then yo...
1 answers
Sigma Notation Write the sum without using sigma notation. $$ \sum_{j=1}^{n}(-1)^{j+1} x^{j} $$
Sigma Notation Write the sum without using sigma notation. $$ \sum_{j=1}^{n}(-1)^{j+1} x^{j} $$...
1 answers
In Exercises $25-28$ , the terminal side of $\theta$ lies on the given line in the specified quadrant. Find the values of the six trigonometric functions of $\theta$ by finding a point on the line. $$ 4 x+3 y=0 \quad \mathrm{IV} $$
In Exercises $25-28$ , the terminal side of $\theta$ lies on the given line in the specified quadrant. Find the values of the six trigonometric functions of $\theta$ by finding a point on the line. $$ 4 x+3 y=0 \quad \mathrm{IV} $$...
5 answers
A public transportation bus makes the position-time graph oiet (0 h intctval shown. Thete arc four SCgTeis the total tTip: What is the average velocity (magnitude and direction) of thc bus during illervuls Jnd 4J5/( *10'xIo'Uuxratl
A public transportation bus makes the position-time graph oiet (0 h intctval shown. Thete arc four SCgTeis the total tTip: What is the average velocity (magnitude and direction) of thc bus during illervuls Jnd 4 J5/ ( *10' xIo' Uuxratl...
5 answers
Consider the sides and ratio given belowA) b ~ 25.981B) b ~ 8.661 D) h ~ 17.321C) b ~ 9.527E) h ~ 30F) h ~ 16.455G) not enough informationH) none of these0.5
consider the sides and ratio given below A) b ~ 25.981 B) b ~ 8.661 D) h ~ 17.321 C) b ~ 9.527 E) h ~ 30 F) h ~ 16.455 G) not enough information H) none of these 0.5...
5 answers
D Question 2Check all of the examples below that are equal to 1 mole at STP:58.93 g copper22.4 L methane38.99 g of sodium oxide6.022*1023 Ne atoms
D Question 2 Check all of the examples below that are equal to 1 mole at STP: 58.93 g copper 22.4 L methane 38.99 g of sodium oxide 6.022*1023 Ne atoms...
5 answers
A) By dividing the range into ten equal parts, we can evaluateWhat will the formulae for evaluating the above integral be if andindicate the assumption you made before choosing this formulaAN[6
a) By dividing the range into ten equal parts, we can evaluate What will the formulae for evaluating the above integral be if and indicate the assumption you made before choosing this formula AN[6...
4 answers
Consider the vector field F(x, Y, 2) = (~Zye* , Sxz, yZ) . Find curl F and div Fcurl Fdiv F
Consider the vector field F(x, Y, 2) = (~Zye* , Sxz, yZ) . Find curl F and div F curl F div F...
5 answers
Given the equalion Y In (4+y*+4) =9, evaluate Assume that the equation implicitly dofinesdifferentiable function of x.
Given the equalion Y In (4+y*+4) =9, evaluate Assume that the equation implicitly dofines differentiable function of x....

-- 0.022678--