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Chapter 24, Problem 057Your answer is partially correct: Try again.Identical 41 HC charges are fixed on an axis atx = +2.8 m_ particle of charge 16 pC is then relea...

Question

Chapter 24, Problem 057Your answer is partially correct: Try again.Identical 41 HC charges are fixed on an axis atx = +2.8 m_ particle of charge 16 pC is then released from rest at point on the positive part of the axis Due to the symmetry of the situation; the particle moves along the y axis and has kinetic energy 1.4 passes through the point x Y = 4.5 m (a) What is the kinetic energy of the particle as it passes through the origin? (b) At what negative value of will the particle momentarily st

Chapter 24, Problem 057 Your answer is partially correct: Try again. Identical 41 HC charges are fixed on an axis atx = +2.8 m_ particle of charge 16 pC is then released from rest at point on the positive part of the axis Due to the symmetry of the situation; the particle moves along the y axis and has kinetic energy 1.4 passes through the point x Y = 4.5 m (a) What is the kinetic energy of the particle as it passes through the origin? (b) At what negative value of will the particle momentarily stop? (a) Number 3.39 Units (b) Number -13.68 Units



Answers

Identical 50$\mu \mathrm{C}$ charges are fixed on an $x$ axis at
$x=\pm 3.0 \mathrm{m} .$ A particle of charge $q=-15 \mu \mathrm{C}$ is then released from
rest at a point on the positive part of the $y$ axis. Due to the symme-
try of the situation, the particle moves along the $y$ axis and has ki-
netic energy 1.2 $\mathrm{J}$ as it passes through the point $x=0, y=4.0 \mathrm{m} .$
(a) What is the kinetic energy of the particle as it passes through
the origin? (b) At what negative value of $y$ will the particle momentarily stop?

Hello and welcome to this video solution of numerous here let's say. We have got to charges Q. Nature position that X plus minus X comma zero along the X axis. We take two charges Q. Each of them charged Q. Right now we have the potential at the At the zero comma Y. Where another charges there is given us the equal. Doing direct you to just say so we have to take a summer both. So two times off. You know what? Well by excellent. Not the distance between this. So let me go a simple diagram. So here we have a charge At -6 and classics and there is another judge here let's say. So we calculate the potential at the green charge. So the distances this right? This distance is equal to due to what off X squared last week of school. Right? So this is the potential due to the two charges Q. Or at a point on the Y axis which is active distance away from the center. Next we calculate the potential energy of it. Right? The potential energy you will be equal to um hmm Due to the charge placed at zero. So does this judge you Now. Here we have this equal to two Q. Small cube. Well what for pipes and and not group of world X squared. That's why it's great. Right. There's a potential energy. We we got next year to calculate the final kinetic and the rate of the system of motion. So here we can say. And I think energy initial plus potential energy initially will be equal to kinetic energy, final last potential in a different and great. So here we have kinetic energy final equal to initial kinetic energy. Plus you were in my industry. No initial grind again. The job. The first charge is given us. Okay, that is already given us. Okay, let me write down here for the time being last. Yeah, we have E Y minus you will fade. So for that let me write down to Q. Who? What for pipes? And we have got distances like one bite X square plus why I squared because why is only reliable. And here we have the root of our off X square plus. Why? Yes square. If you're plugging all these values. So here we have, let me plug in the values Here is equal to 1.2 plus. Uh two times of if the Thanks to the four of -6 Here we have -15 things can go wrong minus six and we have four by thanks 8.85 times tend to the door of minus well. And here we will have one by one of three squared. That's fourth grade And has won by three sq 3 square. And if you calculate the complete things will get the kinetic energy of this particular call the three jewels. Yeah. There's a solution to party. There's a second part B here. You have to calculate that. At what negative value of why will the particle momentarily stop? So when the particle stop the final kinetic energy will be zero rate. It will be equal to zero. This means we applied the same expression out here. Yeah. Mhm. U. F. Will be equal to K. U. F. Will be equal to. Okay, I love you. Bye. Now. We write down the expression of the final uh potential which is too cute. You Over four by excellent north route over over X squared. Bless. Why? Why? You have squared? And here we have 1.2 plus new. I will be called to took you. Mhm. Over 45 That's alan not rude to ward off X squared plus white I squared. All right. Actually. Why? Yes, but what you expect now we all know all these terms. We have played the same expression here like this before and here. We will have to calculate the Y. F. So here we'll have Y. F equal to -8.5. He does right. I hope this is clear to you and have a very good thank you.

For port A. The potential at the point of diagram V equals K one Q one over our one plus Que two que two over our two citified. Since about charges are symmetric and equal. Two times K comes constant times. Q. Over our distances separation caring is symmetrical, so we plug in the values V Eagles to times Combs Constant, eight point 99 times 10 tonight Newton We're squared Proclaim square times the charges, which is 2.0 times 10 26 Coombs tend to negative. Six cools Small charges. That's your new rail. Then you divided by for persecuted therm reference referencing a diagram sort of distances. Separation for each one will be a square root one meter squared plus 0.5 readers Square adam up square Root it and then you get a potential I see equals three point to to times 10 26 faults that is party part B. Potential energy equals Q tons of voltage Q. B. So it plug in the values in negative three times 10 to make of six. Coombs multiplied by the potential that we found three point to to times 10 to 6 vaults or Jules per cool, and that gives us a value of negatives. Nine point 65 times 10 10 A second Jules for the potential energy.

So here is a problem. So this problem says figured 21 31 chose an arrangement of four charged particles with an angle theater 30 I think 30 points predicted. And Distance d. is two cm. Okay so particle to has charged you do. Right so we can right here this is practical to has charged cure to here That is eight 00 into 20 power -19. So part because three and 4 head charges Q. three and Q. For you. Okay, in this problem we can see you. So now what is the distance it is us That what is the distance deep between origin? This is origin. Right okay. So this is basically deep from the origin. Great. And particle to and particle too. If the net electrostatic force on particle 1 to 2 other particles is jane. So if uh this condition is given to us. And secondly, if the particles three and four are well moved closer to the x axis but maintained their symmetry about that access what they required value of they will be greater than less than or same as in part it. So we've been seeing here how this solution is done. So here we know in triangle abc that is supposed this is the drawn figures. We have. So in triangle abc we are supposing here that this is a right and veterans so entangled abc the R. Three R. Three. Where is artery here is the artery of charged particles three from particle one is equal to A B. Right? So can we say that this is a hybrid news? Yes. So a B is a hyper museum in the triangle. Abc. Now he sees a This inside this is a this inside and whose distances d. We have already discussed it in question that this is deep. Right? So this is from deep this like this is this dude. Okay, so now this is 2.00 cm. And given in the question now we are converting written meters. So in meters it will be 0.20 m. Now fast eater is hurt based upon high powered ministry. So here's basis in writing the trend basis. The here you can say A C. Right and hypothesis nothing. But this is A P. We have already discussed. So it will be A C. Will be 0.20 upon our three. And hypothesis given by distance are three, write A B. Is given by three years. Right? No. Now the angle between it is 1:32 30. No. So what else is left? We are calculating here from this Pastika formula we are calculating are three. So we called the distance are three. That is high partners of china, A. B. C. Simply. No, Here we can see our three equals two are proof. Right? So these are equally distinct. Right? So it must be the angle is same for it. So that's why we can say This is a three was to our food. Okay Equals 2.0. What we want. No. E three is electric field by particle three at location of particles what four? A tree this is a tree Straight from 1-3. Judge particles john you can see so this is bike Particles three at location of particles one The electric feelings and didn't at this E three. So now it really is given by nothing but KQ three by our three square right? This is this we know okay is a constant and r is the distance between Particle one in 3. Okay So here we will put simply over Luke is a constant. So this is given very 19-20 power nine in Duqu virus you can say this is only the charge, this is this is showing negative thing is only showing the nature of the charge. That's it. That is Negative in nature that is negative charge. Right? So Q three is negative. You guilty? So this is my iris. 1.6 into 10 to the power minus 19 Fulham divided by route over a route three whole ball 75 Polls. If I were writing here, we have already called calculated zero 231 but this was in traction for informed, it was like this. So we are calculating because to find in the accurate way so now E three equals to a food. We know that why? Because this distance is same angrily same and they hold the similar triangles are there. Right? So we can say E three. That is Due to Particle one. You can see electric field will be what eatery and the same electrical will be generated to the distance for that is E electric bill. If war is invaded. So now we can say Italy equals two equal. Yes. So here the value comes out to be after calculating this, we will just solve the situation. This is a normal formula for the electric field. Right. KQ three divided by Artery Square area. Okay, so this will be E three equals 2. E four equals 2.7 into 24 -6 years. No, If Italy equals two. E 4 then we can say X three and white components of both will be Equal respective. Right? So here E three by an equal by components are equal and opposite in direction. Hence cancel out each other. So here we can see the three by in Diagram. Italy way and evil why are equal and opposite to it easily if the cancer's eat other. Okay, now the X component of E port, it wants to move what X components for the uh check field. You can say Italy and the four will be equal. We have discussed the book, so it will be what a component of the force simplification. See So so X component is calculated by what this is. E four in the diagram. So the teacher is made uh two days meets the x component for the record. E four cost. So post tita is given that is tita is 30.0. So we will calculate for it. Finally we will be getting the component E three X plus E three X equals two. E four X. It was true. 2.34 in protective cover -6 Newton. Now, are you in the distance Of Charge Q 2? Are you see distance of charge Q two From the Location Cuban? Yes. So this is us two can be right here. Yes, we can. Right here are four. Let us see here it is are too R two is nothing but we are writing you are you is nothing but the plastic. Can we say this? Yes. So this is our two S. D. This is D. And this is the capital D. So D plus D. It makes now where they're moving We will get the if we already know from the origin. The distances what .020 m. We have already discuss devil. That this isn't meter. This is given to us. Right? 20 cent centimeter you can say sorry. I'm really sorry point you can say yes to two centimeters. Right, Okay. So here it is. What is All right? So here 0.20 plus D. Is that we know not. So we need to find it out. So it too is what Tito is electric field by charge Q two at the location of cuba. So we can say cake. You too upon our two square. So r. Is the distance from charge 12 you Right? So for the net force to be zero on particle one. Net electric field at the location of particle one must be zero. Yes. So net electric field at location particle one must be zero. So what could be done? This is E three X plus E correct should be equal to This implies that it was two E 2. Okay, can we say this? Yes. Yeah, no E two is nothing but this becomes two times because it creates a close to equal rates. These both are actually equal. Yeah, no we've been sold for it. So it will be no cake you to buy our two squad again we will put the values Q2 is given to us are too is given to us and we need to find capital D. Here. So this will come out to be after solving the situation. We will get deep words to nothing but point 0192 m. Now we can say in cm it will be 1.9 cm. So this is how we solve this problem. And for the part two For the part two we can say as the particle three and 4 are moved closer to the original right? As particles three and who are past. You can say moved closer to the reason. Right? So for this, the distance of the particle One from each other from east particle three and 4 builders degrees right? So the distance is decreasing here. Right? So the electric field by each particle three and 4 at location Of Particle one will increase. One will increase. Yes because distances just freezing. Right distance is the reason. This distance is different. So if you let me tell you this is like this, let us say this is moving forward here and this particular is moving forward here. So the distance between them, you can say this is decreasing right? Yes, because high foot news is decreasing. So this means that electric field yes, increasing as practical ones. Okay, so to make the net electric queen zero at the origin we want the net electric field at the original zero. So the electric field by particle too must be but must also be increased so that it can sense the net electric field by electric bill. Net electric field by Article three. And so to decrease the electric field by particle to this particle too. The distance of the particle too from the region must decrease. Right? So let us write this. We got to understand, we understood that how to solve this problem. Yeah, so as a discussion so ask for discussion, we can say that after this, We can include that 2° electric field by particle to the distance of the particle to from the original must decrees so this is and this is part a and we have discussed this, in fact, the I hope you understood the concept. Thank you.

In this question. We have four charged particles 123 and four and then, uh, place in this manner. And then, uh, article one. Is that the sense the at the left of the origin, how they go to is, uh, descends Big D right. The origin and train for is placed equidistant from the Y axis. Okay, And then we are given that, uh, Q two Q two is It is positively charged. It times 10 to the negative 19 columns Q. Thank you for their negatively charged negative. 1.6 times 10 to the negative 19 columns. Okay, so we want to price in this in this question, we need to find the distance Big d between the origin and particular to if the net electrostatic falls on one due to the other three. Party girls are zero. Okay, 80 Then be just to find out what happens to the big D equestrian for move closer to the X axis. Okay. Okay. So, um, to solve this problem, okay, Clearly is about columns law. Okay, so the first thing we need to write down columns law have equals two. Okay. 21 to 2. Divide by our square. Okay. And then, um, so we want to make sure that the net falls on article 10 So, um, we can just suppose Particle one is positively charged and they were just self recording me. Okay, So the electric force on one by two we're moving into the left, uh, f by two on one. Okay. And then the electric falls by parliamentary re pointing in this direction. Yeah, everyone. And then you have a full one. Okay, So since are the girls three and four, uh, symmetrical equidistant please me from article one, and by symmetry, uh, the vertical components. What off? Ah, F 31 and f for one pence out. Yeah. Okay. And so, uh, from the oh, from the free body diagram of, uh, how to go on. Yeah. Take right to be the positive. All right. And so we have, um, have 31 present data. Plus at +41 present. Data minus 21 equals to zero. Uh huh. King. Then our. So what we have here is, uh, so since after he won F one are the same. So we have two k Q one Q three day bye Bye. Mhm. Yes, We need a distance. So are one tree where and present data. And is he going to K Q one Q two day. Bye bye. You speak Be square. Okay, so Q one can cancel. Okay. Can be. And so and they really they really need to go back to the program. So this is our our one tree. Okay, So and we have our one tree, cause I data is equal to D. Yeah. So one dream is the over side data. Okay. Okay. So you have to you tree you. Bye bye. You're a science data square. Their data is he Go to you too. Bye bye. Small deed has been be square. Okay, so we can actually substitute, uh, many two of q three and q two in this case. So, uh, and if you come here, you see that the in terms of money to Q two is five times a Q tree. Okay, so we can actually just right like this, uh, to Hussein Cube, 30 degrees, divided by the square. Does he go to Hi, guys. You. Bye. Bye. You play. Speak. Be square. Yeah. So you have to, uh this is what we can do. So class B d divided by D square, is equal to If I were to resign Cube 30 degrees, then, uh, one class B was small. D is the patrol five over to thank you. 30 degrees square it there. Yes, yes. Small. The parents I two whose I Q 30 degrees, Great route minus one. Okay. And then you substitute the s two cm two and then using a calculator, you get 1.92 cm. Okay. Okay. So this is the answer for part a Then in part, B, uh, particulates tree and four move closer to the x axis. So the situation looks like this. He now the she and for closer and then one is here, too, is here. Okay, So the question now becomes what happens to be D uh, yes. Particle one needs to have zero. That's for us. So, based on the diagram, you can tell that, um um, the horizontal component due to F one tree and 14 Well, actually, one Sorry. Kft one and 41 Okay, it increases. So to counter the uh huh to counter there to counter their, uh, also there to the right. Then we need D to be closer to the origin. Okay. So that cancer can cancel the horizontal components due to F one and F for one. Okay, so the answer Yes, less than okay, Because the heart is on the components. Uh, actually one. Mm hmm. For one increases as she and four, of course. Ah, to the X axis. Eight. So? So for after one to increase a D needs to decrease. Okay, so that's the reason why I should be. That's then. Okay. And that's all for this question.


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