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QUESTION 24Beinix3040 AnsicrConsider the Eroup ci threa +2.,4nC poin: chargee shown in the iigure: what = ihe elctric potentlel energy ol this syelem ol charges rel...

Question

QUESTION 24Beinix3040 AnsicrConsider the Eroup ci threa +2.,4nC poin: chargee shown in the iigure: what = ihe elctric potentlel energy ol this syelem ol charges relative Io inlinity? ( = I/anco * 108 N.mic?)3.0 cm40 cm4.7* 10-6) 4.3* 10-6) 4.5 * 10-6/ 4.1*10-6

QUESTION 24 Beinix 3040 Ansicr Consider the Eroup ci threa +2.,4nC poin: chargee shown in the iigure: what = ihe elctric potentlel energy ol this syelem ol charges relative Io inlinity? ( = I/anco * 108 N.mic?) 3.0 cm 40 cm 4.7* 10-6) 4.3* 10-6) 4.5 * 10-6/ 4.1*10-6



Answers

Three charges lie on the $x$ axis. Charge q1=+2.20 \muC $q_{1}=+2.20 \mu \mathrm{C}$ is at $\mathrm{x}=-30.0 \mathrm{~cm}^{x}=-30.0 \mathrm{~cm}$, charge $\mathrm{q} 2=-3.10 \mu \mathrm{C}^{q_{2}}=-3.10 \mu \mathrm{C}$ is at the origin, and charge $\mathrm{q} 3=+1.70 \mu \mathrm{C}^{q_{3}}=+1.70 \mu \mathrm{C}$ is at $\mathrm{x}=25.0 \mathrm{~cm} x=25.0 \mathrm{~cm} .$ Calculate the potential energy of the system of charges. Example $17-3$

Mhm. Find a girl. So for his problem we need to calculate the electric field at a point P. That we are going to copy in this case these the point in red that is cows by a long, uniformly charged threat that is along the s assets and a small charges fear Q. Which is in here. No to do this. We are going to some the contribution Or the Paterson of the two fields um that is produced by both of these um charges. So in this, since we will have that then the threat is positive. That we will have an electric field only in the why a company because um it is an infinite threat. So all of the X. Component of the electric field counselors shorter. And we will only have um vertical company. So this is the, that would feel cowed by the threat and the electric field because of the charge to it will be attractive and it will be in the line that connects this to the charge and the point B. And this is the electric field produced by the charge you. So with this in mind, we just simply need to write first what are the electric fuel and produced by a line? Uh uh yes. A chart uniformly threat. And um pulling charge too self or a threat. We will have that the electric field is the following. We have this turn And also the linear density over the distance to that point ping that we in this case we know that distance is seven cm. That's why the distance. And it only has the company and a white company. So it is home in that direction we said it positive because it is pointing upward. And for the case of the charge it is something a little more um complicated but we could see in the figure and this is also given in the figure that this is the uncle that we are given. This is the angle tita. And so to obtain the electric field produced by a charge cube in that point it will be the usual the usual electric field produced by a point charge which is this over the distance the a square. This is the distance from cuba to the point P. And the direction of this is given by we can see in here that this um this bet tour if we translated to the access it will be like something like this. So we will have that both companies are negative. So then um at the company is given by the cosine of teeter in the X component and the Y component by the sign of tita. Yeah. So with this too weakness we can obtain the net electric field cows by these two charges. So the net electric field is the son of electric field because of the threat and the electric field produced by the charge Q. So we will see here that weakens some company with companies. So we will have for the that's component. This following minus cosine of theta in the white part plus in the white power we will have something a little more. Let me writing here it will be something like this one. Over to pine absolute zero London over why minus white company of the that you feel produced by the charge Q. And this sign of tetum and all of this in the company in the white confidence. So once we have said this we can first obtain the distance. The so the distance the we can see in the trigger it will be it will be this distance in here. It's like it's like the hi pot anus of these um of the strangles. So it will be the square root or well in this case because we need the D A square. We we can we just obtain that. So it will be zero point 07 m square disease. Seven centimetres in meters plus we can see in here that this side is five centimeters lost. Seven centimetres. That's 12 centimeters. That in m is 0.12 m. So that's what we have in here square. So if we assume this to going to put this right in here so We will have 0.07 m squared plus 0.12 meters square. So these will give us 0.01 93 m sq. Another thing that we can calculate is the angle tita and from the figure we can see that we can obtain that using the function to detention function. So the angle is given by tangent of minus want Kind of -1 the hi protagonist over the it's company So well in this sense. Well hypotheses now at the like let me put the figure out again. It would be it will be the the vertical side of these um of this triangle and the horizontal side of this ankle. So it will be as usual the angle is the white part of that distance over the ex parte or the X company of that distance. So it will be 12 centimeters over seven centimetres. And putting this into the calculator. We obtain a poly off right 59.7 Greece. Now we have this um we can substitute we can substitute for each component to make it easier. We're going to do each company. Each component supported lee. So are you gonna get first the X company of the net electric field. So that in here the previous expression we know that this is only this turn in here so it will be minus the magnitude of the charge. Q magazine of data that we just already obtained Or Pie Excellence zero D square. And this is we know that the charge. Well, we know that this turning here the the inverse of thought is nine Times 10 to deny it meters per meter square over column square were also given the the charge to which is let me just say it again, it is -2Q. But in this case we need just the magnitude. So that will be two Colom's cosine of 59.7 over The square that we have calculated, it is 0.0193 meters um square. Sorry. So this give us a value for the X component of the electric field of minus four point It's 99 times 10 two. 11. Newton's her colon. No, we need to obtain the white company of this. That electric fuel. And that is this term here. I mean it is just this term in here. Um that will be using here to make it easy. Yeah. So let me move this to here. And this is what we need to calculate in here. You know like thing here. Um So we know all of this and this is Mhm. Two times the the columns constant Times the given value for the linear density which is 2.5 Coghlan's through. Meet her also. We are given the distance which is Yeah, That is since why we know that is seven cm. So it's 0.07 m mm And for the other term we will have minus two columns over the distance to that point. Also the columns constant with his nine point times 10 to deny newtons per meter square overseas. Where and The distance to the point which is 0.0 193 m square. And this time sign of 59.7°. So putting this into the calculator, we obtain a volley off minus one point States 22 times 10-11 Newton's park alone. So putting all this into the these two values that we just have a team into the, into the equation for the net electric field. We will have something like this of like the Netherlands revealed is just details company in the Y direction, in the X direction and the white company in the Y direction. So it will be minus or point seven times 10-11. New tubes per second in the wide ripped in the M adds disruption plus minus 1.6 times 10 to the 11 mittens. Para cologne in the white company. And if we want to determine the magnitude and the direction of this back toward this net back or we just simply need to obtain the magnitude of this bad car. And after that, the angle. So it will be like the the square root of the company square plus the excuse the White company square. So um, if we put the values that we just have obtained this in here, take the square and this and here take a square. And After that with some way in Sunday and take the square root. So we will have a value of approximately five times 10 to the 11 and Newton's carrick alone and the angle just passed before we use the minus tension function. So it is the white company over the X. Companies. So we will have like something like this that meant pretty like yes, like in the way we can see that the negative sign goes away. So it would something like this mutants for alarm for over 4.7 times 10- 11. You transport alone. So when we put this into the calculator, we obtain a bali off 199°. So this is the magnitude of the networks and this is the direction of the net electric field. So this is it for this problem. Thank you.

Mhm. This problem because the concept of the electoral electric potential energy due to the system of such particles. And to solve this problem, we are going to use the situation and first we need to calculate the length of the diagonal of the square, the length of the diagnosis. This lent as eight times route. So from the question we can try it. The electric potential energy of the system is the colon constant care into Cuban Q. Do that is minus of kill square upon a. Yes, Cuban guilty which is caring too minus killed square. Uh upon care to plus Cuban cure fooled. That is KQ square upon. Hey? Yes. So to uh joe took a tree that is key Q square on a plus You too Joe four that is K minus kill square upon a rope. Yes. Uh to take your food that is key minus Q square upon. Yeah. Now from this you can cancel out minus K. Q square upon a will kick you square upon it. And again this minus kick you square upon. David kick you square upon it. So by simplifying we got the electric potential energy of the system is two times K. Q square upon Hey, with a negative sign house absorb the value. So you equals- of wrote to into the colon constant 9 8.99 In to Tenders nine Newton major square parque colon square and two the just Q. Which is a Cuba in 2 4.4 micro column. So 4.4 and two Tenders -6 school um squared Upon a and is 60 centim or zero six. Need to okay. Uh, the directive potential energy of the system is -0.41 juice.

Problem. 24 points. 16. They have this arrangement of some charges, the mentions and he started units of charge has shown here we were told that get the convention that the potential zero at Infinity. We'd like to find what the potential at the center is, and we're told as a hint that thoughtful examination of the arrangement can reduce the calculation. So let's, uh well, let's take them at their word and see. See what we can think of about this rain. So one thing is that the corners are unequal distance away from the center, and we know that the potential, the contribution to the potential that some charge makes only depends on the distance between the point of interest in that charge. So these all have the same distance. And then if we look here two minus three plus two minus one adds up to zero. So at the senator, the contribution of these four charges all cancel out anywhere away from that and you're you're back to having to take all of them into account. But since this point has, uh, the symmetry of being equally distant from these, and they add up to zero it works out. So now we just have these two, four times. Q two charges the reach of distance of a over two away. So this is gonna be one over, or pi Absalon not, uh, work you two over a over to plus that the other charges identical. And then this works out to be 2.21 bolts.

Hi In the given problem, there is a combination of four charged particles. First of all, this is a positive charge Plus 5.0 Q. Then here this is another identical charge plus 5.0 Q. Then on the line joining them there is a midpoint of these two charges. And from this charge from this mid wind there is another charge that is also positive but Having a magnitude of 3.0 Q. And finally the fourth charge particles, this is negative minus 12 Q. And all these distances are given us B. Each. All these expenses are now as we know, electrical always goes away from the positive charge. So electrical, you do this Plus 5.0 Q will be downward and electrical due to this lower plus 5.0 Q will be upward and these two electric fields will be equal and opposite so we will cancel each other at and this observation point is marked as speak so at point B. Electric fields due to two Plus 5.0 Q charges are equal in magnitude as the distance the same. And the charges also saying so the magnet will be seen, so they are equal in magnitude but opposite in direction. So, net electric field at B. Due to these two charges will be zero. Now the remaining two charges Because of this plus 3.0 Q charge electric field, it is a way from the positive charge And you do this -12q. It is towards the negative charge. Like this. This will be so these are the two electric fields. Let it be even, Let it be E two. So finally, net electric field at this point B will be equal to as these two are opposite in direction, so they will be subtracted. So, first of all, due to this minus 12, you this is K. Q. The magnitude of charge. No need to use a sign as the electrical is a vector country. So this is K 12 Q by distance, which is too deep. The distance of -12 cue from this point, we will become deeply steeped, needs study and minus K trig. You divided by the stance. Again the square. So here it will be electric field at P E P is equal to Okay into 12. You buy for the square. Okay, Into 12. You by four. The square mine escape into three Q by T square. Now this is four. Threes are 12. So finally this is K three cube I. D square minus K three Q by the square. So this comes out to be zero. So there is no net electric field at observation point B. Thank you.


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