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Pijcc fin_ Jnswets Tne provided answerlol Ans "Cn Woi< Must DeahownDeterreceive full credit Io cogreclFour point charkes placed 0t thc coructa of 0 squilre $$ shown Mgrre Each side ofthe s4uare has Ienaih 2.0 Delening thc mgnitude f the electric field Ihc Doinl the center of the square4MCEXG(3 pts) ae elec potentia Vecoscalar quanttyr(1Opts) What the electric notentizthe four charges DointElectric Potentialpts) positive test charge placed at point What is the direction of the electric fo

pijcc fin_ Jnswets Tne provided answerlol Ans "Cn Woi< Must Deahown Deter receive full credit Io cogrecl Four point charkes placed 0t thc coructa of 0 squilre $$ shown Mgrre Each side ofthe s4uare has Ienaih 2.0 Delening thc mgnitude f the electric field Ihc Doinl the center of the square 4MC EXG (3 pts) ae elec potentia Veco scalar quanttyr (1Opts) What the electric notentiz the four charges Doint Electric Potential pts) positive test charge placed at point What is the direction of the electric force on the test charge? (provide answer degrees relative to the horizontal axis) Direction of Force on test charge 74A`



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Two point charges $\left(q_{1}=+4 \mu \mathrm{C} \text { and } q_{2}=+3 \mu \mathrm{C}\right)$ are fixed in place according to the figure below. (a) What are the magnitudes of the horizontal and vertical components of the electric field at the point (0, 4)? (b) What are the magnitudes of the horizontal and vertical components of the electric force on a charge $q_{3}=-2 \mu \mathrm{C}$ placed at the point $(\mathrm{o}, 4) ?$ (c) In which quadrant would a positive charge $q_{4}$ have to be placed in order for the electric field at point ( o, 4 ) to be equal to o?

In this problem we have on arrangement of a square. Um, where there's charges on two of the corners of the square, so the orientation is not unique. But for this point, I'm gonna choose it to where Q one is here. Cute too is here. Um And then they tell us that point A is in the middle, and point B is on the corner closest to cute, too. So that would, for my picture mean that b is up here. Now they tell us that each side of this square is three centimeters, so that means that 0.3 meters and then they give us some of these values. So Q one is equal to plus to micro Kula mes que tu is equal to minus two micro columns. Okay, so now what we need to do is we need to figure out some of these lengths here because we're gonna have to know these lengths in order to calculate Ah, the potentials. So first I'm going to do this triangle that I have drawn here. So this triangle is simply 0.3 0.3 and then a will be in the middle. So whatever we find the high pot needs to be the length from Kyu won A will just be half of that. So we have the high pot. News is equal to the square rope square root of two times 0.3 squared. And there's a two here because both sides of the same for this tells us that the high part news is zero 0.4 24 meters. Huh? And so now are our radius, Um, from one to a which will also be the same as the distance from que tu es. Since we have cemetery here is equal to half of this number, which is simply 0.21 meters. Okay, so now that we have this in part A, the book is asking us to find the voltage. Remember the voltage for a point charge. It's simply Q over four pi epsilon, not R. And then you must add up. The voltage is from every charge. So if we're trying to find the voltage at point A, we need to find the voltage at a duda que one plus a voltage at a dude. A cute too. So we can do that. The voltage et ai will be equal to Q one over four pi absolutely not are one plus que tu over four pi Absolutely not, aren't too. But since our one is equal to our two, this is simply equal to Q one plus que tu over four pi epsilon Not our one, or are too. And then we see that kyu won and que tu actually have the same magnitude but opposite signs. So when you add them together here, you're gonna get the voltage at point A is simply zero votes, okay, and that's it for part A. So now if we move on to part B, the book is asking us to find the voltage up at the top of our square at point B. So just to remind you this is point B, this is Q one. This is cute too. Okay. And we already found that this length here, okay, which is our one in this now is equal to 0.424 meters. So now we just do the same thing we did in part a. The voltage apart at location B is equal to Kyu won over four Pi epsilon not are one plus que tu over four pi absolute not are too. But now our wanted our two are different values are too is just a side of this square the distance between que tu and B So this is simply 0.3 meters And now you can simply plug in these values being very careful that Kyu won, um, and cute to our micro Coombs He must convert into cool ums and you'll find that the value is negative 1.75 times 10 to the fifth votes. Okay. And the reason this is negative is because que tu was actually a negative charge. You get a negative answer when you plug in it Now in part, See, we're gonna have a point a point Charge Q three equal to negative five times 10 to the negative six cool ums. And it's gonna travel from point A here, up toe point B. Okay. And we want to figure out how much total work is done as that point charges moving from A to B. So we can simply remember that work is equal to negative. Tell to you so this will be equal to negative. Ah, you final. Which is you be minus initial, which is Yuet huh? So this will simply be equal to you, eh? Minus you be. And now we just remember that you is equal to Q not V. Where cute not is the charge that we're considering moving or changing potential energy. So this will simply be equal to Q three, since that's what's moving times V A minus V b. Okay, so now we know he a is zero. So this whole thing goes to zero here, and what we're left with is simply the work from A to B is equal to minus Q two times the voltage at point B. Um, the voltage is negative. Thank you to is negative. So when we plug in these values, we find that the work from A to B is simply sorry. This is a Q three is simply minus 0.877 Jules, and this work is negative, which is, as we would expect, because a negative charge Charge three wants to move from low to high potential, and V B is at a higher potential. So it's trying to move to that point

I have driven this problem based on the concept of and a quick feel at the point is to find a half a point, you or take away our script. Electric field of Cuban at B. This is the one p even his car too. Okay to one upon our one square substitute that will Syracuse in but a two Get your weapon are to the script R one is called to order. You've got to say so. Netflix along Why direction you will get for a night filled along by election even sign of 31 rest. Ito sign of 30 men. So if this angle is given 31 and this is also sort of entity Mhm. So it is to be since even in school to a to two e Sarah knock 30. But so there is net electric field Had to be mhm and all by it is just a moment. Hello. Why exists And fish second part? Yeah, the direction of oh, and a pretty extreme near Kyoto making mm 31 degree from origin to Yeah, third. Uh huh. Direction of and a profit at the Did you two Cuban making 31 degrees from horizontal as surrender figure and the nature of net force. So, in a magnitude of not electric bill is to eat Sign of 31. That is to okay, June R squared sine of 31. 19 to 10 to the number nine. Q is for my problem. So four into 10 to the Borman six r is given what is here and to sign up 30. But after solving NAND force, you will not electrical. You will get 7156 and to turn to the powerful new print curricula to be part acceleration of the particle baby Q A s curto and keep so acceleration will be Q E upon and no substitute seven Directorate Will we have major 7.56 Trying to keep our four charge on the particle is eight Micropal um Onboarding problems Mass of the particles given one point to get up. So acceleration Evil range 15.4667 Yeah. Yeah. And to the power tool. Narrator for second square. That's all. Thanks for watching it. Mhm

Hi. The given problem here, this is the X axis. This is the origin at which we are placing a charge you three a charge you one has been kept here. It is having a negative charge. Let this point is a along the X axis at which this charge has been kept minus Q. One. The distance at this point from the origin is 0.200 meter. Then another charge positive in nature. Rescue has been kept here. Suppose that are going to be the distance from the origin is minus 0.300 meter. No, it is given that the net force acting at this charge U. Three due to these two charges charged you to put that be and charge minus Q. And put a day has given us that would be F at all. And that is equal to four points to zero micro newton. The value of human is minus 4.50 No problem. And value of kyoto is plus 2.50 No, no problem. So using this expression F. At all, there are two forces at this car's guilty. S Q three is a positive charge. It will be attracted by this minus Cuban by a force effort. Or do you do A. And it will be repelled by this positive. You too. If at all due to be both had in the same direction. And this net force fo will be given by the sum of F at all due to a yes effort to you to be so using cool. Um slow for the electrostatic force for F. O. A. This is A into Cuban into cutely you fight it by oh A. Which is little 0.200 m to the whole square plus for F. O. B. The game. And that is you two into Q three at all. This is three at B. This is due to the spend 0.300 the whole square. And this force come out to be 4.0 micro newton or 4.0 into english bar minus. Thanks new one. Now taking the common things out which includes the value of K. Which is 9 to $10 per nine. Then Q. Three. That can also be taken out as a common living inside for Cuban. This is 4.50 only the magnitude as the direction already. We have used in the diagram. 4.50 into 10 for minus nine column invited by 0.4 metre. Making us square off 0.2. And here this is 2.50 into 10 for minus nine divided by just squared off zero point three which comes out to 0.9 and it should be all in to 10 dish par minus six. Further taking this bandage for minus nine also has a comin out get nine into 10, Parts nine into 10 for minus nine into Q three bracket 4.50 divided by zero point or. And here it maybe written has 400 50 54 Similarly here this is 255 9. You see 24 into 10. H one minus six cancelling this. Finally this is nine into Q three else in 36. This is 450 multiplied by nine and 250 multiplied by four is equal to four into 10 days, part minus six. Then cancelling this 36. We've done nine if this is four and here it is U. Three into 4050 plus 1000 divided by four. This will to four into 10 for minus six. Finally this Q three will come out to be 3.2 into 10 dish par minus nine Poland. Or we can say Q three is 3.2. My broken lung politics is nano. And here it is the answer for the first part of this problem. No. In the second part of the problem we have to find the direction of this force and it is obvious this force is a king towards right direction of this force. Right now, we have to find a position at which if we put this charge Q three, the net force experienced by it may be zero. To suppose the position is here at point B. At a distance X from the origin at which the net force is zero. So here as the charges guilty, positive. This negative charge will attracted towards itself means this is effort. P. Due to A. And this positive charge will repel it. So effort I need you to be this shoe. This too should be equal and opposite F. F. T. Due to A. Should be equal and opposite to affected you to be So plugging in or non values here. Yeah into Q three. But at b into you charge at a Cuban divided by the distance which is this x minus 0.2 00 x minus 0.200 The whole square is equal to again U. Three. Again ask you to divided by the stairs and here it will be X plus 0.300 the whole square and slinky and Q. Three and plugging in all other values. What the value of Cuban, this is taking the magnitude only 4.50 into 10 for minus nine. Well um x minus 0.200 To the whole square is equal to 2.50 into 10% minus 9. 11. Divided by 0.300 plus. Acts to the hospital, cancelling this bandage for minus nine also. And then solving this equation. Making a cross multiplication. We get 2.50 divided by 4.50 is equal to 0.300 plus X. Invited by x minus 0.200 and then making a square root and making a cross multiplication. Again, we get the final answer to b minus 1.76 m is actually the position which we have assumed to be at positive X axis. Actually desert negative xx is somewhere there. This is a real position of the charge you three here. If I put it it will experience zero. Course answer for the third part of this problem. Thank you.

This question We have tree equal both of your charges being placed at a cornice off any credential triangle. Recommit Eddie for this triangle. These sites are three set of this in the one ahead of vertical line to the top church. Just that p So you know, very symmetric No, along this for the goal line. B what a label. A few points. So we have a point. Just be lordy p. This point shall call a And there we have it pointed its central, the triangle. Just be. And there you have a B c D. E there in order and close together. Where? E It's at the bottom off the triangle. So he had to squeeze in. See Eddie? So yeah, see every F d. And finally at all the way below ability trying go is f So for the first about this question, we want identified it direction off the electric few net electric few at e yet if so, at a we know that it is very close to P close to recharge p. So P will provide the greatest, uh, greatest magnitude off electric few. It's Dobie. Don't woods closer. Oh, all the charges are positive, so electric fuel lines are outwards pointing. So people point downwards at a and the electric field from the other two charges. Obesity Uh, the X direction Kids supposed to 60 x direction. Just ey The white direction will be too weak to compare it to a t. Ah, electric for you coming from Pete. So the net electric fuel be downwards. Okay, I'll be right because it's symmetric. Sacred natural triangles or the charges are equal distance away from point B. And as such, the electric fuel should be zero at that point. Finally, for f right for F, it is below all, tree off the charges. So all tree China's will be pointing doll. Let's f resulting in that don't work electric. Few So s argued earlier the electric fuel coming from this to bottom charges they are horizontal components along the X axis will cancel out and only left 50. Why component richest downwards. So since P is also providing $8 electric field at F the Net electric, few must be dull Words not identified. Electric few uh, it e right to be missed out on e So for E at this point, the electric field coming from this two charges is only horizontal, right? They will cancel each other out. We have no net electric few, but so the oni determining factor is the electric few from P. We just don't. So, for for e, it is also double its the hottest This imply. Sorry. Realist too at identifying the direction of the lecture, if you see. Okay, so for C, it is a point that is just slightly below Sorry, but will be. And remember be yes. Where the electric few is cereal. So slightly below that through the main, the main change in the electric few would be the reduction off the $4 electric fuel from Pete Presley. May and change e is due to do you reduction in e few from the church at Pete and s. Mitchell here. This reduction minister don't. What? Electric force. It's no weaker it is. We could burst upwards. Electric force from this two charges at the altar ages Bottom ages we made is relatively d c. Right. So the upward forces iss Stewart if d c maybe same and as such. We have a nit. What fourth? So it up. What electric few at point C. So for C must be upwards. No, this implies that pointy. There must be some region near Point D, which is zero, because there's a need for it to transit to zero in order for the upwards electric few to become Don't What's it F and that was it. Eat great. So there's some in between point that must be zero. The electric view must reach zero before it cause to the negative direction which is down. What? So in order to find what is this exact point that it's downwards? We gotta assume this point is set points. That is why a buff the above the bottom off the triangle. All right. First, we what a fine wife. Teetotal hacked still to hitch, given the site's trees. You Sitges tree square dinosaur 0.5 square skirts to be about two boys. Six You and, uh so we can use this to find the electric few. At this point, we want it to be zero, right? You netted actually feel to be Sewell. So the contributions are frumpy. We have okay, does que but by 2.6 minus y square because it is in the downward direction. So we had a negative sign and there we have toe up what directions you actually feel coming from the to bottom charges. They gotta have a few that's pointing in this direction. This verse in this direction, it s arguably fold by symmetry. The horizontal components will cancel out any only interest i d for to go components. So the vertical component ISS Miss KK he times q times the distance between these two charges and just to be close to 1.5 square plus y squared so by fighter gresty room this call this distance over here, right this distance just 1.5 scraped last white square. But of course, the vertical component is you have to take the trigonometry. Remember that. Ah, assuming that this and go with us, Tita which implies that this is Tito. To get the medical components, you have to take thes sign or veto. And from this right angled triangle, you know the scientist, er she goes to why over square roots y squared thus 1.5 square and we know that both off the vertical components from these two charges are the same. So we just multiply this by two is you have to off these charges simplifying this equation. This is, Ah, final equation. Where? Bias in terms off CF. So you get off the common factors, which is Katie Times Q and the the try to carry off the infections and for this equation were to solve it numerically. But there's a transcendental equation. And two So for that receivable, why you want to do is to plot to graphs. But you're the plot. The graph off. See if I goes to 1 45 square first way square, the poetry of a to in another function just to weigh 2.6 minutes way square supporting these two functions on the same graph we didn't find what is the in tow section between these two graphs, right? And we see that still have two points we have one. Just like was to Is your point it 66 cm as well as why close to is your 0.37 tree? No, this is your way. 66 year corresponds to the center off, uh, for a collateral tricker which is basically point B. Many see center, which is where we have the electric few is zero because it's symmetrically, uh, at equal distance from all the points. The rest is 0.3 century is the point us below b, which is our point. This is our point of interest and have all the answer would be 0.37 treat.


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