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Charges of 1xl0 4 and 2x10-+ Care located at the two lower vertices of the triangle,as shown in the figure below . Find the E field (magnitude and direction) at the...

Question

Charges of 1xl0 4 and 2x10-+ Care located at the two lower vertices of the triangle,as shown in the figure below . Find the E field (magnitude and direction) at the third vertex, point P.EzES3 mn3 mQQ2 2x104C1x104C3 mn

Charges of 1xl0 4 and 2x10-+ Care located at the two lower vertices of the triangle,as shown in the figure below . Find the E field (magnitude and direction) at the third vertex, point P. Ez ES 3 mn 3 m Q Q2 2x104C 1x104C 3 mn



Answers

Charges $-q$ and $+2 q$ are located at $x=\pm a$ a. Determine the electric field at points 1 to $4 .$ Write cach field in component form. b. Reproduce Figure $P 27.32$, then draw the four electric field vectors on the figure.

Before we start calculating electric fields, let's make sure we understand the situation. There are three charges. Q. One Q to thankyou three located along this line, and the distance between each of the charges is eight centimeters now. To the side, there is a point P which were interested in calculating the total electric field at and the distance prank you three MPs tens of years. And that's the same askew MVP. And in this angle here is 53.1 on both sides and the distance between que Tu and P s 67 years. Now you write the force diagram appoint P. You have an electric field, even one due to charge one pointing this way since you won his native Q three is negative, too. So there's the three pointing this way now. I broke these down into the microphone inside. Even. Why e three. Why? And that's the left Here. I have E, too. You want tax and the three x these air. Three additional electric field vectors. They're pointing to this left that didn't want draw three separate areas for so I've indicated by one arrow. So now let's use the formula that is equal to K magnitude of Q over R squared, where ours the distance between the charges in the location And so by symmetry, we know that the matter that you want any three appointee are the same and playing in the values here. For those we get 8.99 times 10 to the ninth. Best risque. Now Q is five times 10 to the minus six that's given to the problem and in the distance is just 0.1 meters square. And so this gives 4.49 times 10 to the six news per column. Now he, too, is going to be found in a similar way here. Ah, really similar. In fact, the only thing that changes is the queue. Here. We're going to use Q two of their charge, and we'll use the distance between Point P and Q two here, but same exact formula and same exact process. And I get 4.99 times 10 to the sixth Nunes for cool now in total. You, why is equal to even why plus e to y plus the three y? But since charged two is located horizontally to our point P the white component here of E to zero. And if we go back to our previous picture, you won. Why, Andy three. Why point in opposite directions and they're of equal magnitude. And so this one a big zero. Because if you won, why have some value e three? Why will be negative, that value and so little cancel Now e x The sum of the contributions and the extraction is equal to Yvonne X plus e to X plus the three X In this case, eat to excess, not zero. But you won't. Actually three X are still the same. But in this case, they don't cancel since they point the same direction. Instead they combine. And so e tu, In this case, I'm Ryan eat to excess. He too, since there was no e to why he too exited entirely too. Plus two times even one. And I'm gonna isolate the x component our writing co sign a 53.1 degrees. So this, too, comes from the fact that even X and the three X's are the same. So I combined them in the one and put it to outfront. And then the coastline is isolating the ex component. And then the one is just in reference to the large magnitude. Eveyone here. Now we can plug in everything that we know here. We don't need to. We know what you want. And so we find that E X is 1.4 times 10 to the seventh meters per Coolum. And so since e Y zero the totally is this and it points to the left and so that

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

So in this problem we have these three charges that they're off the same sign on their placed in this triangle that is being that was sketched here. The size of the triangle are on the length A and the Chargers are Q plus. Now we know that I actually feel due to point charge is e equals electrostatic, constant times the charge magnitude over the distance from the point. And since we have three equal charges and they're placed symmetrically around the triangle, it is clear that the point where discharges on the same sign will all neglect each other are. Is that the point where it is the point from where every charge is at the equal distance? So we need to find some specific point in the triangle and on that specific point from that specific point? The distance between the charge and that point is the same for all three charges. Since this is a specific triangle with all sides being equal on all angles. On the three angles are 60 degrees. We can say that the century is the point where the field electric field will be zero, so we draw one dashed line from one point charge, then from another point charge. Mhm. This is just a sketch from another point charge and this point here, As you can see, it is the central point. So the central point has the same distance between So this distance are here, are here and are here. This distances are are the same because this is a specific type of the triangle. This is the triangle that has all the sights equal. And in case of such time triangles, the century is at equal distances from all creative three virtues is, or all three points in this case point charges. So the point being that is at the century is the point that he has zero. And I could feel because the actual fields off the same sign neglect each other and then elected neglect each other at the points from where that point is at equal distance from every charge simultaneously. And this is the same central point in this case Now, for the part b mhm, we have the same situation between to find what is the electric field at the point this upward point, I will draw it like a point just like this so I'll do the schedule months before. So this is the triangle. These are the charges, and we're us to find. The slower to charges is to charges that are on the base of the triangle. What is their contribution to the electric field at this point here? So this will be the point. Be clearly, if we look at horizontal components way, we'll have thio better off electric fields so you'll have one vector a little bit like this. We will say that this is a charge. Kill one, and it's a charge. YouTube and electric fields corresponding. Thio charges Q one and Q two. Here we will draw them. So this will be electric electric field correspondent to the Charge Q Q one so that this one is originated from Cuban and this will be E to which originates from U two. Of course, the formula is standards. Formula for points charge electric field. As you can see, the inspectors have components. There is a result component, so this will be their horizontal component. When we add these two components together and their vertical components should be so the the one eggs and e two bags. Since the charges are of the same magnitude. Their components will be of the same manager. For example, horizontal component. He at one X is equal to the one co sign off 60 degrees. This is clear from the geometry since this angle here and this single here is the same like in this case is well so these air angles of 60 degrees and we know that we see that the result of component is electric field itself its length time because scent of 60 degrees. So in both cases, me to go sign of 60 degrees, it is basically the same to the same charge if you want. Oh, and the distance is the same. Distance is the case is a So this is this is this our square is actually a squared. So this is a squared cosine 60 degrees in a swell here. So since Q one is able to kill to, this implies that you want X minus two X is equal to zero. So there is no contribution for the from horizontal components. Now for the vertical components, they will add together. Onda, we will perform the addition So the white component of the electric field or we can say that this e y equals the total electric field. Other points be vector times the for example times horizontal unit vector. This will be equal to two times since we also know that ey one and E y two will be evaluated in the same way. Like horizontal components, just it. It will be a science function instead off the coast and function. So this will be two times e he science function off 60 degrees which is equal to two times the electrostatic constant one and the same magnitude of the charge that originates from which country build originates a squared times Sinus off 60 degrees and reducing all of these two to the final form you attend. This is equal to center, so 60 degrees is approximately 1.73 so and also it's actually it is two times it is one point 73/2. So in the end, when we evaluate sign associate degrees and multiply value off this sign with do we obtained that is equal to 1.73 times que que over a squared, which is a solution for this part of the problem or this component or the vertical component of the resultant electric field at the point P. We only have the whole field would only have a logical component and this will be its management. So this is the end of the problem. I hope you find it's helpful and I hope to see you in another lesson.

In this problem, we have a set up Q one. You, too. And their separation is the 13 centimeters we have also interested. Point over here on P and the distance we don't pee in the queue Wines, five centimeters that this had been puta que tu is 12 centimeters. Ah, so for part A, we have four configurations off. There were signs of Q and Q two. So we want to label the Electra feud for different configurations. So suppose we have positive and positive then for the point p. This is pointing up this pointing to this direction for that one is pointing to this direction. So the white component has to be pointing up. And if we have positive and negative, then for the interested point, biggest key wise, positive. Manny's point to this direction we'll keep people to two is negative. So is pointing to this direction. In this case, the X component is not zero, as can see clearly for third case, negative and positive. Ah, we have this point. So because otherwise negative. So the electric field is pointing to this direction, and a que tu is positive, so it's pointing to this direction In that case, X component is not Ah, is No zero as well. And for the last case, if we have ah, negative and negative. So we have two points. We have this interesting point over here because we being skewering cute, they're both negative. So the electric it is pointing toward them. In that case, it is possible to set to the X component being equal to zero. And the white components is pointing down, okay. And so for part B, the only possible case, just a negative and negative. Parsi Ah, we want to find out the very of Q two into the very off the Electra feud. So we already know that to the at one peed. Ah, the electric field is pointing down, so there is no any component along the X direction. So in that case, E induced the bite cure one, which is the one equal two negative 1.4 pi absolutes. Ah, we just look at the X component. So you want X Times? Q 21 is our knock. You one? Yeah. You want divide by the separation between the, uh, q and Pompey, which is five centimeters squared. So this is this is a you want because we're interesting to the Were you interested in the X component? So we need a time's a factor. Five over 13. Okay. And, ah, the X component induced of my e two is Ah ah. So we should not say cute Q one here. We should just utilize the body of Kyu Wan. So right here it's simply three micro clubs. And for a to x equal, negative one over for pie. Absolutely not cute too. We just look at the magnitude. Okay, So divide by 12 centimeter squared and times 12 over 13. So this factor gives us the X component off E too. So we have Ah, the one x you see. You want X equal? A to X, right? Ah, right. Embassy. So you want X is pointing to this direction e to exit pointing to this direction. Right. So this one should be positive. So, uh, their relation we will have is ah, the one next plus a two x equals zero. Okay. And you can actually solve for cute, too Equity. Negative. Sound point to Michael corms, and then we can try to figure out to the magnitude of the electric field at one p. So the electric feud with people to e people. Ah, because we in this case, we just look at the white component. So there's becomes negative one or four pi ups or not times three micro corms. They will lie five centimeters squared and times 12 over 13. So this gives us the why. Component. Okay. And a minus one over four pi absent a lot times 7.2 micro forms. Do you want my 12 centimeters sweat and times five over 13. So the final value is 1.17 times 10 to the seventh. New temple calm, okay?


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