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Three charges are arranged on the corners of an equilateral triangle, with side length d-3 cm, as shown: Charge 41= 2 /C , 42= -4 UC, and q3= +4 UC.9293...

Question

Three charges are arranged on the corners of an equilateral triangle, with side length d-3 cm, as shown: Charge 41= 2 /C , 42= -4 UC, and q3= +4 UC.9293

Three charges are arranged on the corners of an equilateral triangle, with side length d-3 cm, as shown: Charge 41= 2 /C , 42= -4 UC, and q3= +4 UC. 92 93



Answers

Three charges, each of value $Q$, are placed at the vertex of an equilateral triangle. A fourth charge $q$ is placed at the centre of the triangle. If the charges remains stationery then, $q=\ldots \ldots \ldots$ (A) $(\mathrm{Q} / \sqrt{2})$ (B) $-(\mathrm{Q} / \sqrt{3})$ (C) $-(Q / \sqrt{2})$ (D) $(\mathrm{Q} / \sqrt{3})$

Even in a collector triangle. So we have any collector triangle, right? This is any collector trying Whose? Three sides. Sorry. Cool. Uh, this is point be and then this is C. This point is okay, right? Andi, this is the midpoint, and the mid mind is point D. Okay. On each or tax. That is a point. Charge cume. Right? You. And in between b and C, it is another charge which is capital killed. Okay, so we need to find of this capital Kim, the magnitude of capital. You're right. Now let us find out. Uh, foresees, uh, eight on cue, which is eight point it right. Due to rest of the charges. No, let me draw Victor diagram. So let's say this is our point. A in point A, we have charged killed. Right. So this is Kim charge. And here it is. Another charge kyung and this is a B. This point is him, as I said earlier, and then here is, uh, why I'm see why I'm see, we have Kim charge. So, first of all, uh, since, uh, these are positive charges here for this will be rebuild this direction. Let's say this is force strong, be. And then similarly, this will also reap all, uh, the charge 80 in this direction. And let's say this Forces FC. And here is the Kim charge. And let's see, this is a negative charge. Then this will attract cure in this direction. Right? And since this is a point DDR four force from this point, his f d. Right now let us find out the net force. Well, this angle is equal to six degrees. Since we have any collector triangle, this angle is equal to 60. Well, then the Sengalese, if this is 16 and then here we have. Right. So let me. So this angle is also equal to 60. And this angle is also equal to 60. Now, let's resolve into components, right? This is ah F b. Who sign off 60. And this is FB sign of 60. And similarly, here this component is FC no sign of 60. And this vertical component is FC. Sign off 16. Right. So these Horizonte components cancel each other, right? So what is on incompetents? Cancel each other. So we have, uh, f see Signed 60 bliss, FB sign 60. They're given that the force on the charge, which is a Kim Air s equal to zero. Therefore, the some of these two components must be equal to F D. Right. So the X equal to Efty Okay. And now, by plugging the values well, FC well, FC's key, you know, squared, divided by a square right and sign Thirties real tree divided by two Let's f bees again Que que square divided by a square and sign sixties through three divided by two minus Ft Will every ski times you know im skeptic You're divided by ah list distance. Uh, this distance right here on this distance is simply route three. Hey, divided by two then we have since here are scared there for three Hey, squared, divided by four. Right. And this must be equal to zero. And on simplifying we have k q r divided by a square into ruled tree here. Okay, right minus. For kyung, divided by three is equal to zero. So treat your minus for curing. Divided by three is equal to zero. We need to kill So four cure divided by three z four wrote three kyung. Therefore kyung is equal to three growth. Three times came divided by four. And this judge has to be a negative charge. So this charge is a negative charge. Negative charge. Otherwise, that force would not be zero.

Hi, everyone here. We have to use Colin slot in Vector for So next is a next force, baby. A one plus active Afghan will be keep Cuban to you too upon a square. Because I'm 30. I kept minus sine of 30 Jacob and escape your whole country. He square minus cause of 30. I kept minus sign of clergy. Jacob. Yeah, Okay. So the magnitude can be calculated as right. Yeah. Mhm. Yeah. After solving it, you will get Keep Jewish Square a square, Jacob. So it's a magnitude human. Right. Q B square by a square nine in cooked into the apartment nine chart on each say, because here, Cuban Spartak YouTube is car Tokyo three is Carter Cube. So this legendary will get and two is given 7.3 10 to the power minus six and distance is given 193 m So magnitude of the gentle force you will get 155 Newton. Hello. Negative via access, right? No second part. This is the answer of eight. If charged geometry mhm is moved to origin Cuban. You too becomes closer to cutting. So next feel. Yeah, Land force On Q three, it's greater than octane. Any part? A sea pirates. The total force on Q three. Been point downward? Uh huh. Yeah. Okay. Having the magnitude. Okay. He will square by a square substitute develop 19 to 10 to the power line. 7.3 10 to the power minus 60. Square upon quite for 65 square. So it is to me 1.3 Newton at all. Negative by access. Yeah. Mhm. Mhm. That so. Thanks for watching it.

So for this problem, you are bringing three charges together. You found out that it took zero work and you want to figure out the value of the third charge. This is kind of a more difficult version. They think number three where you're bringing in three charges and asked for the work. Um, so if you're totally awesome, this problem go there first, and then we can build on that. So basically, um, anytime there's asking, what's the work done to assemble charges have to do it piece by piece of peace. One is what's the work t least to get a formula. So right now I'm just gonna get a formula. So I'm gonna say this one has charged Q this when I was charged. Q. This one has charged Cube. I'm calling H Q question mark. Um, and so the goal is to figure out. And then they're all separated by distance. D, And then the goal is to figure out what's cute question mark to make work. Zero. So we need to come up with a formula for the work done, um, by some external agent on DSO You can say that work first. You want to consider assembling just thes two charges and then you get work is K Q. Squared because it's Q Q Q squared over D. Hey, um, and then second, Now you need to add on until drum like that. So you brought these two together? Second, you want to add your third charge to question mark to the mix, and it's also a distance d And then, um, to get how much work is needed, it's gonna be It needs to kind of fight off both of these charges that are, like already here, like it's kind of hard to join the gang. So it's gonna have two times k Q of age times que of the question mark writer by D and, um, so and then you need to ah, see what? We want these to be some together to be zero. So you want. I'm just like I'm kind of mosey up here. You too. The rest of the problem. So you want. I'll call this work. Wanna work, too, with the total work? Um, t equals zero. And so you want kay cues? Okay, Q squared over d T equal to K Q Q question mark over D and then the DEA's can't soul. The K is cancel one factor of Q cancels and you got, um Oh, excuse me. Negative. So then you got cute question. Mark is minus Q over, too. So it's gotta be a little about half half this week is the other tragedies basically.

In this problem, you have been given a triangle and there are three charges on its three corners, two of them being plus que hedges, B and C. I've been wanting being minus Q at corner cake and were to find out the net Force that each of this corner's experience that would solve this problem. Let's first calculate the force between any two off the searchers. Between any pair of the charges, the manager of the church will be given by one by four packs of and not times que square. Since all the charges have the same magnitude, you could've been our square and that is calculated dance as my intention to live on mine times the chantry GIs given as by micro plumps it's cool, divided by the length of the site of the triangle. Just given this 0.3 meters. So this time, sir, to be about 2 50 mutants numbers focus on each of these corners one by one. You know the first corner corner, eh? Since this charge, Harris negative and the other two charges are positive the forces that this corner with experience all in order and you look like this which means the neck pores like this charge will experience will be held on the symmetry claimed, which is at an angle 30 degrees with respect to bottom. What? The triangle, huh? In that case, the Net force can be written as two times the bang the shit off the force on each direction. Times Co signed three degrees since the course hand components, which is the component of the forces on the symmetry plane. Will that land? What? As the perp critical components, which is opposite to each other, we'll cancel to each other. So this is then calculated as two times 2 15 times square three try to and that is a bold for 33 unions. As for the other two corners for corner See, for example, one of the horses is he Nord on the other force Because both of these two charges are positive. This forces a reported that this force southward she was in the scouts Symmetric course lies at an under 60 degree with respect to bottom the triangle. And in this case, the total force is then two times manager of time school science, 60 degrees on that is then calculated. Just ask 250 Newtons. Finally, for the point I was talking about Florencia till now there's talk of a point B which is the top one with the triangle which has a charge plus que And for that reason one off, the forces here will be in work. It can, whereas the other force will be outward as the repulsive force Come on. The net force will be again on a symmetric line that mango 60 degrees with respect to the side of the triangle on In this case, also the total force that has given by two times spent, we should have times causing situated prayers and which is the same list. Either case it's concluded as 250 Newtons which means to off the corners. B and C will have the forces 215 minutes whereas corner they will see a higher force, 433 new tenants


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