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The two charges 41 & 92 shown in the image below, are fixed in place (not free to move). The net electric field due to the two charges is zero at the location (...

Question

The two charges 41 & 92 shown in the image below, are fixed in place (not free to move). The net electric field due to the two charges is zero at the location (-6Ocm; 0).(0, cw)q1 ~3nc(~2oc-,0)(+2o ck,9)A third Icharge (q3) is now placed in the same region: Unlike the other two charges, charge 9a is free to move. What is the initial acceleration of charge G3 . if it is released from rest at point p? charge f 93 ZnC (nanocoulombs) mass of Q3 Smg (milligrams)

The two charges 41 & 92 shown in the image below, are fixed in place (not free to move). The net electric field due to the two charges is zero at the location (-6Ocm; 0). (0, cw) q1 ~3nc (~2oc-,0) (+2o ck,9) A third Icharge (q3) is now placed in the same region: Unlike the other two charges, charge 9a is free to move. What is the initial acceleration of charge G3 . if it is released from rest at point p? charge f 93 ZnC (nanocoulombs) mass of Q3 Smg (milligrams)



Answers

Two point charges $q_{1}$ and $q_{2}$ are held in place $4.50 \mathrm{~cm}$ apart. Another point charge $Q=-1.75 \mu \mathrm{C},$ of mass $5.00 \mathrm{~g},$ is initially located $3.00 \mathrm{~cm}$ from both of these charges (Fig. $\mathbf{P} 2 \mathbf{1 . 7 2}$ ) and released from rest. You observe that the initial acceleration of $Q$ is $324 \mathrm{~m} / \mathrm{s}^{2}$ upward, parallel to the line connecting the two point charges. Find $q_{1}$ and $q_{2}$.

All right, So, uh, in this problem, we have set up Ah, Capta Q over here. And we have to other cues here and there. And then we know that this is between the capital Q Q one. So this is, uh, three. Set a Penis. This is three centimeters as well. And the distance between Cuba and a Q two is 4.5 centimeters and that we know the capital cues Negative. One point 75 micro Combs. So, uh, the mess off cap accuse five grams. And, uh, initially we know that ah, acceleration, like have a queue is three. 24 meters a second squid. So we want to find out the charge of Q one Q two and another conditions. This acceleration is pointing up. Okay, So by using these conditions, we can see that the Q one Q to be have to. I mean, they're they're charge. Ah, have the same magnitude. The reason is, if q one cute have different charges like ah, different magnitude than the force will be something like this. They do not have the same magnitude, right? In this case, there will be a net. Ah rested you on the on the X on X direction, so the acceleration would not be pointing to the Y direction. So based on this reason, we can just say that the Q one equal two. Cute, too. Sorry, Could it Iand another conditions since Q one since the forces pointing up. So, uh, by using the Fools division, it has to be like this, right? So because Q is ah cuse negative cues, Navy charge. So Cuba has to be positive, and the Q two has to be negative. So we just say that is equal to Q. Okay, so the Net force on the capital Q. We have the expression f equal 1.4 pi Absolute knots times Ah que times cure content Ham Scout cut times Captain Q, which is native 1.75 Michael Corms Divide by the business, which is three centimeters. So this is the magnitude of the force exerted by Kyu won, and we need to We just need to find out the white component So times white component just we just need two times the factor. 2.2 25 year life. Three. So this vector comes from, comes from supposed this is data comes from coal. Cynthia constantly Have you utilize this triangle? You'll see that too coarse and data equal to point 25 or three. Okay. And, uh so this is the fool's excited, like you one and ah ah, And the force exerted by Q to they have the same expression, actually. Ah, so we just the times too. And minus mg, which is the gravity, The vibe I am. This will give us the acceleration. So we see that we know that this sequel, Thio 3 24 meters a second Squid. Okay, so in this expression, you can see that the only almost bearable is this cute small cube. We already known the mass and with the G. So we're just uploading the videos and the sofa. Cute. You're gonna actually find that cube, find that equal to 6.2 36 times 10 to the negative faith schools. So in that case, Kyu won. It's ah, positive. It's a 6.36 hunting to the ER in the name of a school ums and que tu is the opposite one. Okay,

In this problem We're going to be calculated the electrostatic force on Q one. The charge of the origin from the other two charges Q two and Q three positioned as shown in the diagram, we are given all the charges mm Norris in particular. Thank you to and Q three same AG two opposite assigned very important. Going back to the diagram noticed that Q two and Q three are both the same distance from Q. One and also the lines connecting those charges to Q one are making the same angle with the positive X axis. All very important. So let's now start looking at the forces that are on Q one. Q one positive to negative. That means an attractive force. That means the force of two on 1. It's going to be in this direction. Q one positive to three positive. That means that forces repulsive along this line. So this is F 31 for future use. If this angle here is 23°,, then this angle here also will be 23 degrees. No if the charge managers are the same and their distance from the other charge that you're looking at, the force on is the same. And that means command to that force forces will be exactly the same. So let's make that explicit. So let me write the expression for the charge to one. The decay times the magnitude of charge too, magnitude of charge one over are 12 square Now let me ask what's the same. Okay, certainly it's just a constant Q two and Q three mantras are the same. So I can replace Q 292 to 3 million to Q one is still the fourth charge. We're looking for the fourth song let's say the same. Are 12 and R 13 are both 1.3 m. And so this is our 13 squared now. Well, that looks to me to be The magnitude of the force of three on 1. So they are the same. No, we'll need that right now let's look at F net X. Now that's going to mean we need F 21 X and F 31 X. We'll have 21 X. Trying to triangle Yeah, X. component is going to be the adjacent side to 23. So that and it's in the power of direction. So this is going to be F 21 Koh Sai 23°.. I have 31 that's in the negative direction. And and the X component is again the adjacent side was going to be minus F 31 Co side 23°.. But I just mentioned and just showed you the 21 man, 231 man to the same. This is zero. There is no net NX. And I could put an E. On here indicating electrostatic because we know there's mechanical forces but we don't we don't need to do that. So now let's look at F net. Why now in both cases, yeah, they are the opposite side of 23 degree angles and they're both in the positive Y direction. So it's going to be F 21 sign 23 degrees plus F +31 notice. There's gonna be no cancellation here. So it's gonna be too F to one side 23 degrees. So we now have announced your value and we can put in our formula here. So this is gonna be too times the bank to k. Times the magnitude of cute too Overseitude of Q one sign 23 degrees over. See what I called L squared just to make it so that that it's easier to remember that they were the same. And we can put in our numbers two 8.99 times 10 to the nine. No. 10 major square Coolum squared and charge two in magnitude is five Times 10 of them out of six columns. Q one is 8 times 10 to -6 Cool homes and don't forget to sign 23 And that is over. That is over 1.3 m Squared. And this works out to be 0.166 new tints. And seeing that this vector only is in one direction only in the Y direction. This is also this is F net the magnitude of that factor. So that is the magnitude of the net force and Q. One and the direction to make an explicit direction is plus why and that we were already knew once F net x zero. So that's the direction. So that was part A. That was part A. To get the net force a part B. They wanted to know what the acceleration would be. Remember when they see a celebration they talk about a vector means magnitude and direction. Uh huh. So we know once we have the net in this case is only F net. Why? That M A. Y. So a Y. Is going to be F net Y over em. And that will be 0.166 Students. And they give they give a mess of 1.5g, which is 1.5 times 10 to the -3 kilograms. And this works out to be 111 meters per second squared. The man who had been 111. The direction because it's a plus that implies plus why direction? So we have so we have 111 m per second. That's the magnitude in the plus five direction. It's all kind of combines all of you, so that is the acceleration and that's the rest of the problem.

Through this question. You want to use the electric force equation that equals que times absolutely of Q one Q two gir R squared now for the values. Given the problem, they give you all the charges and the distance. You need to just plug it in to usually find the force. So the K values 8.9. It's a constant decay cause April 19 times 10 to the night for Q one and Q two. We always use the origin one of the points at the origin. That's kind of like our reference point, and the second charge would be five times 10 to the negative six schools. Now, since we used absolute value doesn't matter. It's negative or positive. It's just five times and it *** six schools over the distance. 1.30 meters has coming. The problem square. We'll get a value. Is your point to 1 to 8 Newtons. No notice that the values of the magnitude of the charges were both Q two and Q three R five times on next six schools, so they actually have an equivalent force acting between them. The only different thing is one of them's acting in the opposite directions in the repelling direction because you look at Q three and Q one. Both charges are positive, so it's actually repelling each other. That's the only difference between itude that magnitudes actually the same. So since one repels the other after F one accident, the opposite direction. So now we can draw a diagram represents the direction of the active use different color. This red represents the F the force in the 3 to 1 direction the black represents force to the way they should be around the same that look, look a little off. But they should be the same length and pointing in the same. They're both 23 degrees now. If you look at it, the X components, actually the same back in different directions with actually cancel out soon Acting, you know, worry about the X or know what me for is the why the white direction of the force So do that. We have to do a little bit of Trig. So to find for the y component of this simply just want to take the force that we found earlier, which is to 1.212 in unions and we want to take this. Multiply that by the sign of 22 back to give a value of 0.831 new things. If you notice that, um, in the other one that force from 3 to 1 exactly the same the magnitude of the force of the same. And we also multiplied by the sign 23 degrees, since it's also have an angle 23. And so that would get you also 0.831 years. So the X is the comebacks. Components cancel out while the white components will add up. So first we want to add it up. Uh, 3.831 plus your 0.831 should give you the answer for the magnitude of force 0.166 to unions, it says for the first part. Now, for the second part, you want to use that same force than that force that were you determined earlier, and use that to determine the acceleration of of if the charge one had a massive 1.5 grams. So as you know, probably no equation. If you close to me now We're given fourths given mass, so we need to find acceleration. So the ice like that we supply the bite. I am So we can just get nicely a acceleration and get a That's over. Was that program now? Since we're given these values, we have the open 166 two new ins from before the first part. No, we have the mass. I'm gonna use 1.5 times 10 to the negative three kilograms. Teoh Convert s I units. It's equivalent to 1.5 grand is given the problem. But using kilograms, That's how units usually makes your You should want to. You should use S I units most of the time just to make things consistent. And so he plugged that in into your calculator. You get 110.8 meters per second squared and that is the acceleration you're looking for

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


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