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Problem 18.A.06Three point charges are arranged along straight line, as shown, with d = 18.5 cm, qB 1.96 pC and 4c 3.87 pC. The total electric force on qc (due to t...

Question

Problem 18.A.06Three point charges are arranged along straight line, as shown, with d = 18.5 cm, qB 1.96 pC and 4c 3.87 pC. The total electric force on qc (due to the other two charges) is 3.86 directed to the right: 4A 48 4c2dWhat is 4AHC

Problem 18.A.06 Three point charges are arranged along straight line, as shown, with d = 18.5 cm, qB 1.96 pC and 4c 3.87 pC. The total electric force on qc (due to the other two charges) is 3.86 directed to the right: 4A 48 4c 2d What is 4A HC



Answers

Three point charges lie along a straight line as shown in Figure $\mathrm{P} 23.8,$ where $q_{1}=6.00 \mu \mathrm{C}, q_{2}=1.50 \mu \mathrm{C},$ and $q_{3}=$ $-2.00 \mu \mathrm{C} .$ The separation distances are $d_{1}=3.00 \mathrm{cm}$ and $d_{2}=2.00 \mathrm{cm} .$ Calculate the magnitude and direction of the net electric force on (a) $q_{1},(\mathrm{b}) q_{2},$ and $(\mathrm{c}) q_{3} .$

This question cover the concept of the operation of the electric field. So For part A. and five a. The Cuban is negative and you do it also negative. So the electric failed to Cuban is towards Cuban. Okay, on a And I said this is Eva and you took your two is to ask you to and let's say this is So let's we're considering the electric field along X as a positive. So the net electric field uh, a let's say e a candlelit dinners, the electric fooled by the church to minister electric fuel for the judgment and similarly, four point B. The electric field to to the judgment is towards Cuban. Let's say this is even and the electric field by the church Q two is towards cute. Let's say this is cute. So the electric field at point B is even plastic. Okay. And the distance between the charge Cuban and quite gay Is 25 sentimental Afghanistan sentiment, that is 15 sentiment. Okay, so now let's solve for part A so for part a not electric field. That point is The value of the electric field due to the church. You're too, is KQ two upon the distance of air from the church to square minus K. Cuban upon urban square. Now let's substitute the value So we can write the electrical years. The value of K can be taken common and that is 19-29. Your 10 m square. Oh, cool. Um square into the value of categories. Uh, 12.5 and two tenders -9 columns. Okay. and the distance R two is 0.1. We just square minus 6.25 into attenders -9 Poland's Upon 0.15 m square. And the net electric field at AIDS. Yeah. 8715 Man Newton. Popular for the second part B. The electric field that bees the electrical by the jazz Cuban. That is a few times human upon Ireland square plus K. Times Q. +21 R. Two square Are the net electric field that want bees. The value of care that is nine. Could understand nine, No. 10 m square or plumb square into The Valley of Cuban is 6.25 In to tenders -9 columns Upon our one is 0.1 m split. Yes, 12.5 into tenders -9 columns upon The distance of Point B. From. You do is uh 025 interpreter. That is 0.35. We just square. Okay, so the net electric field that B. Is equal to 3420 Newton. Popular now for part C. If a proton is placed at point A. The force and Crotone as equals to the electric field. That point A. Into the charge and proton that is E. Or the force and protons, they look gratefulness. Uh 8715. You can popular Into the Child and proton is 1.6 to 10 days -19. Fulham Are the 4th and proton is one point ford And two tenders -9 15 newton. And the direction is towards what does it do? X. X. Okay. This is the solution part C. In the earlier part we have assumed the direction for the chip towards xX is so for E. V the direction is guards. Was it a mixed success and in part also the direction is towards positive X axis. Yeah.

So the charges are at thus 1.25 That's what This to be zero on this to be negative 1.8. So we're supposed to find, uh, electric potential with respect to argue all and the other point who? Geez, 1.5 centimeters in this direction. So for part a, remember that these numbers are Ardian Centimeter for part A, which is what unsure about the origin is okay, que one and that you would respect origin. Que que one over r one Does Q do over r two. So in this particle, their guests with nine times 10 to the nine sk and 4.5 micro problems of 4.5 tons 2186 Michael on charges placed at 1.25 centimeters or 0.125 meter. Thus, the second George has got negative two point do for my Tokudome. So this just put the negative sign 2.252 point 24 transgendered on 86 Microcosm divided by are the radius or the distance is 1.8 meter or 0.1 eight zero. So this is the potential with respect to the origin. Now serving this number, we get that the potential is 2.12 times 10 to the six. I won't. Now, if we call this point to BB and we're trying to find VB, then that distances the other ones and the artist would be replaced by this which I am going to write down straight. Que is nine times 10 to the nine charge 4.5 times tented us six for the 1st 1 and then using the better for us, we will have 0.125 square. Thus 1.5 centimeters 0.15 square. This is a distance minus 2.24 times changed on 86. That's just there. The distance for the second. Ah, you know this sign. This line becomes 0.18 squared state of porn 015 square. Now I would have passed it in the calculator already on. This comes out to be one point 21 So I'm standing there. Six world

In this question we have two point charges on the y axis. The positive charge 4.5 micro cologne. Is that why he goes to 1.25 cm. And then uh negative charge negative 2.24 micro column is uh 1.8 cm below the X axis. He wants to find a total electric potential at the origin and at the .1.5 cm zero. Okay. So to find the total electric potential. Okay. So we just need to some the individual contribution because electric potential is the scale of the quantity. So uh we just need to some of the individual contribution. Okay, So at the origin. Okay, I'm going to call this Q one A Negant Charge Q two. And this is KQ one over R one plus K 2, 2/2. So you just substitute the numbers. It's okay. Is 8.99 understand the part nine. All right. And then to one is 4.5 times. And upon negative six divided by 1.25 times. And the negative two minus 2.24 times. And upon negative six divided by 1.8 times. 10 to the power negative too. So, using a calculator, um the answer is 2.1- 10. 10 to the power six votes. Okay, So this is the answer for a they have a baby. Okay, at the point 1.5 cm 00. Okay, the electric potential. Okay. Oh yeah. Okay. It's still the same General phone KQ one over R one plus KQ two over our two at this time? The R one Is this distance And are too is this distance? Okay. So we need to use uh category serum to calculate R one R 2. So we still on for dinner. OK. and 7.9. And then 21 is 4.5 times 10 to the -6. Then our one is squared off. Um zero point mhm 015 square plus 0.0125 sq. And then my nurse 2.24 times sent upon negative six by square roots off 0.15 square plus 0.18 square. Okay. Then using a calculator. The answer is 1.21 Hence 10 to the power of six books. All right. So here are the answers for parts A and B. And that's all for this question.

So So now we're starting again. So we're going to look at the situation where we have to point charges and we're going to take a look at the electric field that calculated for them along the way. And so I've already started here by drawing our situation. So we have our two charges, uh, minus six point two five and a clue here and then minus twelve point five mental, two rooms here on the right, and we're going to take a look att both point a and point feet and calculate the electric field there. And then also from port on electric, felicity and so for party. And we want to calculate the election field that point a here, produced by these two point charges. So thankfully, we got them in the line and we're just going to take a look at the equations we need. So on electric field from point charge one over four pi. I'm not time cute. Just the charge of the quick turn over r squared the distance to the point. And then we also want to keep in mind that e total. At some point, it's just going to equal with some of all of the electric fields from all of the point charges acting on it. Okay, so in arcades that this is going to be even. Are you eating plan? We have to to protect it. And then you want to keep the mind. Also value for one over four pi ups or not, you are conversant equal to nine. Ten to the ninth. Noon time Meters squared. Coolum squared. Okay, so now it's actually then calculate this green. So even so, we'LL call of the charge in the middle Here, charge one equal to one over four pi. It's not time to over our square. So are in this case, is going to be fifteen centimeters. Thank you. Find a six point two five nano Cool. Um but we want the value, not my unit. So we're gonna have to move Nano Cruella Mine is mine alone and then we want to do meters, centimeters, centimeters No should be fairly comfortable doing that. And now eat too. So here thinks we'LL get a little bit tricky. So here we have actually the charge on the opposite side. And so some of the negative charge more than I have to flip it sign because it's going to give thie officer contribution. Oven ought to feel here for this one. We're just going to call positive and the distance ten on emissions squared. And so when you take the time to plug in the numbers here and actually they calculate it, he will call it Okay, it's going to be equal. One, three, seven i zero never her cool pet. So fairly easy enough. The only point we need the mind is way have this fine convention. So it's pretty easy to see from the picture itself. We have to same find charges, but they're on opposite five, and we want to look at all they're going to ask you there. And if you're familiar with the play of physics, it's sort of like a destruction destructive interference. Okay, maybe that's for later date. So we'LL move on to a party where we're going to capture anything, what to feel at Point B over here, and so we're going to do the exact same way. So you won is going to be this guy here and so we don't have to do anything with the charges. We can just carry this negative. Fine. All the way through. And then we have Q to find a six point two five, you know? Nah, no. Cool. And then now our distance again. Ten centimeters clear. Okay, so you could remember the ten to the minus nine here. Me too. Covenant. Defector. Have one over for pie on that time. Twenty five, then a cruel, um, again, he remembers that Nano Coolum here in here will, uh, cancel each other out, man than some of all the distance here. So it's going to be thirty five centimetres. Point three five leaders and squared. Okay, Fairly easy enough to do in this case. So, uh, only calculation to you, But you should be quite comfortable enough here when we go out to some of the two electric field. And we solved up off the electric field, pointy and the electricity of the point. Thank you. No, finally part. See, we want to try and find the force If we played a proton now and point day, so, yeah, we're blue protest because remember that a proton has the hard of you one point times ten to the minus nineteen. Cool. Okay. And so now, here We're going to need an equation for Fourth Colonel Electric and some charges. So electric force going to be Q time. So you being the charge that we're dealing with the charge will be the charge of the proton and easy. So now that we're dealing with point A, this is going to be he's electric field the fourth, eh? This equal to cue the proton. So this guy appears this piece time? Yeah. Where is the electric field that calculated over here. So that's one three seven five zero Newton curriculum. So hee okay. And again, we'LL leave the calculation to you. But at this point, you should be fairly comfortable with the situation we're dealing here, so there's nothing to tricky here we have. Ah, the fourth. And so we can remember when we want Teo actually take the direction here. And so the direction of this force is going to be going this place right waken see this fairly easily. We have ah, positive. Ah, charge here being the proton and then we have the larger negative charge over here and it's a shorter distance away. So you're gonna have a stronger force going in this direction. And so we could say the direction here should be too right gently. Okay. And there is your problem. You're finished. No, man. What do I do? What else? What else do I do? My film.


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