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Three charges are arranged as shown in the figure below. Find the magnitude and direction of the electrostatic force on the charge q = 4.84 nC at the origin. (Let r...

Question

Three charges are arranged as shown in the figure below. Find the magnitude and direction of the electrostatic force on the charge q = 4.84 nC at the origin. (Let r12 0.280 m.)6.00 nC0.100 m-3.00 nCmagnitude directioncounterclockwise from the +X-axis

Three charges are arranged as shown in the figure below. Find the magnitude and direction of the electrostatic force on the charge q = 4.84 nC at the origin. (Let r12 0.280 m.) 6.00 nC 0.100 m -3.00 nC magnitude direction counterclockwise from the +X-axis



Answers

Three charges are arranged as shown in Figure P15.11. Find the magnitude and direction
of the electrostatic force on the charge at the origin.

All right. In this problem, we have to set up. Ah, So this is the origin, and this is X equal negative 0.3 meters. Ah. So charge with 59 acorns. His place here, and, uh, charge negative 69 of clubs and placed here and at X equal 0.2 meters. A charge equal full. None of combs is placed here, So we want to find out the force on this one on the scented one meal. One excited by the other two. So, uh, become my forces has expression one over for pie. Absolute knots. So the force exerted by the left one. As you can see that this is positive, this one's negative. So the bulls, excited by this one's pointing to left. So this is, uh, five niner corms. Times negative $6 forms. Bye. Bye. Ah, 0.3 meters squared. And the fool was excited by this one's pointing to the right. So this is minus for none of qualms. Times negative. Six niner combs Divide by 0.2 meters squared, and that you can just do the calculation directly. And you can see that the solutions to 0.4 Michael Newton is and this is opposed a value. It means that the force, the net force on this charge is pointing to the right. Okay?

So for Problem 20 were given our X and Y coordinates on also our church particles that corresponding revisions. Have Q 1 23 at 230.2 m and 0.3 m and origin, respectively. So we are toe finding it electric forest at point Q. Three. So first we need to go to the free body diagram of country. So yeah, uh production for us at Q and Q T and introduction for us. Our Kyoto Q three. So let's call it us if Q one and Q two so we're in that first will be ableto f g one line us if Hughton Okay, so this is quite okay. Q one Q three divided by the distance between them, which is 0.2 screw minus. Que Q to Q three divided by the distance between them, which is 0.3 m squared so we can fuck throughout the G. Jeez. 0.99 times 10 days from the nine multiplied by quantity. Cuban times glittery with these for understanding student active. 19. Want to buy six times 10 raised to the negative name, divided by 0.2 squared minus five times 10 degrees to a negative name multiplied by six times and restore the negative name divided by 0.3 squared. So calculating this, we get the that electric force at Q three off the tree, so this will be two point for them. Stand his to the negative. Six. Newton's indeed positive X direction. So here is our answer.

Hello. So the question is from electrostatic given that charge Cuban is placed at a region. So if we draw a line So Q one is placed at origin. Okay. And it's coding it out 00 and other charge Q. Two and Q. Three hour placed it given it you to to all placed it You .1 Age. You intend to the power -8. No Q. To charge. Yes Please stay. And to your .1 and two. So that place is 0.1800. And the charges Q. two. Let me like the magnitude of you going to do to you also. And third charges placed it The U. n. Let us this is the point zero and your .24. And this is guilty. Now the values of Cuban to Cuban is 1.4 into 10. to the power -8. She was too -1.8 into 10. to the power minus eight column and 2 3 is equal to 2.1 into 10. to the power -8 column. Okay now we need to evaluate the value of electrostatic falls on charge. Beauty falls on this charge. So you two is negative so its forces inward and Cuban is positive. So it's false is outward. So this is false on three due to two and this value is false on three due to one. Okay, so let me evaluate the value of after even that is equal to one x 4 by absolute note into mhm. You went you three over All 1. 3 sq In two direction is J. Okay it means positive by access and after they do in the similar ways. Take me like this then I will substitute these values one by four by capsule. A note Q two Q three Over all, 2, 3 square. And the direction is along exits direction is 0.180. and Y it may like you need director you need to factor out to trees. 0.180 into I. Okay minus zero point to fall into. J. Mhm. Divided by squared 0.18 sq plus 0.24 square. Okay, so the value of our +23 unit vector is equal to. Yeah, let me evaluate the value of this unit vectors. Mhm Yeah Square with 0.18 sq 0.18 square plus 0.24 square. Okay, so uh that is taking the reciprocal of it? Multiply 0.18 So that is 0.6 into I Okay minus 0.8 & two. In the similar way we can evaluate the value of our two to you. Also Our 2 3 is equal to Do you .1 age square Plus 0.24 sq. So that will be zero 09 That is our 23 square 0.9 m script. Okay. And I won three. Let me evaluate the value of 13 So when three is okay This is a region and 0.24 sq 0.24 m2 square. Okay. These are the values of our penalty and now it is the time to substitute these falls. Sonett folks will be, let me value it. Victor F. That is victor F. 31 plus F 32 So after everyone is Taking one x 4 by actually not woman. And the country is also woman. They love to trees. 2.1 into 10. To the Power -8. and inside it. So one is 1.4 entertain to the power -8 divided by I want this you're going to fall square and in their direction, J plus you two minus that is already compensated in that direction. 1.18 to 10 to the power minus eight, Divided by 0.09 in two unit rectories. 0.6 I minus 0.8 G. 0.6 i -0.8 G. Okay so let me evaluate the value of this force. So they will be equal to mhm Firstly first x component is 99 into 2.1 E minus eight. X. component I it component multiply 1.80 -8. Do I did by 0.09. Multiply 0.6. So that will be 2.268 to 10 to the power minus five into I Newton. Now the jet component is let me check whether it would be positive will never do. Okay, So that will be 1.4 E minus a. Divided by zero point in your car. Scream minus 1.8. D minus eight. Yeah, divided by multiply biased. You appointed Do I did by 0.09. Multiply 99. 32.1 a minus eight. So that will be one plus 1.56975 into 10. To the power minus five G. This is basically in the vector from now, we need to evaluate the magnitude and direction on charge. Beauty. So magnitude. If we take it victor F magnitude is equal to that's right Plus 2.268 E -5 squared to the power. So magnitude is 2.7 six into tend to the Powerball -5 Newton. And direction is F. Y. Or what fx In general in the world is equal to In the vector from this is this, this is victor F and the magnitude is 2.7, 16 to £20 minus five, and direction is f Y. S 1.569. So do I did buy 2.268, So that will be 34 .7° with respect to the positive x axis. This is like this 34.7 Degree, and this is what this is F F X. This is their flight. So these are the required themselves. So hold this closure.

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


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