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Thren particlas have the following charqe and position coordinatesParticle I5 at the origin of the coordinate systeriand has charga 0f-17.38 10*6 C Partlcle located...

Question

Thren particlas have the following charqe and position coordinatesParticle I5 at the origin of the coordinate systeriand has charga 0f-17.38 10*6 C Partlcle located on the axis at #7.35 10-J neters and nas charge 0t +92 * 10 6 @ Particle located on the axis at + 9_ 10 * mneters and has charge of -70 10*6What Is the angular direction of the total electrostatic lorce vertor acting on charge 4? degreesThe angular direction should be in "standard convention; which counter clockwise from the pos

Thren particlas have the following charqe and position coordinates Particle I5 at the origin of the coordinate systeriand has charga 0f-17.38 10*6 C Partlcle located on the axis at #7.35 10-J neters and nas charge 0t +92 * 10 6 @ Particle located on the axis at + 9_ 10 * mneters and has charge of -70 10*6 What Is the angular direction of the total electrostatic lorce vertor acting on charge 4? degrees The angular direction should be in "standard convention; which counter clockwise from the positive axis_ Also_ dont forget to use 'degree mode' on your calculator for this problem



Answers

Consult Concept Simulation 18.1 at for insight into this problem. Three charges are fixed to an $x, y$ coordinate system. A charge of $+18 \mu \mathrm{C}$ is on the $y$ axis at $y=+3.0 \mathrm{~m}$. A charge of $-12 \mu \mathrm{C}$ is at the origin. Last, a charge of $+45 \mu \mathrm{C}$ is on the $x$ axis at $x=+3.0 \mathrm{~m}$. Determine the magnitude and direction of the net electrostatic force on the charge at $x=+3.0 \mathrm{~m}$. Specify the direction relative to the $-x$ axis.

For this problem we have five particles arranged as shown Where particles 1 2 and three are 10 units away from particle five. And particle four is five units away, particles 123 and four. I'll have a charge of negative E. And particle five has a charge of positive E. And we want to determine what is the exposition if particles one and 3 can move, what is the exposition of particle one? If we want to rotate the direction of the net force on particle five by 30 degrees and then in part the if we wanted to then move particle three such that it rotates back to its original position. What would the X. Value of exposition? Particle three B. In that case. So let's start by sort of making our assumptions and gathering information for particle a. Here. Um I can see that because Particles one and 3 have the same charge and are the same distance from Particle five, the magnitude of their forces would be the same but they're in opposite directions. And so the A force from one on particle five. And the force from three on particle five cancel which means that the some of the forces in the X direction Will be equal to zero in the y direction. Particle four is half the distance away from particle five as particle to is which means that the magnitude of the force from particle four is going to be equal to four times the magnitude of the force from two. Because if we think about columns law, it's an inverse square law. So if you Double The distance then he force is 1/4 as much. Okay, this also tells us that the net forces in the Y direction. So tha Originally is equal to 90° We want to rotate that 30° counterclockwise. So now our new fatah Is going to be 120°. We just added 32 90. Um and so If data is equal to 120°, we can figure out what tangent of data would be equal to. So tangent of our new data would be tangent of 120°. But that should also be equal to the y component of the force divided by the X component of the force. The why component of the force is going to be again three times the force from to you. Because we have a for sorry we have four times the force from particle four and then one times the force from particle to their in opposite directions. So for minus three we'll leave you with, Sorry for -1 leaves you with a net force of three Times F. two in the Y Direction. And in the X direction that is where F. One resides. Uh So we will so that's going to be the force from particle three minus the force from particle one. Um And we can note that particle three is going to have the same magnitude of forces particle too because again the charge and the distance are the same. Uh So we can rewrite this yet again to be three F two Over F to -F one. So now we want to solve for F one And you should get that F one equals F two Times 1 -3 divided by the tangent of 120. So I skipped a few algebra steps there, but it should be pretty straightforward to see that F one is equal to F two times 1- The Tangent. Our Sorry, -3 over the tangent of 120. So again, we've got to erase to make space but our next step is to use columns law to relate the magnitude of F one to the X position of Particle one. So F one is equal to F two Times 1 -3 over Tangent of 120, but it's also going to be equal to one over for pie. Absalon not key, one is E, Q five is E. So we'll have e squared over in the distance. Here is the X value X one that we're trying to solve for. So over X one squared And we can do the same thing for F two. So this is going to equal again, one over for pi epsilon. Not again we would have E squared, but now it's not going to be over X one squared, it's over the distance 10 here squared. So I'm just going to write D here but D is going to be equivalent to 10. So I'm going to write that down somewhere. So I don't forget And we can't forget. Our 1 -3/10 Of 1 20 here. Sorry that's being squeezed into the side but we can go ahead now and do some canceling 1/4. Perhaps learn not cancels. He squared cancels and we're left with When you solve for X. That X squared is equal to D squared over one minus three divided by tangent of 1 20. And so when you actually get a value for X we would find that X. Is equal to 6.0 five. So if X one is 6.05, that would give us A rotation of 30° counterclockwise for part B. We noted that originally F one and F three canceled and that is what made the force in the direction it was originally so we need F. One and F. Three to cancel again. And so if we need to move F. Or sorry, if we need to move particle threes so that they will cancel then particle three also needs to be moved to 6.5. So I'll note that X one should be a negative six point oh five because it is still left of the why access but there we go

So in this problem we have four charges minus e minus, e minus and minus C. I'm its charge of policy at the center, the distances are given 10 10 10 centimeters and five centimeters. So if the force on plus ee doo doo, let's say charge too, was some f than F is equal to okay e times minus E by 10 centimeters squared. Now notice that the minus means that the forces in the downward direction on because the charge magnetar and the distance of the same, the same force will be accepted by Charge one and charged three. But charge forward is a different matter because charge for is closer, the force will be larger and the forced her to charge for is K E minus e by five square because it's only a five centimeters, which is which means that this is four times if so, the net force. It's simply notice that we have two forces f and F in the hearts under the direction 13 If I'm sorry, 1 14 and another Earth, which means the Net force is in the awkward erection and it's equal to three years now. After doing some changes, The Fords has rotated by 30 degrees in the counter clockwise direction. Let's see, this is the F Net on for this definite. There must be an FX, the ex competent of the force. No, because than 30 degrees is one by all. Three. It means that FX by three f must be equal to 10 30 which is one barrel. Three. So ethics is ruled. Three F now ethics is the some off the force. Do tow Charge one and charged three, but they'll be in opposite directions. So that's if one minus three. No, because we changed the position off Charge one in case a but not charged three s reveals just B f. So this gives us a solidly question. Road three f is equal to F one minus f. So f one. It's simply wrote three plus one f. So the fourth needs to become one pass through three times the initial force. No, because force is inversely proportional to a distant square, we can write F one by f toe is D two squared by Demon Square, which means Route three plus one F, which is everyone by F is equal to ditto square which is the distance initially. So that's 10 centimetres squid divided by the final distance, which is Let's call it something square and that is it. The F gets cancelled. Andi is equaled. Oh, if you're simply square root on both sides, 10 centimeters divided by square root of one place fruit tree. This gives us 6.5 centimeters and that is it for part two. We want the force to go back to its original position. Which one? Which means that the force in the F direction must be zero. Which means because the Charge one is now closer to the center. We simply need to pull charge three to the same distance so that the two forces, due to the charges on the X axis, cancel each other simple as that. So for part B, we simply move Charge three to distance six pond, 05 centimeters. That is it. Now, One thing to notice is that why this distance is 6.5 centimeters, The X coordinate would be minus 6.4 centimeters because charge one would be on the left side of the origin Simples that

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.

Here for the solution. Used Pythagorean Forum to solve for the distance from 2 to 3 here by using the Pythagorean theorem, we get sequel 200 0.18 m square plus 0.24 m square, and from here he gets equal to 0.3 0 m. Have electrical. Two k Q one Q two by our square now sold for the force by both particles on the third. So F one and three equal to K here by substituting the values of yeah, Cuban Q to end our and sold for this we get f for one and three. We get 4.54 multiplied by 10 to depart minus five of world. Now for I have 42 and three equal to K. Harris will develop you and killed three and ask Then, from here we get it. 3.74 multiplied by 10 to the power minus five and downward and rightward. Now, after when three has X and y force so sold for each in other mm. To do this though need to solve for theta value can do this with the given length values so cheetah can t take all to 0.24 m divided by 0.18 m. And from here we get to take her to 53.13 Larry now for the wife sign 53.13 degree equal to y. Divided by 3.74 multiplied by 24 minus five. And and from here we get y equal to 2.99 multiplied by 24 minus five. And for ex costs 53.13 degree equal to X, divided by 3.74 multiplied by 10 to the power minus five. And and from here we get X equal to the 2.24 multiplied by 10 to the power minus five. And now find the some of the vertical force is the force from particle to is downward. So it is subtracted from the force upward. So we get Force one and three, minus 42 and three. So it will be 4.54 multiplied by 10 to depart, minus five and minus 2.99 Multiplied by 10 to depart minus fine. From here we get 1.55 multiplied by two and three par minus five pen. Now the vertical and horizontal forces add up at an angle to write an upward. Using Pythagorean tore, um, one can solve for the value so have finally equal to underwrote 1.55 multiplied by 10 to depart minus five and whole script plus 2.44 2.24 multiplied by 10 to depart minus five and whole square. And from here we get difficult to 2.7 to multiply by 10 20 power minus five. And yeah, now use the values there to solve for the angle of the vector. So angles, Tita. So 20 take all 251.55 multiplied by 24 minus five and divided by 2.24 multiplied by 200 part minus five. And And from here, we get to take her to minus 34.7 degrees. So this is a complete solution. Step by step with the explanation in detail. Please go through this


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