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A point charge, q = -5.00 nC, m = 2.00 x10-14 kg, is shot vertically upward froma thin, infinite, planar sheet of uniform charge with surfacecharge density of Ï...

Question

A point charge, q = -5.00 nC, m = 2.00 x10-14 kg, is shot vertically upward froma thin, infinite, planar sheet of uniform charge with surfacecharge density of σ = +4.00 nC/m2, with an initialspeed of 2.00 x 103 m/s What height willq rise above the sheet of charge? Ignore gravity3.54cm0.635cm1.97cm1,2cm2.43 cm

A point charge, q = -5.00 nC, m = 2.00 x 10-14 kg, is shot vertically upward from a thin, infinite, planar sheet of uniform charge with surface charge density of σ = +4.00 nC/m2, with an initial speed of 2.00 x 103 m/s What height will q rise above the sheet of charge? Ignore gravity 3.54cm 0.635cm 1.97cm 1,2cm 2.43 cm



Answers

A point charge $q_{1}=+5.00 \mu \mathrm{C}$ is held fixed in space. From a horizontal distance of $6.00 \mathrm{~cm},$ a small sphere with mass $4.00 \times 10^{-3} \mathrm{~kg}$ and charge $q_{2}=+2.00 \mu \mathrm{C}$ is fired toward the fixed charge with an initial speed of $40.0 \mathrm{~m} / \mathrm{s}$. Gravity can be neglected. What is the acceleration of the sphere at the instant when its speed is $25.0 \mathrm{~m} / \mathrm{s} ?$

Welcome to question number twenty three point four six. Chapter number twenty three, Electric Foot and Chill. We have given that there are two charges. Queue and queue to here and Cuban has five micro column charge. So which is it cause to fire with terrorism and six column and cute too has a cause to to my Google in charge. So this is a coast too, into tenders to minus six Coolum. Both are posting recharge. That means the force acting on Cuban bike. You too is opposed or the repulsive force. So we see that this is a repulsive force. Sins. They have same sign off charges, so force by Cuban on cue too, is towards outward and forced by Q. Do is two on this one. So the question is, find out the exploration off this fear and digestion when his spear is twenty five meters per second. So we're given that initially, when the queue to is that six centimeter distance, six centimeter distance, its velocity of the Q two is because too twenty five forty forty meters per second. So this is yeah for two weeks for a second, so this particle is moving to our scuba NW and Cuban is fixed here. Human is fixed. Your security is moving towards a Cuban with velocity and forty meter per second. When is Cuban and cute you are six centimeter distance apart. So the forces acting between Cuban and cute too and Cuban exert on cue to fourth in this week. But the particle is moving this way, so definitely the particle will dislodge it. But you can well, this late and velocity will degrees until this talk. So the particle has Vela city calls to forty meter per second but the forces acting this way so the particles will have it swear city decreasing, decreasing. And it just so some point where the well a city becomes a hero. But we don't need to care about the particle having well a city close to zero because we are asked to find out the acceleration of the particles for the next deceleration when the particle velocity is because we want to find Mika per second. So this has forty percent. So in the middle of a for some there it has, well, a city twenty five meter per second. So we need to find out this distance between human and too. So that's it. This is Constantino. So we have to find out the day here. Well, let's say this is Crimea. So So this is the so this is deeply This is in question. I have assigned this six intimately requested it, so use different. That's used different single time. All right, so we have used this formula here. That is a cause to get close to having me square can't clinch it for me. And hey, the production of the formula And here the force formula between two and two. Now here's the no cardinal because it cost to force because who mass into expedition. And this is working or decorum. Whatever. Then argue the particle to two has in you silly will remain same here when the particle is at find some final situation. So this has some kind of energy initially and some potential to here. And this will convert into the kind of technology here and the potential energy. So here the particulates higher velocities with the kind of energy is higher and it decreases to find them. But the guy is lesser than you F So this is a course with this one. So we will use this equality to find out the values here. So this is conservation off energy from So let's do the calculations now. So we have gaining silly close to half M V I squeal, which is equals to take this month. Mass is therefore into the industrial Ministry caging into fourteen to square. So this is it. So this is a close to three point Kojiro June, no finding or the cave to find energy, which is half heavy final square, which is this value. So you have how foreign tender so ministry cagey. Twenty five swim and this is a course to one point two five two. No finding out there potential energy, which is you. Why is because too one by four by absence, not Q one Q two over the initial distance between them is six centimeter or zero point zero six meter. So we have nine into tenders for nine and to kill and cook each other. So we have. Do you want here Thank you to hear or what distance, which is zero point zero six meters. So using the Cal collected here, I have finally the value of this is of course to one point for nine eight into Similarly, we can find out the ufl But we don't know that you ever since we don't know that distance between in Cuban Aren't you two finally So we will replace this value as a variable here. So this is Cuban cute too Over de plane. So this is your time now. So using this quantity here we put the value to the case you and Kev and U F ear and final Devil of the Deep Lane. So we have you have because to k I bless you a minus ke f because it cost too three point two plus one point two five minus one point four nine. And this will lose because of this one we have When by four by Absalon two one cue to over different. So deep time is close to three point for for it the value of this is it close to three point for for eight June supporting this valley we have for by Absalon government one minus So Ah, so yes. So this this is one minus and this is also Mama's. So we have Q one cute. Let me write it again. So you're deep pain, this value. So this comes out with three point four for aid is equals to one by four By Absalon Kyu Won Q Do over depression. So this gives us deep time because too one by four by absent note, Q one here, too, over three point four forty, which is a course of Samos forms. So you're D prime gives equals two zero point zero two six zero seven. You can use the calculator here to find out the value that by putting the value the Cuban into here. All right, so we have find out the finally the distance between human and cue to where the particle reaches this much man city. Cool. Right now we need to find out the exploration of the particle many. It is at that instant. So we have if it close to one by four. By Absalon Q. One Q two or what are square? Your art is equals to this much distance. Zero points zero to six zero sale and we don't. So your explanation is, of course, to force over em. This equals to one over for by Absalon Q. One cute to over a square over muss supporting the values here nine into Dennis one nine five into the additional minus six column into six. So too intended to him in six. Over here are square, which is zero point zero two six zero seven We'LL Square over your months, which is four point zero zero two industrial minus six. Ministry Cajun. So finally, we have a cause to three point everyone in attendance flower for Mitya but Satan's work. So this is the unionists with upper seconds. Where is a unit of exploration in the value is three point three one in Davis worked for me. So as a sphere a protest the point charge its speed decreases. But it's explanation keep increasing because the electric force wanted to keep increasing. So that's your answer for finally, so you can take a look and slights again. So this is our first lead Now, this is our seconds right now. This is our terms like thank you very much.

Welcome to the problem number twenty two point two six. So this is what you need to go slow in this question were given that there is a known conducting or the gentle, sweet off charge having uniforms, jar density or surface identity, which is Sigma having five independence? A minus six column per square value. So we have a charge surfaces and city having sigma, and this is a shit possessing one charge density. And there's a cute charge, which is ad distance D. So we have given a key part. In April. We are having Q at distance three. Mix centimeter from the shit of charge. And in second guess we have being caused one pan from Sindelar. So we need to fire the Q, which makes it the motion. It's or it means there. So looking at electric field into this plus sick much. So this is posted jobs so they have to feel is up. So definitely the Q will experience forced to electric field. So this is f hey and FT is your costume Q in and we know that the electric field, due to the shoot off jobs having sick much other city, is equals two Sigma Tau absent. So we have Q Sigma over to Epsom. No, get off. M G force is acting down one. So this is mass M, which is It comes to eight independence minus six kg and years of forced on work and total force should be Jiro, which means there it should be gravity. Plus I have. So this should be mg should be closed too. Q Sigma over to obsess. So whatever the force acting Bala gravity should be balanced with electric force so that the particle cube remains at the same position for remains addressed. So this gives us cubicles to mg times too, you know, or Sigma and G is equal to nine point eight. We get second square and in a world is a close too. Eight point eight five four into the other two minus twelve. Well, um, square by square. So putting all these values so pulling all these values. So this gives us Curie Kallstrom two point seven eight into the Thunderdome Anistan Cola Now look and the formula again This is independent of the distance. If it even if it is a three centimeter or one point five centimeters the same force. Electric forces acting on the Q chars in the same gravitation, forces acting on the future. So it's all independent ofthe distance. This is because we have electric field youto the infrared shit of charge independent ofthe distance. This is independent of distance. It's all over space. This is the manageable of the electric field. The particle is here closer to the shit the same electric force acts. If the particle is very, very far away, the same electric force killed killed. So that's where we have cute for both and people. So this is the answer for your A and people. So the same cue. So that's your answer for this question. Thank you. Watching the video.

So to answer this question, we must use confirmation of energy law. So we can said that the Cayenne tick energies equals cooling fly. In this case, so one have over here. Let's do the expressions and boo. So one have and B squared is equal to cool as well. Which is take you, who is constant times charged one and charge, too over the rays. And since forgiven all these, uh, constants, we just plug it in. And so for velocity, so one half. So let's actually Francis, isolate to the variable. We may not be easier for all of us, So if you don't be squared equal tuned tu que que have a second charge over their eighties times its mass. So that's an arm. Sorry. Make sure you can differentiate your on TV times its mass. So if you plug in all the valleys to time nine times 10 to the power. Sorry, What's cool for the 10 to the power of nine. Can the first charge, which is three. Three my food and yes, which is three Micro Coombs three. Sorry, It's actually the first charges that c five. I mean, it doesn't really matter which one. We, uh, which charge we take first. But I just like to keep it in order of the question time. This negative nine since its micro Coolum and micro is to the power of negative night tend to the part of negative nine times a second charge, which is positive. Three micro, uh, micro cool. So times three times 10 to the power of negative nine over threes, which is eight centimeters. Yep. So which is airplane? You're 8 m and times the the mass, which is just six times 10 to the negative five. Yep. Kg. So six times to the constant. So I'm just referring back that the question to find out these constants and six cents into the negative five kg it's important that we have all these in standard units. So velocity squared. So now we just can compute this on. Actually. Just take the square root of this since we need to do square both sides yet. Hold on. Let me get off this so I can do a proper square with time. Yep. You There is years from now. So now all we need to do is just grab with both sides into the square. So if you swear your port side, we're gonna get the answer. I just thought this interact How quickly we're going to find out if the velocity is equal to one 1 50 m per second and that's it for this one thing.

So in this problem we have and insulating. So it's fear. And this fear, we're told, has a radius of 0.12 meters and it has a total charge of five times 10 to the negative six cool homes. Then we have an additional small charge. Um, of Q equals three times 10 to the negative six cool ums and a mass of six times 10 to the negative five kilograms. And we want to shoot this small point charge directly at the center of this large sphere and see how close we can get. So we shoot it straight at it, and we want to see how fast does this initial velocity need to be in order to get to the point where this point charges only eight centimeters from the surface of the large sphere? So since we have an initial and final point, this is a good hint that we're gonna use the energy conservation. So we simply have energy initial his energy final, and then we have que initial plus potential energy initial is equal to kinetic energy final plus potential energy final. Um, and now, uh, we wanna think about what's happening here So if this if it gets just to the point where it can get eight centimeters away from this surface, since these two cents, a big sphere and the point charger both positively charge, this big sphere is gonna be constantly repelling the point. Charges can be slowing it down and therefore this a centimeter mark will be when the velocity of the point charge actually become zero. So that tells us that kinetic energy final will be zero. Um, so then also, we need to know potential energy of these charges. So remember we can think of it as potential energy is equal to Q r charge. It's moving times the voltage difference that it goes through. So now when we plug this in, we have 1/2 m the initial squared plus que voltage initial as equal to Q voltage final. So now we need to figure out what this voltages for a large sphere remember, if you're outside a sphere, we can we can pick a spiritually symmetric object and treat it as a point charge. So therefore, the voltage outside of this fear everywhere will simply be equal to the voltage from a point charge which is just a total charge, divided by four pi Epsilon, not times the distance you are from the center of this fear, So plugging this in we have 1/2 m. The initial squared plus little Q times Big Q over four pi Epsilon Not and now we need to find the initial distance. Um, so that initial distance we're just going to call our initial. For now, it's one over, which is equal to Q times. Big Q over four pi efs on not are fine, okay? And now what we're trying to find is this initial velocity that we have to shoot this object with. So, um, one thing to notice is that if we have Q Q over four Pi Epsilon, not our initial well, we're told initially the object is starting very, very far away. Um, so we can treat this as cake You over for pie? Absolutely not. Times infinity or in the limit as our initial goes to infinity and this just become zero. So now our equation simplifies immensely. We have 1/2 mass times initial velocity squared. It's simply equal to K. Q Q Q Over four pi. Absolutely not. Times are final and then remember, our final has been measured from the very center of the large sphere out to the point where it is so. Our final will be equal to the radius of the large sphere plus 0.8 meters, which will simply give us Ah 0.2 meters. So now solving for the initial, the initial is equal to the square root of two Q Q over four pi epsilon, not m times R f. And when you plug in all the given values in the problem, you just find that the initial is 150 meters per second.


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