Questlon Comipiotion StatusThe figure shows eighd charged particles fixed in place to form square with an edge length of 6 cm.The diagonal of the square is 8.Scm , ...

In Fig. $24-53,$ seven charged particles are
fixed in place to form a square with an edge
length of 4.0 $\mathrm{cm} .$ How much work must we do
to bring a particle of charge $+6 e$ initially at
rest from an infinite distance to the center of
the square?

24.50. We're wanting to find out how much work it takes to bring this charge Capital Q. Here along this indicated path to this point with thes charges, the indicated distances and away. And with it the charges in these angles are also give it. So if we think about it for a second, we're given quite a bit more information than we need here. Um, for example, the past doesn't really matter because we know that since the electric force is conservative, that the, uh changing potential energy from one point to another only depends on the distance between them and not on the particular path taken. So we don't need this. Similarly, the potential between these and this is the only depends on the distance is so we don't need that either. And so we, uh, just write the work down is the change in potential energy. So this is one over or by uh, absolutely. I'm not factor big you out of this. So we have kyu won over to D plus you two over D. However, um, Q one is negative. Two times you too. And so this actually all cancels out and it take zero network to bring this charge to the indicated point

The question we have given uh the old chinese police at the corner for uh the squads and the distance between them is to do something about it. So we need to find the direction and obviously my tour of political, I mean the direction with the back to. So a very simple question. What we need to do over heritage. First of all we will cloud that. I ground right associate the stage. Uh huh. Like this one and that will try to return. So said this is a square. Mhm. Yeah like this and again this is the other side the Royal Winter or let me draw by the pain itself. At this age, the Squire. Okay people might be some not what looked like that one but see this is a square. Okay. And now what we do is do is whatever this is cute charge. He won't charge over here. This is cute to charge. This is hugely charge Q four charge. Sorry. This overhead you for judge. This is you five jobs. Q six charges and Q seven U seven charts and you'll charge. OK I'm going to write the magnitude of each one. So Cuban equals 23 plus three. Obviously Q two equals two. EQ three equals two minus of five. U. E. Q four equals two minus of two. E +25 equals two plus of three until six equals two plus E. And to mm seven equals two minus of five. E. Curate equals two E. So the very simple question each have a distance of D. Which is equal to two centimeters two centimeters. So I need to find the uh my Children direction of the at the center. Okay so a very simple question to failure to this cute will be upward direction downward direction and just will be uh our direction. And obviously the distance between these are the so this will be to see the you know that the electric field will be same for this one and they survive charges is cm and distances the same and politics. And so this cancel out this one and similarly for this one and this 13 and three in this cancel out this one that similarly for miles heavy. And when it's heavy this cancel out this one. Okay, so Only electrical uh Damien over here that due to this one I will defend to the Cuba in this direction. And that Q4 is also in this direction. Okay, because this is negative and the positive both of them have the same direction. So they will just end up. So in it magnitude wise that will become sought to be E eight plus of equal because they both have in the same direction mandatory budget. And obviously what will be the direction of this one? In the X axis? Because prolonged accesses. So this will be in the extracts and all that means I cap. So we can write it A J. Mhm collective E. In terms of vector that is E eight which is one upon four pi epsilon willkommen then uh Q. Is what you ate you ate. So you eighties right mm and plus two, four and many to only because we have already resulted in direction. So we do you not use minus sign over there? So E plus E. On the exchange that is G is quite so the easy but the square so there is about 0.2 degrees centigrade 0.2 m into a cap. Because if the direction in the X direction. So when we put the value fund by Photo absalon or which is which is equals to nothing but 8199 into and the development of nine into E three E. So three into 1.6% of the power of minus 19 Upon 0.02 square cap. So when we do calculate in, it comes out to be 1.08 into gentle develop -5 Newton particle. Um, Camp. Okay. Thank you.

24 points. 60. So we have this situation. We're moving an electron from far far away, um, to be a distance of eight centimeters away from some unknown charge. Q. And we're told this takes a work of 2.16 times 10 to the negative 13. Jules, we have to do, um, we want to find the charge on this ball, and then we imagine that the charge is split up into these both, uh, smaller charges. And then we moved the electron to the middle of them, and they're all eight centimeters away from the center here. And we want to find out what the change in potential energy is. So first we know the work, and that has to be equal to the charge of our test particle times change and potential. So then negative E times Q over four pi epsilon, not R. This must be equal so that they were given the 2.16 times 10 to the negative 13 Jules. And so then just putting eight centimeters in for our and the amount of work we have been solving prick you. We get the queue is equal to negative 1.2, I must tend to the negative fifth Cool owns now in Part B. We have the same net charge, and the electron is the same distance away from all of it. So here, bell to you is the same as as the work Well, if this is true in general, but it's also the same then as before, because in terms of the potential energy, moving it to a point where it's equal distant from charges that add up to the same charges. In this situation, the actual amount of work is the same, and if you like you can work through it the long way to verify that. But this is also sort of a conceptually important thing, and so you should be able to recognize situations like this where there's ah, something that could potentially greatly greatly simplify what you have to do. And also I need. It's a deeper understanding of the physics that just like adding up the potential from each charge and then discovering you get the same answer and then, you know, not really appreciating the significance of that

Okay, So if we look at the diagram that's in the textbook, I modified it a little bit by color coding the charges or the same charges as we see here that the red dots are scene, the green dots are same, and similarly, the blue dots are seen, so the red dots are plus three e. The blue notes are classy, the green dots are negative. Five. And finally, there's a black doctor. Just queue, for that's negative Too weak. Now we see that diametrically opposite charges actually cancel each other because that electric field for the diametrical opposite charges cancel each other. Because we see that cute, for example, que tu and Q six, they have the same charge. So electric Field, produced by Q To will be cancelled by Q six and same thing for these red dots and green dogs. The only charge that will survive here is Q for and Q eight because they are not similar and the direction will be pointing on the right side because Q for his negative and Q eight is positive. Also, to calculate the electric field, we have to add the electric field for Q eight. The magnitude plus the magnitude off electric field for Charles Queue for So for the magnitude, we don't care about the signs. So for Q For this will be, um, twice e divided by four pi Absolute Nordisk red. And for they spark, we'll have e divided by four by absolutely not the spread as well. And then we add them together, which finally will give us treat you over four pipes. Eleanor D squared on that's equal to three e by four pipes learned discord. And then finally, we use the numbers. We see that the electric field is 1.8 times into the bar. Negative five. New convert. So if you're wondering how we got described here, so the way we calculate electric field is we put a unit charge in the middle off cue for and Kuwait and receive that the distance from Q eight and the black small dot here is D. Since and since it's a positive charge, so the electric field will point to the right, and then we have ah, this big black dog queue for and this small dot dot since Q for his negative, So the electric field will be again pointing on the right side and that that's why we get this over. All rights, a direction. So we're calculating the electric field on this point. And because of that, we have this de Aza distance here. And as we mentioned that we're calculating we're taking the absolute value for the electric and so we don't care about the sign of the charges. So that's why we are able to add these two charges. And that's where we got Treat you and three e finally in calculation off net electric field. All right, Thanks for watching. I'll see you next time.