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[30 points] Franklin's Experiment Consider Twa unitorm circular disks charge per-areasof +o with radius And and centered On Teit the same axis; surfaces and th...

Question

[30 points] Franklin's Experiment Consider Twa unitorm circular disks charge per-areasof +o with radius And and centered On Teit the same axis; surfaces and thev ar parallel and the tolloning 4asumu separated by that the electric perpendicular distance fields produced by either sheet For for an intinite sheet: are the Sie(a) [5 points] Sketch the everywhere, total (both plates combined) electric Ad write down Ihe field lincs everywhere. magnitudle of the total electric field+0(b) [5 points

[30 points] Franklin's Experiment Consider Twa unitorm circular disks charge per-areasof +o with radius And and centered On Teit the same axis; surfaces and thev ar parallel and the tolloning 4asumu separated by that the electric perpendicular distance fields produced by either sheet For for an intinite sheet: are the Sie (a) [5 points] Sketch the everywhere, total (both plates combined) electric Ad write down Ihe field lincs everywhere. magnitudle of the total electric field +0 (b) [5 points] What is the voltage difference, AV, between the two disks? (c) [10 points] In terms of the voltage difference, AV, what is the magnitude of the force of the positively charged disk on the negatively charged disk?



Answers

Figure $19-33$ shows a system consisting of three charges, $q_{1}=+5.00 \mu \mathrm{C}, q_{2}=+5.00 \mu \mathrm{C},$ and $q_{3}=-5.00 \mu \mathrm{C},$ at the vertices of an equilateral triangle of side $d=2.95 \mathrm{cm}$. (a) Find the magnitude of the electric field at a point halfway between the charges $q_{1}$ and $q_{2}$. (b) Is the magnitude of the electric ficld halfway between the charges $q_{2}$ and $q_{3}$ greater than, less than, or the same as the electric field found in part (a)? Explain. (c) Find the magnitude of the electric field at the point specified in part (b).

I see well over here. Uh even the following this on the and first of all let distance artists even as to sentiment that Protonix president distance from the excesses. So basically, first of all, we will what we will do it. We will in the first part we know that let jellicles to our okay, so the articles to our and the distance from the center and this is our distance between them. So the minute of has been due to the central electron at a distance as it is even by nothing. But so first of all we will draw the diagram is well because because without diagram we can't. Okay, so you see the thing over here, this is the electron over here. This electron and water over here decision upload all over here. Did you have questions of girl and yeah, this is E. C. This is S electron s Okay. This is obviously this is a tremendous support. Um so the dependable way to ask this one because this is because uh this is from china and this is why that's because electron hasn't had negative. That this is uh this will be this our distance that will do nothing but the the square plus our square. And this will be also the square plus at this point the P and the proton. This is where I exit. This is sexist. Well, which is to this is due to. So now we know that what that is easy. The mantle of electronic resistance, the do the central electorate distance is given by what Due to this one cent electron, you see that will be care easily upon during the square, right? Because this is a preventable distance itself. So now we have given Kiev hello, we already know keys nine And a tron 2600 years of -90000 negatives. So we're just talking about the manager because we already know that action will be the death. And and you describe your given to something. So that will be nothing but Europeans. You got to Squire. So when we do calculate is he comes to be 3.596 into the developer of -6 Newton parque colon. And but the action of the field is to be negative because it's so obviously they have to kill a negative is because this will be the government threats. And so when we calculate in terms of the breath and as well, so this will be in the minus of Jacob. Right? Mm hmm. Well now in the next part, in the next part of this question according to the cigar or gentle component of the or little component of empty killed due to the uh side electron cancel. So why why why let me explain it to people. You do this one. Right. Okay. So this is theta So the single women and even sita or the single in the theater to E. Of Bastida. And again of cost it will be considered because they have equal magnitude and a positive direction. So this will this will be considered because this is the same steps and ST artists. So only the particle component that means of scientific any of santa. We don't even know what a mm hmm. So Darwin's E. X. The second part E X. That comes out to be yeah, our cake. You okay. E. S. Obviously the side deserves our squad And to sign Tita. And two times of this one. Okay. So this will do nothing. But yeah, two times of KESR Square upon Santa. Now the distance between the side electron, end of point is even we are because you're going to get the surplus ours. But when he's called to our, so when this is all the and so this will be get a special satisfied. So Aristotle satisfied to help. So we can write it in jail. I just R squared equal to two into K. E. S. Sign of tika upon our exports are tools that wins the are square into two. And to consider so this will be K. E. S. Sign of tika upon arts. But right. And and K is a sign up sheet up on our squad. Right? So now you can write 90 to nothing but scientific equals two. Send in this triangle. What we do what we can do to this base which are Upon this one or 2 up. So our and our uh canceled out. I don't have experience a lot of sensitive and we want to So you can also put the value of scientific as this bill comes out of the K. E. S upon through to our esquire. Right? So I'm going to just prove the values of X. Comes out to be 8.99 Into kind of a lot of nine into the S 1.600 -19 about this photo. Or do you want one for one? Obviously into these are areas where you're pointing to is quite So this comes out to be I guess He s comes out to be two piles 4 3 into the power of six And the power of what? 10 to the power of what? And we got a uh -6. You can park along. Okay. No in the next part now Let's get equal to our between right, so in the C part we have to take equal to our by 10. Right? In the scenario we know that E. C. Trying to sell a people to do this one. K E C. The EPC because this is just a squad. So this will be 8.99 to 20 out of nine into ec 1.600 minus 19 Upon this journey there is even but our squad so original point to upon a 10 square. So this comes out to be You see everything through central judge that their control to be 3.596. Independent Arab minus gentle devour of minus minus minus. What was that for? Right, okay. And if you take it again. So when you're with people who are trying to do the right and is he with this one? And obviously the direction in the negative way that some. So this value minus of Jacob. Right. So and in the next part the next party according to the figure the ordinary component of the electric field do the side trump council. So that money that you can really E. S. In the next scenario that will be two K. A. Because to be already calculated E. S. Times of scientific obviously both of them are really comparable tells a lot are exploring the scientific. So it comes out to be I think I guess are equal to sustainable are square. So I don't wanna hear that will be satisfied and what it is just one upon 10 R squared up 100. I'm like you know what else I was scared of. 100 and that over there I our school to our square. Oh. Mhm. Yeah R squared plus 100 and the plus artists where it will I described plus a 100 plus satisfied as well. So this will comes out to be 100 plus 1. 100. 1 of 100 are 101 and carried out of the room. Okay. So we'll need to just put all the fellows over here. So when we do good E. S over there that council to be even took out all the values. Then it comes out to be I guess 7.085- 10 to the power of -7. Nugent curricula in in Manistee kappa. This was a thing and in the next part he the rest will do to the central electron and side electron is given by you C. Equals two. We already know is equal to K. E. C. Upon that the square and E. S. Equal do nothing. Work two times of K. E. S. A bone. Our Squire scientific and so we can eat write a report. The value of the scientific. This will continue to K. E. S. Upon our square artist squad. So we'll calculate the value of the scientific. This comes out to be set upon. I didn't esquire plus R squared Develop three. Right. Right. And just like that this death like that. Just like that. Just like a ring. So then limit tending to their tending to zero E. S. Comes out to be back. What will be the es what will be the es we take the square as a common. Okay so when we take the strategy common what will happen to K. E. S. Is constant. There is over here so they acquired and distributed. So spiritual counselor that cuba remaining over there into one plus hours. Quite 100 square three by two over there, severely injured concealer. This will consult the square 31 power will be considered. So when you get into Algeria, when they're tending to zero, what will happen? So when Getting into zero, this comes out to be infinity. Right? So if this is ingenuity and has this type of zero, so this will be undefined or this will be consulted with zero. Like to this issue, then. Okay, Thank you.

So they're given the charge capital. Q. That is a good O negative 6.5 manic alone. So that is then to the barge minus nine Coolum on Judy's of the disc that's given to be 1.25 times 10 to the minus two meter. Now, in the first part of the problem, Uh, we are required to find the electric field at Point X Witches, 0.2 meters from the energy. No, it's a zoom the axis off their disk. Don't be the positive X axis Now recall question 21.11 That is an example 21.11 on. We will lose the situation in order to find that a little food in the first spark. So according to this equation, the magnitude off the electric field is the ex company off the electric field, and that is a condo signal would do it till I'm not dines one minus one or budge art over X whole squared plus one and you don't know that. Now extend our on holding on. You need to find ah sigma, which is the surface charge density. And over here, since it is a disk. The surface jars density is simply charge over the surface area off the disc, and we have to absolutely not let me write that as though. So, yeah, now that is self, the values and just going off. Copy base Fact. Moses. This is a disc. The idea is off. The This is just all a Officer Coates, and that is, by time squared off the radiance, which is capital lovable here. Andi absolutely not as the constant and is equal to 8.85 times 10 to the minus tools. Now we can simply some substitute which of these values over here on Dhe doing that to find the electric field to be one point one four dying's end to the barge. Five. Mutant local. Um, so that's the magnitude off the electric field now coming to the direction. So because the charge is negative than the few lines should be oriented towards, the disk on the electric field has only one component that is the one in the ex direction. So the neck electric fields direction is negative, I cap so we can mark the victor science, since we have already included in that direction, So that's the net electric field in the first spot. Now in the second part, that this becomes a drink if all charges because it becomes a ring. So all of the charges that is that most are distributed to of the disc gets pushed over toe the outer Jim off the drink. Now that's that is when the disc can be considered as a drink. My Rico lost the loot, in example 21.9. So there we got the electric field to be given by the X component off the field only on the physical toe. Pick you X over extract less a square to the power of three over. And here is simply the religious off the rink. Now Kay is a constant and musical do. 8.99 times 10 to the part nine New dumb meters Clash got cool. I'm square, not weaken against substitute all of those values since X has the same value 0.0 do. Only the disk has become every now. So our equation has changed. So, lugging all these variables over here we find the electric field the magnitude off the electric field to be 8.9 times 10 to the par four. No, don't look up now coming to the direction against institute artist Negative. So the electrical lines are oriented towards third drink on the only the X component off the electrical stays and the white component cancel out. So the net field is again in the negative X directions, the negative I get. And again we can market Victor something almost. Yes, it's them ordered into the addiction. In the third part, the disc becomes a point judge now if the charge is brought all together than obviously Ah that this can be considered as a point judge on DDE. You know that electric feud off the point judge is simply take you over. X Square exists the distance off the charts from the center, so substituting the values we get done, I booted off the electric field to be 1.46 Dying standard About five mutant will pull on again. As I explained before, the child's is negative. So the election used to watch the negative X axis hands negative? No, for the last part. Ah, why field in but is getter than feeling part B on why they looked refute in part C is the strongest one, or you can say they literally in body. Part C has the highest magnet has the largest magnitude? No for that explanation. So in part a. The charges distributed all over an area, so the charge, dense agree, is large. So eat differential charge produces are vertical and horizontal electric fields, and in the case in part a hall is on. The electric field is really small, so the next field is relatively strong but literally strong of than part B. But in partly the vertical component. That's all in part favor because the vertical component, the charts density is small. Oh, because now it's a jink as the last. The electric field denigrated is also small. Hence the next thing this smart now in part a on be the field, vertical components are canceled. Oh, so the final necked field is given by the horizontal field component on dhe. This may be considered as loss in field. Oh, because hope, because the vertical component this goes away by canceling out, but in part see the tart. The Darts produces the field without any lawyers, because the chart has only one strong component the ex government on That is why the seemed calculated in Bart, See is the strongest. So overall, the answer is basically because all still radiation. What's changing values off those odds? Density. So, in part it is a surface charge density ah, which is really small because of the spread out off charge spreading off the times over an area. In the second part, it is linear charged density. So that is relatively higher, because just stirring the charges all concentrated along the thing. So the charts transit is relatively hired in Part eight and party and stay little feeling part is higher than partying now. Oh, as I said in the thought part, there is no loss in field because the judge has only one strong component and there is no distribution off judge over an 80 hour. So thanks

In the first part of this question, we're going to tell Claire the genuine potential difference between point B. And so we call this potential differences that we be at much like the relation for Delta V B A. As we be a equals two. Mind it, you don't let's school DX because production differences in the extradition on Delta. Why? Because he had our is in what direction we could like. It does that Delta we be a equals two minus e x ducked out. Uh, why? And because off 90 degree, because the angle between this year and delta Y 90 degree now inserting the values into this equation, uh, you want you ready for data? We be a as we have developed for the excess, uh, 1000 minus 1000 minus 1000 and 200 Newtons local. Um, and then we're before Delta are wise. Three points, you know, sent to me dio and course 90 becomes zero. So this will give us the weather for Delta. We be a as you know what, this is the answer. The first part of this question in second part of this question, we are going to calculate the potential difference between point B and A C. So people Keltner Delta we busy which is a closed toe we b minus with t in order to kill studies that BBC likes tried their relation, dealt up we BC, he calls too minus okay, thanks. And it then Delta R X. Because both are in the ex ex ex it excess and then the angle between them is 1 18 because both have in a opposite direction. Now, instead of divided into this equation will get you ready for that. We will see us that we B c equals two. I get your family, then we have the weather for hey, excess 1000 and 200 per column And then we have the very for this Delta X is Hotpoint Digital zero gravity is far minus two medo And, uh, that cause because I know for 90 degrees equals two minus one. Okay, so this will you are the value for the Dow we BC hey, as it, uh, minus 40 ad world for this is the answer of second part of this question. But see of this question, we are going to kill clear the potential difference between point see And so we need to find Delta. We CIA, which is close to it, is that we see is equals to we c minus were okay outside their relation for this Delta V. C. Well, I t test that we CIA equals two minus he x and then we have delta and they go sign off. Peter here. This you guys are now let's call it equation are to No, we're skilled Florida pita using the Yuan Triangle writing a triangle we can write for the writing Trying glass tables too 10 in worse dungeon in worse over 3.0 meet already wanted by 4.0 So it's sentimentally wanted by 4.0 centimeters. So this will you watch the value 40 ties, tangles, toe 36 point headstone DVD Okay, in certain values into the equation are too you can write data well, you see a equals two minus in tow minus 1000 and 200 new 10 per column and then defended for dental are five points, you know, much bitterness, par minus two meter and then we have the very for cause enough to dies because off 36 point at seven. DVD. So this really was the ready. Ready for do we see as Delta Weezy a equals two? Uh, 40 ed walked. So this is the answer party of this question. In party up this question, we have to calculate the potential electric potential appointed. So we have toe calculate this. We No, there is no difference point. So we cannot kill. Correct We had. But we can assign the weather for me as a zero if we want. Thank you.

Here, we're going to look at relationships with a constant or uniform electric field Between two parallel plates. So we know that the electric field is related to the gradient of the potential potential difference over the spacing. Um, and that is uh, provided that the electric field is in the extraction, that would be similar things if there were other components. We also know that the forests on a particle in that electric field is its charge times the electric field. We know that work done by a force is equal to force times distance. And we also know that the change in potential energy of a particle in a potential is equal to its cute times the potential difference it experiences. So what we're after is to see how work relates to potential energy change. Okay, so hopefully it won't be too much different than what we see mechanically. But the first thing we're going to do is find the electric field between those plates using the potential difference, Which is 360V divided by the spacing, Which is 45 mm. And units will turn out to be volts per meter, which is the same as Putin's per column. Okay, now we're going to put a positive charge near the positive plate and it will be pushed away or attracted to the negative plate and we're going to find the force on that charge. Okay, so we have that little charge sitting up there. Um two point for nana columns Time standard -9 times the electric field, which we just found. And that should be a newton's which will be the same as a column volts per meter. We'll just put that in newtons and it's a small force. Okay. And we'll use that force then to calculate the work done by the field. That's an important thing. We don't have an external agent coming in um and doing anything. So that's just 10 to the mine 1.92 times 10 To the -5 times 45 millimeters. And that should be in jewels if we have used S. I. Units. Right. Mhm. So that work is a positive quantity and people talk a little bit about why it's positive but essentially it is positive because the force is acting in the same direction that the particle is displacing. And finally we're going to find the potential energy change of that particle. So it is moving from the high potential plate. Um and it is going down to the lower potential plate. So it's starting on the positive plate, going to the negative, which means that it is experiencing a negative voltage drop and it is a positive charge should be units of jewels. And what we see is that potential energy change is negative. Whereas the work done by the field was positive and that is concrete congruent with the definition that the work done by a conservative field is minus the change in the potential energy between the particle and the field. Okay, so the work done is it's going to be in an interactive thing. It's working on something and that something will have it potential energy drop.


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