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Four point charges Q are placed at four vertices of a square with sides a, in air:(a Find the direction and magnitude of the electric force on each of the charges.b...

Question

Four point charges Q are placed at four vertices of a square with sides a, in air:(a Find the direction and magnitude of the electric force on each of the charges.b) Find direction and magnitude of the electric field at the crossing point of the square' s diagonalsFind the electrostatic potential at the crossing point of the square s diagonals (assuming the zero potential point to be at infinity)

Four point charges Q are placed at four vertices of a square with sides a, in air: (a Find the direction and magnitude of the electric force on each of the charges. b) Find direction and magnitude of the electric field at the crossing point of the square' s diagonals Find the electrostatic potential at the crossing point of the square s diagonals (assuming the zero potential point to be at infinity)



Answers

Four point charges are at the corners of a square of side a as shown in Figure $\mathrm{P} 23.21$ . (a) Determine the magnitude and direction of the electric field at the location of charge $q$ . (b) What is the resultant force on $q$ ?

Hi, everyone. As soon. Difficult vehicle Fight The Total Force Arm Rescue Force on this will be Have fun in this direction. This will be F two in this direction. This baby have three and this is our foot magnitude of F one F two F three F four teach having gay June July partner Half of government is the site, so net force be with you. Uh huh. Yeah. That son second part. This is the answer of a part. The party Every additional Bless you. We'll ask you. Minus cute my rescue. Yeah, And here it is. Yeah, no mhm. So force all it will be f one. Just believe. Actually, this is er three. And this is effort, right? Yeah. As doing this is to me xx is this is to me by access the land force along excesses Will we have full plus after Cape Jew June a problem. Okay, Half of the diagonal. If I wrote to square escape to into Cuba upon airport to respect so f x, you will get four times. Okay. Do you do about his work similarly? And on the Y axis, Okay, you chew upon hey upon Roupoli Square Okay. Chew apartment airport through three squares of this would be also remember here F I s Some of you have to bless their food. So that force ability fruit off forget you upon a square for KQ football. A square that is mhm. 402 Okay, I forget to write. So I'm putting here, Kay. 22 apart. A script. Their son. Thanks for watching it.

Question 34 states that four point charges are located at the corners of a square with sides of length. A two of the charges air plus Q and two or minus que so I put plus Q and minus que Find the magnitude and direction of the Net electric force exerted on a charge, plus Q uh, capital que located at the center of the square for each of the following two arrangements of charge, Part A is shown in the diagram here. The trend is alternate in Sign plus Q minus. Keep plus Q minus. Q. As you go around the square and company be after that. But this is the scenario they're dealing now. So part of this positive capital Q is in the center in each of them. Smaller, accused, positive or negative around the edges. Just it's clear, actually, would this may. As a legend, I think, Ah, yes, make it really big, but be labeled each of these square charges that we have Yes, there, you we'll shrink it down and his label because we're gonna rearrange the jaggery a little bit, told me. Clearances negative. Que. This is capital big Q. And this is plus little cute. So the first arrangement we around this square at such we want to find the electric, um, country course exerted on positive. Cute. So by doing that which look at the directions of each component here. So in this arrangement, if you look at this positive Cuba push that little blue que of course they black you down. Similarly, this bottom kill Put it this way this red wanna put towards itself And this red with a Pulitzer to someone's always attractive If we know in this arrangements every component, every vector component has an equal opposite vector component on the other side of the black turns cap O que That means because directors everything years the same magnitude of change of the net force in the scenario would be zero eight equal opposite vectors produces. Um uh, scenario Are all the electric courses cancelled out acting on that center Black charge. Now we move our arrangement such that you have to queue on to positive cues on top into negative cues on bottom, such as this one. Capital big Q is still in the middle. Our square still has size of like me get a little bit different scenario, but because it's positive, it'll the top left change black before exactly force on it in this direction as well as this charge building the same downward and seem but opposite direction in the crate on the side. It means each of these two there are two vectors, two vectors because there again equal magnitude of charge, they affect the same way pulling down. But when the scenario now we have one doctor from the top left charge one vector for the bottom, right charge top right and bottom left because of the same magnitude. The X component of each of these will cancel out, and we're left with oy 1,000,000 to consider the why component of each of these sectors. And, you know, again, based on symmetry, we could do a little bit more simplification because everything's pointing in the same direction downward. If we just get one, um, magnitude in the y component of the vector downward, multiply that by four to get the same effect as having four different forces pulling it down again. We don't need to get their ex meal and you to consider why. So you only need to look at one electric force component. Multiply that four, and we should. That should give us your final answer so we can do that here, so F net. Just a little bit of math represent that it's obviously enforce of Q on one plus force between Q and to Q three and Q four. I guess the generous represents one of the charges around, um, Square, but I can represent as four times F Q one. Let's say in which 1 may picking policy. It doesn't matter. So look at the one component going down to the right. Let's say so, Um, one of the ones pulling towards the bottom right? Negative church in that scenario on this angle here is 45 degrees. The length of this branch is a over to link of this one is a or two as well. That means our distance from the big Q to lower case negative. Q. On the right hand side is book are like that. That's that's R squared equals hey, squared over four plus K spread over four square both sides between you, which means a squared term. We'll say this is Ford's. Well, make it clear they spread over four as well. Which results in a squared over two is our our square component. So the Net forces of the K Q. And the magnitude of any one of the charges because they're on the same thank you over a distance term a squared over four and again dealing with the y component of this. So the y component this vector would be the coastline of 45 co sign 45 degrees multiply by four again. This is This is all one example of the force by acting on the Positive cube positive capital que charge from Altoid before we have the total force. So now all we need is a little bit of math again. A washing specify tooth is the negative. Why have direction but a little bleeding over your service? That so Just a little bit of math here we have. Um, also, this is a two of the denominator. Hey, scored over to me. Figure that out. So you have, um, to okay, little cubic. You over a squared coastline 45 was equivalent to root two over to substitute that in over two times for in the negative y direction. Yeah, and so against the question does ask for the magnitude. Amanda in the direction we know the direction is a native Wyatt direction. So, apparently to consider the Net force in terms of magnitude, you don't take a new direction. Looked a little bit of math being. Figure out that the solution is a plea for route to thank you. Q. Over a squared and again, it's occurs in the negative direction. Thank you. So this question isn't a lot of symmetry and mold of it. In the first part, read four charges Each vector cancels each other's out based on their position Kitty corner opposite corners of the square when they moved in. The arrangement with positives on top of ending is your bottom begins again, Um, certification of the geometry to recognize that we're going to compute the value of one vector and multiply by four. Recognizing the only the y component has the extra borders cancel out. Being are potentially very, very complicated. Equation is solved massively, essentially one term, and that's why buy for their, you know

Hi. In the given problem, there are four charged particles which are kept at the corners off our square. Let the square B A, B, C and D Then the charge is kept and its corners are here. This is charge having a magnitude off Tokyo. Here, This is the charge having a magnet Europe just you. Then here This is the charge. Having a man lead you dope for you. And finally, this is a charge at corner. Be having a magnitude off three Q. Each side off this square is given us A. So it's Dagnall will become side into Ruutu means a route to So in the first part of the problem, we have to find Net electric field acting at discharge. Cute acting at the position off this charge, Q means at point B. So if you look, there are four electric fields. There are three electric fields acting at this point B one because off the charge Tokyo kept at a and as we know the direction off electric field is away from the positive charge. So if we consider all these charges to be positive, so this is electric field, you toe the charge kept at a then the electric field at position off Q means at be due to the charge kept at sea means for Q. This is like this away from 14. Then finally, electric field. You tow this trick you and that is also away from three. Q. Means this is like this so we can name these electric fields as this is e a electric field. You toe the charge kept at it. This is e see electric field you to the charge capped at sea and this is e d electric filled you to the charge kept at be No, we know expression for the electric field due to a charge Q At a distance, our is given sk que by our square they're K is a constant for air whose value is one by four by absolute not. But we have to find this answer in terms off concerns. So we will keep this S K only so, first of all, as all their distances are except this Bagnall, the diagonal is having a length a route to so most of all electric field e a will become equal tok in tow. Tokyo The charge at a divided by a square, then e c. Electric field at B. Due to see this is K into four. Q. Understands again a square. And finally, Edie. He's going to kill three. Q divided by the square of distance, which is a route to so the square of this area, too. We become a square, so these are the three electric fields we have to add them. Soto add them. We will use component method off tradition, as this angle is 45 degrees, so this single will also be 45 degrees. So there will be two components off E. D. If you consider these two directions as X axis and well, I axes, then we can see e d X is equal to e. D. Cost 45 degrees means it will come out. Toby K. Treat you by two route to a square because the value, of course 45 degrees one by route to similarly, the value off E B. Y. And this component will be e d. Sign 45 degree and we know the value of sign 45 degree is also one by route to So this is also the trick. You by two route to a square. Hence, finally, the net electric field along X axis means e x will come out to be the algebraic sum off E A and E b X So it becomes K. Thank you. Bye. A square plus Okay, three Q by to Ruto a square. Then on taking this k, you buy a square as a common out remaining inside in the bracket it will be too plus three by two through to which finally comes out Toby Que in que by a square into 3.6 So if we write this electric field in vector form, then the unit vector along X axis is icap so I can write it like a que by a square into 3.6 I cap Similarly now we will find the net electric field along y axis and that will be given as the some the algebraic sum off electric field Easy with E B. Why? So it becomes scared into fort you buy is square plus Okay, treat you by to to a square again taking this cake you buy a square has comin out in an inside. This is four plus three by two route to. So finally, if you write this one also in vector form, it comes out. Toby K que by a square into 5.6 j cap. So finally, the net electric field at the position off charge Cue here Comes out Toby. Okay, Que, By a square 3.6 icap plus 5.6 j cap. And this is the answer for the first part off the problem. Now, in the second part of the problem, we have to find the net electric force exerted on Q. And that is quite easy because we know the force acting on a charge. Q is given us the product off charge with the electric field in which it has been kept. So here the answer comes out to be okay into Q Square by is square 3.6 by cap plus 5.6 g cap and it becomes the answer for the second part off the problem. Thank you.

How strings. Let's start our discussion. Electrostatic force. Okay, Now suppose you have a square. Okay? I'm giving the corner numbers off this square. Born toe 34 Suppose on these corners in the corner were in charge. Who is placed in corner to charge? Tokyo is placed in corner three. Charged three Q is place and in corner four charge took us place. These are the corner numbers. Okay, Now we have to find out the exact force that is exerted by these charges. Tokyo trick you and took you on this charge. Q. Okay, So the force on one do toe do that is force on one. Do toe to is in this direction F one. Okay. And it will be okay. You want cute? Oh, by the square and a job. The square is a centimeter. Okay. Hey, Square. So what's the value off ruining? You do a que in tow? Took cube and toe. Took you by s with K F 12 Okay, I am taking only the magnitude here. So it will comes toe may toe ok, que square by a square F one Newton. Ok, and I'm showing their direction here. This isn't this direction. Okay, Now the force on one due to four. This will be in this direction. Four for one due to four. Okay, then it will be okay. Q one Q four by a square. The value off Q one is Q and Q Forest took you then It is similar to have one too, and it will comes to obey. Okay, Cue square by a square, you don't No. See, these f one and F 14 are at 90 degree. OK, but let the angle between them is 90 degree. So now we have to find out the result in force between them. Suppose I name the result and force off fund for and F one toe, half dish. Okay, so we know the formula of a certain forces are f result and will be Underwood Afrin square plus after square plus toe are fun after course data. Now the angle between them is 90 degree. Okay, So value. Of course, 19 0 So it will comes at fun square place after square. But for this case, it is af 12 square plus f one force quell. This time will be geo due to course 90 and half resultant his after show. Okay, now, if you put the values basically the magnitude off F one and F 1 40 similar So it will comes to be to have fun to square and it will comes. Toby's your toe. Do kick you square by a square. This is the venue off after sh seeing this in the square? No. We resort the forces due to one and four in after sh with half dish birthday. The force is also exerted on one due to three. That is F one thing. The value of F 13 magnitude is okay, Q one Q t by a root two square Because the Dagnall off the square is off site a route OK from here it will comes to be own tart. The charge trick you is life. Okay, so it will comes to be free Kick you square by two s quit. No, we have to find out the next result and force on this charge one. Now, after between abduction after country, the angle between after dash and F one tree is Jiro is chill so of by the result and formula. You see in the figure If I will put this the value of course. Tutor here, Jiro. Then it will comes to the Afghan square. First have to square place to have fun to have toe So happy days Because to Jiro it will comes Toby after because toe have fun. Plus after basically the whole square form level generate it weakens Lord with the route So Afghan plus after will it comes off. It means that half resultant or half net will be We have to just simply add them Toa que square by square plus three by toe Kick you square by square. This will be Toto plus three by two Kick you square by a square. Hence, this is the net result and force on child or not, It is the only magnitude on charge. Cool. And its direction his decide. This is the natural Surgeon Force. Okay, basically, I'm making us. They're easy. This will be the net resultant force in charge one in this direction. Okay. And this is the magnitude. Well, this is all for me for this video. I hope you will like the video. Thank you.


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