This is ejector 21. Problem number 16. So we have four point charges that were placed in the corners off a square. Um, so you can see that Let's call this Cuban first charge is negative. Then here comes the second charges. The positive off, 1st 1 positive and negative. So, um, instead of dealing with numbers, first of all, um, let me, um said off the problem in a way that initially we don't have to deal with the numerical values. Okay, let's assume that you want equals negative. Kill, right? And cute two equals Q and cuter equals positive cue again. Right? And then a few four equals negative. Cute. And it's cold the length of each side of the square to be a and were asked the net force on each charge and the direction of this force so definite for each charge in the direction off this neck. Oh, f connect. Right. So this is actually a very long problem. I'm gonna salt a little, sold it for one charge, and I'm gonna go because of how you can calculate the intellect. And then I'm going to reach a general conclusion so that you can build up all that now. So let's start with calculating the Net force acting on the first charge that I re labeled as you want. Okay, so Q one oh is going to experience an attraction as far Askew two is concerned, right, Because kids is a positive charge. So the direction all the force that after two pardon me to observe on one. Let's go at to one right this f too long. Let's write it in the vector form, you can see that it's gonna be easy. Reefer. Dussel equals to the magnitude of this force. Que que swear? Right? We're finding the magnitude over. This is between the two is a square times the unit vector you defector, Since this force is pointing to you too, while conventionally again, any force appointing in the positive extraction is defined by data. Better is if I had to correct. So if do on Vector can be written as Jake you do, or a spirit I had because if 21 is in the positive extraction now which using the same logic with strapped, figure out their direction or the vector form off u x three one now have 31 between your calculating force exerted by the third charge on the 1st 1 on the first date, right? So let's try to try to determine direction of this force, Since, um, kill three is positive and you want is negative. There's an attraction going on between the two, right? So then it's the Cuban is gonna be attracted towards Q three. Therefore, direction up 31 is going to be down. So let's remember conventionally down means negative wire direction. So Rigoni's negative J hat as far as you know, veterans concert. And as the magnitude is still kay, he was squared over a square right, because the magnitude of the 1st 1st time's managing to the second charge divided by the square of the This is between the two. Since the distance between the two is a let's put the Inter victor, there is negative J hat. So far, so good. Now we have the fourth charge. That's a serial force exerted by the port. Charge on the first charge is that for one, this F or one is it has components in both X and y directions. Okay, so let me show the direction of it. It's a negative charge. And you? What is a negative charge? There is a repulsion going on between the two. Between. Ski one is an experience of force that is away from this Q four. So this is direction of F or one Now. I drove it at an arbitrary angle from geometry and figure out what that angle is. First of all, the distance between the two happens to be. The high pot news right of a triangle has the length of a start from here, a square plus a squared square that the sward of two is D. This is between you want into four second. We've we have a right triangle like this whose legs are actually equal to each other. Then the angle here has to be 45 degrees right? Which means the angle here is also 45 degrees is you can see, for one is applied with the angle. Let me draw clearly. Wreck This is ask for one. You said that this table is 45 degrees, right? So it was good here, 45 degrees. Um, now let's train decompose. Let's find the y comported F four. Why is at four y times site off free Climb. Then what? The ex cop for it for one ex then equals two f for one whole side. 45. Right now. What is that for? One is the magnitude which happens to be king. You swear over this time let's forget the distance between these two. Georges, it's a and spirit of two. It's not a war. So a spirit of two. They were. You swear this, right? This this square This is the magnitude. For what? Now, if we're right, the, uh, Specter formal for one that that would be f for one times. First sign. 45. Right? Because this is the ex compartment times. Remember? F for one call sign 45 is in the negative extraction. So we're gonna put a negative. I have here Waas want sign 45. It's in the positive direction, though. Why comported up at 41? So therefore we're gonna put a positive g head there, So let's plug it in for 41 k squared off over to a square, Right? Basic lose to a square times too. So and then course I'm 45. What is course I am 45 is one where we're squared up to. So let's book that in there too long. Over spring. It's true negative by hat, Plus Jake, who spurred over to a square and +41 is the same again. Signed 45 is also Cypress From Equals. Both signed 45. That equals one skirt of to J F. Now let's write a little nicer. Um, que que squared over to a skirt of to a squared Negative. I had plus Que que squaring off over to a spirit of to a squared J left. All right, this is half Or want this response to force that the fourth charges exerting on the 1st 1 to die? I've been one all right. No, there are three forces. If you want the 3141 that are acting on to want that you want to find the net force acting on human, we have to add them. Oh, look at this guy. This guy to this guy, Mr Little New picture. So F net. Let's bullet for the first charge. Okay? In vector for equals two. Well, which one? We started with F to one if 21 plus f 31 What's that for one. Now, remember F to one was cake. You squared over a sprig. I had the huse were permanently square. Try that. Plus if 31 the three ones kick your skirt over our spread. Negative. Do you have excuse for her release were negative. J hat. Now we have a 41 that for one. The cake you skirt over to spread of to a spurt. Negative. I had Hey, Huse word over to spurt to a square. Negative I had for the white component you have pretty much the same. We've just grand over to a spirit of two faced great positive J hat. Right now let's group the ex components and wife components altogether. So cake you skirt over Eastbourne, Linus, because there's a minus your cake. You squared over two. Spirited to ace where I had plus Okay, juice. We're littler too screwed up to be squared. Linus, cake use where? Hey, squared J hacked. Now this term is doing iwas the X component off. Definite right. So this is six component of ever met one And this is why component of if connect one lives. Try to catch up with them individually before we go any further, So let's drop. Um, let's do this. Ash meant one x The X component of f Met equals to, um if we take this term. Right, So in both terms, in Expo in the exploded, we have cake, you square, so I'll never try and rearrange this term. He que scared over Easter minus Caju squared over to skirt to a squared. Right? All right, Now we're gonna quit the denominator so that we can do work that led to a skirt of two cake. You square over to a spirit of to, um, a squared. Alright, Linus, the acute squared over two spirited through base. From here, we have to a spirit of two minus one. Yeah, Q squared over to spirit of to be spared. Now it's time to calculate. All right, so two spirit of two minus one. Que is love. 8.99 times. Center for nine. Q is given to us. Remember, the problem is 4.1 5,000,000 belong certainly has been brought back to full square, divided by two spirit of two A. This is the length off the side of the square is 0.4 meters So we're going to square this from here. We're gonna find the X component of the net force acting on the first charge to be one time center, bro. Seven mutants do in Crete in much the same back for net one for the wife compartment. This time we have a few square might escape this word to skirt of two over. He was heard of to a squared. Right, So you few square it over to a spirit of to a square. One light is too scared of to start. Let's catch it. What it is 8.9 time sensitive power nine fines. 4.15 10 cents per negative. Three square sober to spirit of 2.1 meter square times one minus two. Spirit of two. So the net The Net Force acting on the first charge. The eight white component of it is the negative of the ex cop from here. All right, well, we're almost there now then, if we found the eggs and my components than what is ethnic acting on one and magnitude really is square. Have met one x swear lost their that one. Why square friend so soon equal to one time center here on seventh squared. Plus thinking 1 1% to 7 swears all I know it's gonna be equal to that force. Acting on the first charge is gonna be full to 1.42 times. Thanks for power seven Newton's And how are we gonna catch the direction? Always tension function tens and tater equals two f inept. Want why Divided by one X is, you know, it's a magnet. What is negative? One center bursts. Every ethnic X is a one time center of seven something here we have negative one is the ratio. So the inverse off tension off negative one equals our data data. That is gonna be negative. 45. So let's remember what this negative 45 means. This is Q on Q Jew Q three before negative 41 needs that we have the angle that is actually pointing the center. If this is the center off the square, right, negative 45 means this is 45 negative. Remember, the position is always from the positive X. So then, actually, this net force on force is towards the central, the square. Okay, So, basically, by doing the same process for the second charge, you can show that the magnitude mitt off net force acting on cue to is still one point for two times center power seven. This is true for all come so for a while charges if it actually equals the one playing for two times sent a girl of seven years. News and direction is always for he charge is towards the center. Help us square.