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Problem 29 Hard Difficulty

Two equal positive charges are at opposite corners of a trapezoid as in Figure $\mathrm{P} 15.29$ . Find symbolicxpressions for the components of the clectric ficld at the point $P$ .

Answer

$E_{x}=k_{e} \frac{Q}{d^{2}}(1-\sqrt{2})$
$E_{y}=k_{e} \frac{\sqrt{2} Q}{d^{2}}$

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Video Transcript

here we have Ah, Two equal charges are placed on the opposite corners off a trapezoid. This is a trapezoid. We have a positive que here and another Pause. Tick you here. And this is point P. We had asked to find Ah, the net electric field O r. A symbolic expression for the compliments off electrical at point B. So we had also firing Electric feel here won't be. And this one we call it P one. And the angle here is a 45 degrees, and this angle is again 45 degrees. The distance from this part to this part of one side is D D. In this distance from here to here, frumpy ish to this capital killer. Here is a to D then, um, this distance this Plus, this will be our simply to t minus this distance. So this will be deal or two. And this will be a deal to from here to here, this one in from here to here. This one. So so. The elected feel that point e will be due to elect the electric field off Pastika here. And due to the electric field this plastic you here so if you draw back to diagrams for electric field into the positive kyu won here at this point, this will be the one we call it. This one and the other electric field will be in this direction. Recall this. He too. So the net electric field will be due to even Ah own point p will be you won and ah Hee too. So let's find it a symbolic expression for one so everyone will be simply, uh, Fulham. Constance turns the positive kun a magnitude of the square distance from here two years a d so distance where where he too will be the distance from here to here. So here to hear this distance we needed Well, we don't know this distance to, you know, to find this distance we use we have this distance from here to here. This distance we have D or two, eh? So we can use this distance in this angle 45 and use it goes, Ah, that information we confined Ah, this distance that we know that the cost 45 is the base or hyper views. So bases a deal or two hypotheses we don't know. So we called it Fetch from here Our hyper things will be actually D divide by square root off too. Um So we plugged that distance here for he too Came will be made chewed off. Pasta kun divided by Do you were squared off to square. This gives us a to K homemade shooter. Que me? Just right for pause Ticking Just cube. Bye bye D square. So this is Ah, Electric field in this e to direction Here, let me just is this e too? And this one we have is e one, so we can write the total expression by resolving. So we call this X axis and this is why exists. So we see here he won the electric field. One has got only one component. That's only an ex direction. Where? Electric field. He too has gone the two components. So this one is accent. This one is a Why So we'll resolve eternity to companies. So she was all that light here we have excellent baby every Why so you want is on Lee next direction. We just k human, ain't you? Divide by D square. And in what direction? Zero where he too is Ah in ex direction. It will be minus K. Q uh, squared off too divided by D Square. So what I did, it's like I just resolve this e to into its components. This is e to this compliment in this compliment to the ex company. This will be minus K. Uh, Q. More square swirled off, too, since this is in opposite direction off a past two exits. There for a negative side. And here, this company in trees again. Okay. Ah, squared off to a few more divided by the square, so there will be same, but this will be in wide ocean. This will be an extraction because the angle here is 45 degrees, 45 degrees. So the y component, he too will be okay. Q My lord, we're route off two divided by the square. They're the total expression for he X will be okay. Human divided by the square. We'll just get them. So here, one minus world off, too. And for why the expression will be kay more swirled off too human, divided by the square

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Cornell University

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