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$\bullet$ $\bullet$ Torque and force on a dipole…

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Problem 44 Hard Difficulty

$\bullet$ $\bullet$ Three negative point charges lie
along a line as shown in Figure 17.48 .
Find the magnitude and direction of the
Find the magnitude and direction of the
electric field this combination of charges
produces at point $P$ , which lies 6.00 $\mathrm{cm}$
from the $-2.00 \mu C$ charge measured perpendicular to the line
connecting the three charges.

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Physics 102 Electricity and Magnetism

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Chapter 17

Electric Charge and Electric Field

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Video Transcript

before we start calculating electric fields, let's make sure we understand the situation. There are three charges. Q. One Q to thankyou three located along this line, and the distance between each of the charges is eight centimeters now. To the side, there is a point P which were interested in calculating the total electric field at and the distance prank you three MPs tens of years. And that's the same askew MVP. And in this angle here is 53.1 on both sides and the distance between que Tu and P s 67 years. Now you write the force diagram appoint P. You have an electric field, even one due to charge one pointing this way since you won his native Q three is negative, too. So there's the three pointing this way now. I broke these down into the microphone inside. Even. Why e three. Why? And that's the left Here. I have E, too. You want tax and the three x these air. Three additional electric field vectors. They're pointing to this left that didn't want draw three separate areas for so I've indicated by one arrow. So now let's use the formula that is equal to K magnitude of Q over R squared, where ours the distance between the charges in the location And so by symmetry, we know that the matter that you want any three appointee are the same and playing in the values here. For those we get 8.99 times 10 to the ninth. Best risque. Now Q is five times 10 to the minus six that's given to the problem and in the distance is just 0.1 meters square. And so this gives 4.49 times 10 to the six news per column. Now he, too, is going to be found in a similar way here. Ah, really similar. In fact, the only thing that changes is the queue. Here. We're going to use Q two of their charge, and we'll use the distance between Point P and Q two here, but same exact formula and same exact process. And I get 4.99 times 10 to the sixth Nunes for cool now in total. You, why is equal to even why plus e to y plus the three y? But since charged two is located horizontally to our point P the white component here of E to zero. And if we go back to our previous picture, you won. Why, Andy three. Why point in opposite directions and they're of equal magnitude. And so this one a big zero. Because if you won, why have some value e three? Why will be negative, that value and so little cancel Now e x The sum of the contributions and the extraction is equal to Yvonne X plus e to X plus the three X In this case, eat to excess, not zero. But you won't. Actually three X are still the same. But in this case, they don't cancel since they point the same direction. Instead they combine. And so e tu, In this case, I'm Ryan eat to excess. He too, since there was no e to why he too exited entirely too. Plus two times even one. And I'm gonna isolate the x component our writing co sign a 53.1 degrees. So this, too, comes from the fact that even X and the three X's are the same. So I combined them in the one and put it to outfront. And then the coastline is isolating the ex component. And then the one is just in reference to the large magnitude. Eveyone here. Now we can plug in everything that we know here. We don't need to. We know what you want. And so we find that E X is 1.4 times 10 to the seventh meters per Coolum. And so since e Y zero the totally is this and it points to the left and so that

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Problem

$\bullet$ $\bullet$ Torque and force on a dipole…

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Watch More Solved Questions in Chapter 17

Video Transcript

Hugh D. Young

College Physics

Elyse Gonzalez

Liev Birman

Aspen Fenzl

Meghan Miholics

This textbook answer is only visible when subscribed! Please subscribe to view the answer

College Physics

Elyse Gonzalez

Liev Birman

Aspen Fenzl

Meghan Miholics

Hugh D. YoungCollege Physics

Elyse Gonzalez

Liev Birman

Aspen Fenzl

Meghan Miholics

Hugh D. Young

College Physics