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Problem 25 Hard Difficulty

Four point charges are located at the corners of a square. Each charge has magnitude 3.20 $\mathrm{nC}$ and the square has sides of length 2.00 $\mathrm{cm} .$ Find the magnitude of the clectric ficld at the center of the square if (a) all of the charges are positive and (b) three of the charges are positive and one is negative.

Answer

$28.8 \times 10^{4} \mathrm{N} / \mathrm{C}$

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Video Transcript

hair strands left, start or discussion. Suppose you have a square. Okay? And when each corner of the square I'm naming corners. Name 1234 But jihad positive You is placed positive charges blesh. Okay, now you have to find a neck electric field on the center off this square. See, on this point, the electric field you to one, is in this direction. He went that is OK. And on this point, the electric field on do 23 is in this direction. So even an ET I can Salau because the magnitude off Q. The magnitude off charge at one is similar to the magnitude of chart at position, please. Similarly, the electric field on this point, the center point due to four is in this direction. You four and the magnify electric field you toe to position two is in this direction. So they will also cancel out as because all charges are positive and off similar magnitude. The Net Electrics release Cancel out at the center. No. Suppose in the similar condition is your replaced. One positive charge with a negative charge. Okay, where all other three charges are positive now you have to find other than that electrical on center one toe, three for basically electric field, uto four and electric field due to to good Republicans alone in the skills also So no electric field on this center is in this direction even and electric field Uto tree is also in this direction that is eatery. So we know that on the teeter between even an eatery is Jiro So today's you We know the formula off, not electric field, is that is even square plus he to square plus two even e to cause cheetah. So for this particle case today, as you so cause you know, is one and so this will generate the whole square formula. So it will be even plus Ito, we will simply at them Okay, so basically the magnitude off these electric feel is same so we can write them toe even because the magnitude of charges are saying OK, so to get q by ours Where the diagonal off the square This hero too Where is the side of square? In this case, the value is two centimeter that is Cheeto Point Digital two meter and the value off charges the magnitude charges Q is three point. Well, I would like here the magnitude of charge. Q is 3.2 Lana Coolum. That is 3.2 into 10 days by minus night. Coolum If for sore. If we put the values here that is nine into tenders for nine into. 3.2 into tennis by minus nine. Cooler by Jiro Point Geo toe, whole square. We will get the final answer. Actually, the side off Dagnall is a row 2.5. Off its sights will be a row two by two. That is, in this case, Jiro 20.2 meter Roto by two. That will be Jiraporn Jiro one Drew two meter. This is the dist dance between the center position and the corner position. Okay, so now electric field will be to take you by our square. And that will be two in tow. Nine into tenders by nine into 3.2 into 10. This car minus nine, cooler by 0.1 Drew two whole square. If you put sold this, you will get the answer. 2.88 in tow. 10 days by six Newton Per Coolum. This is the magnitude off net electric field at center. And this isn't at this is in the direction off the negative child. That is in this direction. He next. Okay, but this is all for me for this video. I hope you will like the video. Thank you.

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Top Physics 102 Electricity and Magnetism Educators
LB
Liev B.

Numerade Educator

Marshall S.

University of Washington

Zachary M.

Hope College

Aspen F.

University of Sheffield

Physics 102 Electricity and Magnetism Bootcamp

Lectures

Join Bootcamp