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[-/3 Points]DETAILSSERPSE1O 29.A OP.028.KYNOTESASk Tour TeacrerPractice AnotherTwo coplanar and concentric circular loops of wire carry currents of 5.40 and I2 2.80...

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[-/3 Points]DETAILSSERPSE1O 29.A OP.028.KYNOTESASk Tour TeacrerPractice AnotherTwo coplanar and concentric circular loops of wire carry currents of 5.40 and I2 2.80 A in opposite directions as in the figure below: Let 11 = 12.0 cm and r2 8.80 cm. (Assume the positive direction along the axis perpendicular to the faces of the loops is out of the screen (towards you) and assume the positive vertical direction is toward the top of the screen: )What is the magnitude of the net magnetic field (in pT)

[-/3 Points] DETAILS SERPSE1O 29.A OP.028. KYNOTES ASk Tour Teacrer Practice Another Two coplanar and concentric circular loops of wire carry currents of 5.40 and I2 2.80 A in opposite directions as in the figure below: Let 11 = 12.0 cm and r2 8.80 cm. (Assume the positive direction along the axis perpendicular to the faces of the loops is out of the screen (towards you) and assume the positive vertical direction is toward the top of the screen: ) What is the magnitude of the net magnetic field (in pT) at the center of the two loops? What is the direction of the net magnetic field at the center of the two loops? out of the screen into the screen toward the top of the screen toward the bottom of the screen Let r1 remain fixed at 12.0 cm and let rz be a variable Determine the value of rz (in cm) such that the net field at the center of the loops is zero_ cm Meed Help?



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Two coplanar and concentric circular loops of wire carry currents of $I_{1}=5.00 \mathrm{A}$ and $I_{2}=3.00 \mathrm{A}$ in opposite directions as in Figure $\mathrm{P} 30.64$ . If $r_{1}=12.0 \mathrm{cm}$ and $r_{2}=9.00 \mathrm{cm},$ what are (a) the magnitude and (b) the direction of the net magnetic field at the center of the two loops? (c) Let $r_{1}$ remain fixed at 12.0 $\mathrm{cm}$ and let $r_{2}$ be a variable. Determine the value of $r_{2}$ such that the net field at the center of the loops is zero.

For party ever question is, is to find the magnitude of the magnetic field that's net produced by the current one and current, too, and wire one and wire to sew. To calculate this magnetic field in Part A, which we're gonna called Jeannette or B seven, we're gonna assume that the field direction that was directed out of the pages positive in the field direction that's directed into the pages negative. Therefore, the net field at the center due to the current and both concentric loops is going to be be to the magnetic field produced by wire, too, minus B one the magnetic field produced by wire one. So if we substitute in the expression for the magnetic field from a long straight wire, both of them are going to have the mu not over to pi terms in them, but the currents and the radius is air different, so we can just pull out the mu, not over to pie term when this is gonna be multiplied by I to over our two minus, I want over our one. So if you plug in our values for I to our two, I won and are one and consider that mu not is the magnetic permeability of free space. So it's four pi times 10 to the minus seven. This equals negative 5.24 times 10 to the minus six Tesla or negative 5.24 Micro Tesla. But since we're just asked to find magnitude, we can, uh, change that value. Go positive. So the magnitude of the magnetic field at the center is 5.24 Micro Tester. Okay. And since the value turned out to be negative and the way that I defined our problem in the beginning, I said that the negative value is going into the page. So therefore the net magnetic field is into the page. So we can say, since negative was defined as into the page, the Net magnetic field is into page second box that in a czar solution for part B and lastly in part, see, it says to let our, uh, our one remain as the value of 12 centimeters, and we're gonna let our to be variable and assets to calculate a value of our two. That makes makes the net magnetic field equal to zero. So Veena is equal to zero So we have. Zero is equal to mu, Not over to pie. What supplied by I to over our two minus I went over our one. Except this time we're gonna solve for our two since we're gonna consider it to be a variable. So if we do that, you can multiply both sides by two pi over mu not but zero times to Piromya not is still zero. So we end up with I two over our two minus I won over Our one is equal to zero or are too is equal to, um I to over I won Times are one so you can leave our one in units of 12 centimeters if you like. On we find that our to his here is equal to 7.2 centimeters. Miss give me boxing is our solution for part C.

Hi. I think that given problem. Suppose loop too. The outer loop the bigger loop is rotated through an angle theta about its diameter. So the angle between the magnetic fields of these two loops will also be tita No, the magnitude of magnetic field due to the smaller loop that will be given by New Not I Buy to ours. And you know what I went by to our one. And here it will be four pi into 10 days for minus seven Tesla meter Karam pier for current. This is four Million Pier or four In 2, 10 for -3. And you're in the smaller group divided by radius two times of areas. Yes, this is 1.50 centimeter or 1.50 into 10 days, four minus two m. So here it comes out to be 1.67 Into 10 days for -7. Tesla. Similarly magnetic field due to the outer loop due to the bigger loop using the same formula mu Not I. Two by two are too Form you note again, this is four pi into 10 for -7. Into current in it, which is six million here or 16-10. -3 ampere divided by two times of areas. And it's serious. was 2.50 centim or 2.50 into Attached by -4 metre. So this magnetic field here comes out to be 1.51 In to tenders for -7 Tesla. Now the net magnetic field as a vector. Some of these two magnetic fields in this problem, this net magnetic field is given us 100 nano Tesla. So using triangle of a tradition. This be will be given by the square root of Deveney square plus B. Two square plus device. Or be even be too into course, Theatre angle between the two magnetic fields or angle between the plane of two toys. So plugging in all known values here And making a square of both the sides, they get it squared of B means 100 nano 410 days par -9. Tesla square is equal to that is equal to square off the square root. So square what will be eliminated be one square means 1.67-10 days par -70 sq Plus for B two. This is 1.51 In 2, 10 days par -70 sq Plus two. Y. So be one means 1.67 into 10 for -7 Into 1.51 In two for -7 into cost he to which is missing. Very happy we have to find it. So here it comes out to be 10 for minus seven square means 10 for minus 14 B. B. and all the 10 for -14 will be taken as a common out in the right hand side. Leaving behind a square off 1.67 will be 2.8 Plus is quite of 1.51 will be two point to wait plus 5.04 into cost heater. So canceling this here, we get 5.08 Plus 5.04 cause theta is equal to zero. So 5.04. Cost data Is equal to -5.08. Or we can say cost data is approximately equal to -1. So theater is approximately equal to 180° means the plane of outer coil. Bigger coil Must have been rotated by an angle of 1 80°. Thank you.

And this problem. The concept of the magnetic field produced by a circle of coil is used and the magnetic field produced by a circle coil is given by the situation. Okay so the direction of the magnetic field produced by the Uh current I two is along the out of the page. Out of the page direction and you to Ivan is into the page. So we can write the net magnetic field at the center. We consider that the bases hostage is a cuBA into may not into a to a point two ar minus may not. I wanna point to capital of. Okay so the net magnetic failures may not upon to into. I do upon our minus. I went up on capitol I'll subscribe the value. Okay so for part a the magnetic field at the centers for buy into tennis minus seven Tesla meters point here upon to enter the current titles. Uh Zambia. So three ampere upon the value of our bonus nine centimeter. Or we can write 0.9 m- Ivan is five MPO. And capital artists 12 centimeter or 0.12 m. So the magnitude of the magnetic field at the centers -5.2 In to tenders -6 tester Or we can say the magnetic field at the center is 5.2 In to tenders -6 Tesla. And the direction is into the beach. Okay now part B. If you want to make the magnetic field at the center to zero then we have to make this storm right This town to zero which means I do upon art -1 went up on Capitol. Art must speak even into zero. Are I do upon our must be willing to I went up on capitol or from this um are must speak different capital are into I do a bone Ivan now substitute. The values are equals 12 centimeters In 23 and field. Yeah. Mhm upon five ampere article as 7.2 cm. So for the radius of 7.2 cm, the net magnetic failure the center will be

You know that the magnetic force is given by I times a lacrosse being. But that's the case where the magnetic really is. Uniforms far. A case of magnetic field there is with the land. The change in force can entertain us. I times the magnetic fields. And this is the question that we are going to use on. We're going to apply this equation to eat side off the loop now for each side off the loop. The end is parallel to that side. Off the look on, if that isn't the direction off, right, since the loop is in the excellent plan, So Z zeros at the look on dh B y is zero because, uh, be light is basically we just plug is equal to zero in this equation. Then the director will be quarto. You see the light over end Thanks, Ski cap. Because this just God's Edo here. Now you're going to apply this on DH into this equation on DH. We're going tto do the first part now. So for the first part, the magnetic field lines in the plane Ah, to be sketched, son, it's true that so let's see. This is the X and this is the lie exits. As magnetic field is along, the positive key access on it varies with white. So there is no need for the X axis to be here. So you're gonna use why end, See, Axis? Because those are the only components contributing to the magnetic field Here Z is the direction on why he is a distance with which the magnitude ofthe magnetically changes on. You. See, that, uh, the magnet treated b is that is linear. Live it white. That means this is going to be like this. I'd for why? For the audition. Now, if the light changes, this is how it's going to look. Yeah, so that this part e now 45 we have to find the force. So let's find it for side one. Let's mark the site first. So this is side one. Elder's Phil. Let's call this toe beside mine this toe beside toe. This will be side three on DH. This to beside for and for side one. It's called a force to be F one. So this is given by this equation over here so messily integral over this equation. I Times deal Times B signed Fly and the integral with that. But sci fi is basically one because FIEs 90 degree as the magnetic field is hoping to go large. No, the segment here, basically magnetic field is perpendicular to the plane. Off the whole, it's a stone. So for every so far, every, um, case this was is going to Brazil. Sorry, this angle is going to be 90 victory. This gives So Isaac Constance So it comes out on. We know there's a constant Eliza. Lt's a constant. So they come out a cell on we have. Why on the l is basically the change in lentil on this directions or deal is going to be called to the why? Because this segment is along the lie Exes on the integration goes from single toe on my right and rule. So let's do that letter was Let's find the force that they're fantastical dough, half dimes, the knot for l times I on DH. We apply the right and rule, so that gives the force two words. Take AJ two lights, the positive exact sis, This is the force for the first segment. And for those who don't know what this integration is. So I'm just going to write it over here. So let's go on this way to the party and where Anderson in the jet other than negative one. So if this goes from a Toby to the integration of this is basically right at the part and plus one over N plus one on your slide animals from it. This Kips bay to the parent less one minus eight. A guard and place one forward and placement. That's what I did over you. And if n is minus one, the integration is just going, Toby, the lager them off. Why? And then you have to apply the limits too. So now we do the same for you. F door. So after is equal to integration over I b l b sci fi, this one on the limit side and my sins the limits are staying with told me to explicitly can't colored disentangle. This is Okay, so this this man old Sorry, it's Ah. Okay. So the way we have to see what the The surveillance Basically, Xia date, Because deal is a battle to the x axis. So Oh, our limits are going to be the limits off eggs and not the limits of Wei. That's going to be CTO do l Andi. I is a constant. We notice the constants. Also, l is that the limits off the end on deal is basically the eggs as myself. There on, we have a live from the magnetic field and we find this value. Toby, I thank thee not over l So the value ofthe y He's basically a constant here and is equal to Elsa. That comes out and we just have to integrate with the d X not. And this gives the value, Toby. My time's not times l on and off. The direction is given by right and rule being applied toe the direction of current and magnetic field on DH. You see that this direction is going to the towards now good day like the addiction. So I'm forces gonna hit this. Now we do the same thing for three of three. So far three we have I d being I'm sci fi is one on. So the constants come out off the integral on DH. We have revived from the magnetic field on. We have to find see what be Elise. So for the third segment here. Deal is basically negative. Why you again? Saudi deal is basically Dubai again. So you think that on DH is to be Quinto? I be not. And over too. This is basically same magnitude to what we found here on. Let's find the direction now. So they applied. I tend rule Andrei, get in direction. Toby along. Okay, so one thing to note this deal is actually negative way negative delight Because this is going towards the negative I exist, or so b l there's going to be negative off the light. So this is basically mimic on the direction If you apply if you apply the right and girls to see that direction is so I is, uh, okay, Cap Jake on DH, I'll be is cancer. Jacob Cross ski cap is basically I cap. We can also not include the negative sign on DH. Do the cross for that as negative. J cap cross pendant. It was stiff cake and you get killed in the same answer. So for the last part, we have I forgot to write. The elements of this is just a little over seal on DH. Let's make this place on the arrival of distress or so. But I think this is simpler, Dan. Whatever strange value you had to stake the limits As the current flows to zero and take the we control the white Now we find a Ford. So that is I times, Theo times be again on and on the constants come out ofthe day Cushion We have a life from the magnetic field on the l is the ex again And we have the limits from L. A to Theo So the at the system Now we get the value to be I be not Oh well on In this case you see that Why is see you So for this segment of food segment, that means that interval a zero and this gives the force to proceed next, the neck force is going to be Victor sunk off all the forces. So that gives if one the next F net to be equal do F one vector plus two. It's stored and the next page so f net and the corridor f one miss after less f three less before this is basically serial, as we calculated on F one and every have the same magnitude You on his three year, but they're there opposite in direction. So they add up to zero and we're just left with after. That is a negative. All high times they're not. Thanks. And this is the net force.


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